id	sid	tid	token	lemma	pos
ejpam-6598	1	1	european	european	PROPN
ejpam-6598	1	2	journal	journal	PROPN
ejpam-6598	1	3	of	of	ADP
ejpam-6598	1	4	pure	pure	ADJ
ejpam-6598	1	5	and	and	CCONJ
ejpam-6598	1	6	applied	applied	ADJ
ejpam-6598	1	7	mathematics	mathematic	NOUN
ejpam-6598	1	8	2025	2025	NUM
ejpam-6598	1	9	,	,	PUNCT
ejpam-6598	1	10	vol	vol	NOUN
ejpam-6598	1	11	.	.	PROPN
ejpam-6598	1	12	18	18	NUM
ejpam-6598	1	13	,	,	PUNCT
ejpam-6598	1	14	issue	issue	NOUN
ejpam-6598	1	15	3	3	NUM
ejpam-6598	1	16	,	,	PUNCT
ejpam-6598	1	17	article	article	NOUN
ejpam-6598	1	18	number	number	NOUN
ejpam-6598	1	19	6598	6598	NUM
ejpam-6598	1	20	issn	issn	PROPN
ejpam-6598	1	21	1307	1307	NUM
ejpam-6598	1	22	-	-	SYM
ejpam-6598	1	23	5543	5543	NUM
ejpam-6598	1	24	–	–	PUNCT
ejpam-6598	1	25	ejpam.com	ejpam.com	X
ejpam-6598	1	26	published	publish	VERB
ejpam-6598	1	27	by	by	ADP
ejpam-6598	1	28	new	new	PROPN
ejpam-6598	1	29	york	york	PROPN
ejpam-6598	1	30	business	business	PROPN
ejpam-6598	1	31	global	global	PROPN
ejpam-6598	1	32	pythagorean	pythagorean	PROPN
ejpam-6598	1	33	fuzzy	fuzzy	ADJ
ejpam-6598	1	34	digital	digital	ADJ
ejpam-6598	1	35	fine	fine	ADJ
ejpam-6598	1	36	space	space	NOUN
ejpam-6598	1	37	approach	approach	NOUN
ejpam-6598	1	38	for	for	ADP
ejpam-6598	1	39	selecting	select	VERB
ejpam-6598	1	40	menstrual	menstrual	ADJ
ejpam-6598	1	41	hygiene	hygiene	NOUN
ejpam-6598	1	42	products	product	NOUN
ejpam-6598	1	43	in	in	ADP
ejpam-6598	1	44	rural	rural	ADJ
ejpam-6598	1	45	areas	area	NOUN
ejpam-6598	1	46	n.	n.	NOUN
ejpam-6598	1	47	preethi1	preethi1	PROPN
ejpam-6598	1	48	,	,	PUNCT
ejpam-6598	1	49	g.	g.	PROPN
ejpam-6598	1	50	k.	k.	PROPN
ejpam-6598	2	1	revathi1,∗	revathi1,∗	PROPN
ejpam-6598	2	2	1	1	NUM
ejpam-6598	2	3	department	department	NOUN
ejpam-6598	2	4	of	of	ADP
ejpam-6598	2	5	mathematics	mathematic	NOUN
ejpam-6598	2	6	,	,	PUNCT
ejpam-6598	2	7	school	school	NOUN
ejpam-6598	2	8	of	of	ADP
ejpam-6598	2	9	advanced	advanced	ADJ
ejpam-6598	2	10	sciences	science	NOUN
ejpam-6598	2	11	,	,	PUNCT
ejpam-6598	2	12	vellore	vellore	PROPN
ejpam-6598	2	13	institute	institute	PROPN
ejpam-6598	2	14	of	of	ADP
ejpam-6598	2	15	technology	technology	PROPN
ejpam-6598	2	16	chennai	chennai	PROPN
ejpam-6598	2	17	,	,	PUNCT
ejpam-6598	2	18	chennai-127	chennai-127	NOUN
ejpam-6598	2	19	,	,	PUNCT
ejpam-6598	2	20	tamilnadu	tamilnadu	NOUN
ejpam-6598	2	21	,	,	PUNCT
ejpam-6598	2	22	india	india	PROPN
ejpam-6598	2	23	abstract	abstract	NOUN
ejpam-6598	2	24	.	.	PUNCT
ejpam-6598	3	1	pythagorean	pythagorean	PROPN
ejpam-6598	3	2	fuzzy	fuzzy	ADJ
ejpam-6598	3	3	digital	digital	ADJ
ejpam-6598	3	4	fine	fine	ADJ
ejpam-6598	3	5	b≈-door	b≈-door	NOUN
ejpam-6598	3	6	space	space	NOUN
ejpam-6598	3	7	is	be	AUX
ejpam-6598	3	8	a	a	DET
ejpam-6598	3	9	novel	novel	ADJ
ejpam-6598	3	10	notion	notion	NOUN
ejpam-6598	3	11	of	of	ADP
ejpam-6598	3	12	generalized	generalized	ADJ
ejpam-6598	3	13	pythagorean	pythagorean	NOUN
ejpam-6598	3	14	fuzzy	fuzzy	ADJ
ejpam-6598	3	15	digital	digital	PROPN
ejpam-6598	3	16	fine	fine	ADJ
ejpam-6598	3	17	topological	topological	ADJ
ejpam-6598	3	18	space	space	NOUN
ejpam-6598	3	19	that	that	PRON
ejpam-6598	3	20	is	be	AUX
ejpam-6598	3	21	presented	present	VERB
ejpam-6598	3	22	in	in	ADP
ejpam-6598	3	23	this	this	DET
ejpam-6598	3	24	paper	paper	NOUN
ejpam-6598	3	25	.	.	PUNCT
ejpam-6598	4	1	additionally	additionally	ADV
ejpam-6598	4	2	,	,	PUNCT
ejpam-6598	4	3	a	a	DET
ejpam-6598	4	4	number	number	NOUN
ejpam-6598	4	5	of	of	ADP
ejpam-6598	4	6	characterizations	characterization	NOUN
ejpam-6598	4	7	of	of	ADP
ejpam-6598	4	8	pythagorean	pythagorean	PROPN
ejpam-6598	4	9	fuzzy	fuzzy	ADJ
ejpam-6598	4	10	digital	digital	ADJ
ejpam-6598	4	11	fine	fine	ADJ
ejpam-6598	4	12	b≈-door	b≈-door	NOUN
ejpam-6598	4	13	space	space	NOUN
ejpam-6598	4	14	are	be	AUX
ejpam-6598	4	15	examined	examine	VERB
ejpam-6598	4	16	.	.	PUNCT
ejpam-6598	5	1	examples	example	NOUN
ejpam-6598	5	2	were	be	AUX
ejpam-6598	5	3	presented	present	VERB
ejpam-6598	5	4	to	to	PART
ejpam-6598	5	5	demonstrate	demonstrate	VERB
ejpam-6598	5	6	the	the	DET
ejpam-6598	5	7	applicability	applicability	NOUN
ejpam-6598	5	8	of	of	ADP
ejpam-6598	5	9	these	these	DET
ejpam-6598	5	10	ideas	idea	NOUN
ejpam-6598	5	11	and	and	CCONJ
ejpam-6598	5	12	also	also	ADV
ejpam-6598	5	13	some	some	DET
ejpam-6598	5	14	characteristics	characteristic	NOUN
ejpam-6598	5	15	and	and	CCONJ
ejpam-6598	5	16	connections	connection	NOUN
ejpam-6598	5	17	between	between	ADP
ejpam-6598	5	18	other	other	ADJ
ejpam-6598	5	19	pythagorean	pythagorean	PROPN
ejpam-6598	5	20	fuzzy	fuzzy	ADJ
ejpam-6598	5	21	digital	digital	PROPN
ejpam-6598	5	22	fine	fine	ADJ
ejpam-6598	5	23	topological	topological	ADJ
ejpam-6598	5	24	spaces	space	NOUN
ejpam-6598	5	25	and	and	CCONJ
ejpam-6598	5	26	pythagorean	pythagorean	VERB
ejpam-6598	5	27	fuzzy	fuzzy	ADJ
ejpam-6598	5	28	digital	digital	ADJ
ejpam-6598	5	29	fine	fine	ADJ
ejpam-6598	5	30	b≈-door	b≈-door	NOUN
ejpam-6598	5	31	space	space	NOUN
ejpam-6598	5	32	were	be	AUX
ejpam-6598	5	33	examined	examine	VERB
ejpam-6598	5	34	.	.	PUNCT
ejpam-6598	6	1	furthermore	furthermore	ADV
ejpam-6598	6	2	,	,	PUNCT
ejpam-6598	6	3	an	an	DET
ejpam-6598	6	4	application	application	NOUN
ejpam-6598	6	5	which	which	PRON
ejpam-6598	6	6	utilizes	utilize	VERB
ejpam-6598	6	7	pythagorean	pythagorean	PROPN
ejpam-6598	6	8	fuzzy	fuzzy	ADJ
ejpam-6598	6	9	digital	digital	PROPN
ejpam-6598	6	10	fine	fine	ADJ
ejpam-6598	6	11	topological	topological	ADJ
ejpam-6598	6	12	space	space	NOUN
ejpam-6598	6	13	to	to	PART
ejpam-6598	6	14	select	select	VERB
ejpam-6598	6	15	the	the	DET
ejpam-6598	6	16	best	well	ADV
ejpam-6598	6	17	menstrual	menstrual	ADJ
ejpam-6598	6	18	hygiene	hygiene	NOUN
ejpam-6598	6	19	product	product	NOUN
ejpam-6598	6	20	for	for	ADP
ejpam-6598	6	21	rural	rural	ADJ
ejpam-6598	6	22	women	woman	NOUN
ejpam-6598	6	23	is	be	AUX
ejpam-6598	6	24	investigated	investigate	VERB
ejpam-6598	6	25	.	.	PUNCT
ejpam-6598	7	1	2020	2020	NUM
ejpam-6598	7	2	mathematics	mathematic	NOUN
ejpam-6598	7	3	subject	subject	NOUN
ejpam-6598	7	4	classifications	classification	NOUN
ejpam-6598	7	5	:	:	PUNCT
ejpam-6598	7	6	54a40	54a40	NUM
ejpam-6598	7	7	,	,	PUNCT
ejpam-6598	7	8	03e72	03e72	X
ejpam-6598	7	9	key	key	ADJ
ejpam-6598	7	10	words	word	NOUN
ejpam-6598	7	11	and	and	CCONJ
ejpam-6598	7	12	phrases	phrase	NOUN
ejpam-6598	7	13	:	:	PUNCT
ejpam-6598	7	14	pythagorean	pythagorean	PROPN
ejpam-6598	7	15	fuzzy	fuzzy	ADJ
ejpam-6598	7	16	digital	digital	PROPN
ejpam-6598	7	17	fine	fine	ADJ
ejpam-6598	7	18	topological	topological	ADJ
ejpam-6598	7	19	space	space	NOUN
ejpam-6598	7	20	,	,	PUNCT
ejpam-6598	7	21	pythagorean	pythagorean	PROPN
ejpam-6598	7	22	fuzzy	fuzzy	ADJ
ejpam-6598	7	23	digital	digital	ADJ
ejpam-6598	7	24	b≈f	b≈f	PROPN
ejpam-6598	7	25	-baire	-baire	PROPN
ejpam-6598	7	26	space	space	NOUN
ejpam-6598	7	27	,	,	PUNCT
ejpam-6598	7	28	pythagorean	pythagorean	PROPN
ejpam-6598	7	29	fuzzy	fuzzy	ADJ
ejpam-6598	7	30	digital	digital	PROPN
ejpam-6598	7	31	b≈f	b≈f	PROPN
ejpam-6598	7	32	d	d	ADJ
ejpam-6598	7	33	-	-	PUNCT
ejpam-6598	7	34	baire	baire	NOUN
ejpam-6598	7	35	space	space	NOUN
ejpam-6598	7	36	pythagorean	pythagorean	PROPN
ejpam-6598	7	37	fuzzy	fuzzy	ADJ
ejpam-6598	7	38	digital	digital	PROPN
ejpam-6598	7	39	b≈f	b≈f	PROPN
ejpam-6598	7	40	hausdorff	hausdorff	NOUN
ejpam-6598	7	41	space	space	NOUN
ejpam-6598	7	42	,	,	PUNCT
ejpam-6598	7	43	pythagorean	pythagorean	PROPN
ejpam-6598	7	44	fuzzy	fuzzy	ADJ
ejpam-6598	7	45	digital	digital	ADJ
ejpam-6598	7	46	b≈f	b≈f	PROPN
ejpam-6598	7	47	-door	-door	NOUN
ejpam-6598	7	48	spaces	space	VERB
ejpam-6598	7	49	1	1	NUM
ejpam-6598	7	50	.	.	X
ejpam-6598	7	51	introduction	introduction	NOUN
ejpam-6598	7	52	an	an	DET
ejpam-6598	7	53	extension	extension	NOUN
ejpam-6598	7	54	of	of	ADP
ejpam-6598	7	55	classical	classical	ADJ
ejpam-6598	7	56	topology	topology	NOUN
ejpam-6598	7	57	,	,	PUNCT
ejpam-6598	7	58	fuzzy	fuzzy	ADJ
ejpam-6598	7	59	topology	topology	NOUN
ejpam-6598	7	60	makes	make	VERB
ejpam-6598	7	61	use	use	NOUN
ejpam-6598	7	62	of	of	ADP
ejpam-6598	7	63	the	the	DET
ejpam-6598	7	64	idea	idea	NOUN
ejpam-6598	7	65	of	of	ADP
ejpam-6598	7	66	fuzziness	fuzziness	NOUN
ejpam-6598	7	67	to	to	PART
ejpam-6598	7	68	provide	provide	VERB
ejpam-6598	7	69	more	more	ADV
ejpam-6598	7	70	complex	complex	ADJ
ejpam-6598	7	71	and	and	CCONJ
ejpam-6598	7	72	adaptable	adaptable	ADJ
ejpam-6598	7	73	interpretations	interpretation	NOUN
ejpam-6598	7	74	of	of	ADP
ejpam-6598	7	75	mathematical	mathematical	ADJ
ejpam-6598	7	76	ideas	idea	NOUN
ejpam-6598	7	77	.	.	PUNCT
ejpam-6598	8	1	it	it	PRON
ejpam-6598	8	2	was	be	AUX
ejpam-6598	8	3	created	create	VERB
ejpam-6598	8	4	to	to	PART
ejpam-6598	8	5	address	address	VERB
ejpam-6598	8	6	circumstances	circumstance	NOUN
ejpam-6598	8	7	in	in	ADP
ejpam-6598	8	8	which	which	PRON
ejpam-6598	8	9	the	the	DET
ejpam-6598	8	10	conventional	conventional	ADJ
ejpam-6598	8	11	understanding	understanding	NOUN
ejpam-6598	8	12	of	of	ADP
ejpam-6598	8	13	membership	membership	NOUN
ejpam-6598	8	14	function	function	NOUN
ejpam-6598	8	15	that	that	PRON
ejpam-6598	8	16	is	be	AUX
ejpam-6598	8	17	,	,	PUNCT
ejpam-6598	8	18	whether	whether	SCONJ
ejpam-6598	8	19	an	an	DET
ejpam-6598	8	20	element	element	NOUN
ejpam-6598	8	21	is	be	AUX
ejpam-6598	8	22	a	a	DET
ejpam-6598	8	23	member	member	NOUN
ejpam-6598	8	24	of	of	ADP
ejpam-6598	8	25	a	a	DET
ejpam-6598	8	26	set	set	NOUN
ejpam-6598	8	27	or	or	CCONJ
ejpam-6598	8	28	not	not	PART
ejpam-6598	8	29	is	be	AUX
ejpam-6598	8	30	too	too	ADV
ejpam-6598	8	31	strict	strict	ADJ
ejpam-6598	8	32	to	to	PART
ejpam-6598	8	33	adequately	adequately	ADV
ejpam-6598	8	34	represent	represent	VERB
ejpam-6598	8	35	actual	actual	ADJ
ejpam-6598	8	36	occurrences	occurrence	NOUN
ejpam-6598	8	37	.	.	PUNCT
ejpam-6598	9	1	the	the	DET
ejpam-6598	9	2	fundamental	fundamental	ADJ
ejpam-6598	9	3	concept	concept	NOUN
ejpam-6598	9	4	of	of	ADP
ejpam-6598	9	5	fuzzy	fuzzy	ADJ
ejpam-6598	9	6	topology	topology	NOUN
ejpam-6598	9	7	is	be	AUX
ejpam-6598	9	8	fuzzy	fuzzy	ADJ
ejpam-6598	9	9	sets	set	NOUN
ejpam-6598	9	10	,	,	PUNCT
ejpam-6598	9	11	which	which	PRON
ejpam-6598	9	12	were	be	AUX
ejpam-6598	9	13	initially	initially	ADV
ejpam-6598	9	14	introduced	introduce	VERB
ejpam-6598	9	15	by	by	ADP
ejpam-6598	9	16	lotfi	lotfi	PROPN
ejpam-6598	9	17	zadeh	zadeh	PROPN
ejpam-6598	10	1	[	[	X
ejpam-6598	10	2	1	1	X
ejpam-6598	10	3	]	]	PUNCT
ejpam-6598	10	4	in	in	ADP
ejpam-6598	10	5	1965	1965	NUM
ejpam-6598	10	6	.	.	PUNCT
ejpam-6598	11	1	unlike	unlike	ADP
ejpam-6598	11	2	classical	classical	ADJ
ejpam-6598	11	3	sets	set	NOUN
ejpam-6598	11	4	,	,	PUNCT
ejpam-6598	11	5	where	where	SCONJ
ejpam-6598	11	6	an	an	DET
ejpam-6598	11	7	element	element	NOUN
ejpam-6598	11	8	is	be	AUX
ejpam-6598	11	9	either	either	CCONJ
ejpam-6598	11	10	a	a	DET
ejpam-6598	11	11	member	member	NOUN
ejpam-6598	11	12	or	or	CCONJ
ejpam-6598	11	13	not	not	PART
ejpam-6598	11	14	(	(	PUNCT
ejpam-6598	11	15	with	with	ADP
ejpam-6598	11	16	membership	membership	NOUN
ejpam-6598	11	17	values	value	NOUN
ejpam-6598	11	18	strictly	strictly	ADV
ejpam-6598	11	19	1	1	NUM
ejpam-6598	11	20	or	or	CCONJ
ejpam-6598	11	21	0	0	NUM
ejpam-6598	11	22	)	)	PUNCT
ejpam-6598	11	23	,	,	PUNCT
ejpam-6598	11	24	fuzzy	fuzzy	ADJ
ejpam-6598	11	25	sets	set	NOUN
ejpam-6598	11	26	permit	permit	VERB
ejpam-6598	11	27	varying	vary	VERB
ejpam-6598	11	28	degrees	degree	NOUN
ejpam-6598	11	29	of	of	ADP
ejpam-6598	11	30	membership	membership	NOUN
ejpam-6598	11	31	across	across	ADP
ejpam-6598	11	32	a	a	DET
ejpam-6598	11	33	continuum	continuum	ADJ
ejpam-6598	11	34	[	[	X
ejpam-6598	11	35	2	2	NUM
ejpam-6598	11	36	]	]	PUNCT
ejpam-6598	11	37	.	.	PUNCT
ejpam-6598	12	1	developed	develop	VERB
ejpam-6598	12	2	by	by	ADP
ejpam-6598	12	3	krassimir	krassimir	NOUN
ejpam-6598	12	4	atanassov	atanassov	NOUN
ejpam-6598	13	1	[	[	X
ejpam-6598	13	2	3	3	X
ejpam-6598	13	3	]	]	PUNCT
ejpam-6598	13	4	in	in	ADP
ejpam-6598	13	5	1986	1986	NUM
ejpam-6598	13	6	,	,	PUNCT
ejpam-6598	13	7	intuitionistic	intuitionistic	ADJ
ejpam-6598	13	8	fuzzy	fuzzy	ADJ
ejpam-6598	13	9	topology	topology	NOUN
ejpam-6598	13	10	is	be	AUX
ejpam-6598	13	11	an	an	DET
ejpam-6598	13	12	extension	extension	NOUN
ejpam-6598	13	13	of	of	ADP
ejpam-6598	13	14	fuzzy	fuzzy	ADJ
ejpam-6598	13	15	topology	topology	NOUN
ejpam-6598	13	16	that	that	PRON
ejpam-6598	13	17	incorporates	incorporate	VERB
ejpam-6598	13	18	the	the	DET
ejpam-6598	13	19	idea	idea	NOUN
ejpam-6598	13	20	of	of	ADP
ejpam-6598	13	21	intuitionistic	intuitionistic	ADJ
ejpam-6598	13	22	fuzzy	fuzzy	ADJ
ejpam-6598	13	23	sets	set	NOUN
ejpam-6598	13	24	.	.	PUNCT
ejpam-6598	14	1	this	this	DET
ejpam-6598	14	2	enhancement	enhancement	NOUN
ejpam-6598	14	3	offers	offer	VERB
ejpam-6598	14	4	a	a	DET
ejpam-6598	14	5	more	more	ADV
ejpam-6598	14	6	comprehensive	comprehensive	ADJ
ejpam-6598	14	7	framework	framework	NOUN
ejpam-6598	14	8	for	for	ADP
ejpam-6598	14	9	managing	manage	VERB
ejpam-6598	14	10	uncertainty	uncertainty	NOUN
ejpam-6598	14	11	by	by	ADP
ejpam-6598	14	12	taking	take	VERB
ejpam-6598	14	13	into	into	ADP
ejpam-6598	14	14	account	account	NOUN
ejpam-6598	14	15	the	the	DET
ejpam-6598	14	16	degree	degree	NOUN
ejpam-6598	14	17	of	of	ADP
ejpam-6598	14	18	membership	membership	NOUN
ejpam-6598	14	19	,	,	PUNCT
ejpam-6598	14	20	the	the	DET
ejpam-6598	14	21	degree	degree	NOUN
ejpam-6598	14	22	of	of	ADP
ejpam-6598	14	23	non	non	ADJ
ejpam-6598	14	24	-	-	NOUN
ejpam-6598	14	25	membership	membership	NOUN
ejpam-6598	14	26	and	and	CCONJ
ejpam-6598	14	27	a	a	DET
ejpam-6598	14	28	hesitation	hesitation	NOUN
ejpam-6598	14	29	margin	margin	NOUN
ejpam-6598	14	30	.	.	PUNCT
ejpam-6598	15	1	it	it	PRON
ejpam-6598	15	2	is	be	AUX
ejpam-6598	15	3	particularly	particularly	ADV
ejpam-6598	15	4	effective	effective	ADJ
ejpam-6598	15	5	in	in	ADP
ejpam-6598	15	6	situations	situation	NOUN
ejpam-6598	15	7	where	where	SCONJ
ejpam-6598	15	8	uncertainty	uncertainty	NOUN
ejpam-6598	15	9	exists	exist	VERB
ejpam-6598	15	10	not	not	PART
ejpam-6598	15	11	only	only	ADV
ejpam-6598	15	12	regarding	regard	VERB
ejpam-6598	15	13	membership	membership	NOUN
ejpam-6598	15	14	value	value	NOUN
ejpam-6598	15	15	but	but	CCONJ
ejpam-6598	15	16	∗corresponding	∗corresponde	VERB
ejpam-6598	15	17	author	author	NOUN
ejpam-6598	15	18	.	.	PUNCT
ejpam-6598	16	1	doi	doi	NOUN
ejpam-6598	16	2	:	:	PUNCT
ejpam-6598	16	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6598	https://doi.org/10.29020/nybg.ejpam.v18i3.6598	PROPN
ejpam-6598	16	4	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6598	16	5	1	1	NUM
ejpam-6598	16	6	copyright	copyright	NOUN
ejpam-6598	16	7	:	:	PUNCT
ejpam-6598	17	1	©	©	PROPN
ejpam-6598	17	2	2025	2025	NUM
ejpam-6598	17	3	the	the	DET
ejpam-6598	17	4	author(s	author(s	NOUN
ejpam-6598	17	5	)	)	PUNCT
ejpam-6598	17	6	.	.	PUNCT
ejpam-6598	18	1	(	(	PUNCT
ejpam-6598	18	2	cc	cc	NOUN
ejpam-6598	18	3	by	by	ADP
ejpam-6598	18	4	-	-	PUNCT
ejpam-6598	18	5	nc	nc	PROPN
ejpam-6598	18	6	4.0	4.0	NUM
ejpam-6598	18	7	)	)	PUNCT
ejpam-6598	18	8	n.	n.	NOUN
ejpam-6598	18	9	preethi	preethi	ADV
ejpam-6598	18	10	,	,	PUNCT
ejpam-6598	18	11	g.	g.	PROPN
ejpam-6598	18	12	k.	k.	PROPN
ejpam-6598	18	13	revathi	revathi	PROPN
ejpam-6598	18	14	/	/	SYM
ejpam-6598	18	15	eur	eur	PROPN
ejpam-6598	18	16	.	.	PUNCT
ejpam-6598	19	1	j.	j.	PROPN
ejpam-6598	19	2	pure	pure	PROPN
ejpam-6598	19	3	appl	appl	PROPN
ejpam-6598	19	4	.	.	PROPN
ejpam-6598	19	5	math	math	PROPN
ejpam-6598	19	6	,	,	PUNCT
ejpam-6598	19	7	18	18	NUM
ejpam-6598	19	8	(	(	PUNCT
ejpam-6598	19	9	3	3	NUM
ejpam-6598	19	10	)	)	PUNCT
ejpam-6598	19	11	(	(	PUNCT
ejpam-6598	19	12	2025	2025	NUM
ejpam-6598	19	13	)	)	PUNCT
ejpam-6598	19	14	,	,	PUNCT
ejpam-6598	19	15	6598	6598	NUM
ejpam-6598	19	16	2	2	NUM
ejpam-6598	19	17	of	of	ADP
ejpam-6598	19	18	17	17	NUM
ejpam-6598	19	19	also	also	ADV
ejpam-6598	19	20	non	non	ADJ
ejpam-6598	19	21	-	-	ADJ
ejpam-6598	19	22	membership	membership	ADJ
ejpam-6598	19	23	value	value	NOUN
ejpam-6598	19	24	.	.	PUNCT
ejpam-6598	20	1	pythagorean	pythagorean	PROPN
ejpam-6598	20	2	fuzzy	fuzzy	ADJ
ejpam-6598	20	3	topology	topology	NOUN
ejpam-6598	20	4	is	be	AUX
ejpam-6598	20	5	an	an	DET
ejpam-6598	20	6	advanced	advanced	ADJ
ejpam-6598	20	7	form	form	NOUN
ejpam-6598	20	8	of	of	ADP
ejpam-6598	20	9	fuzzy	fuzzy	ADJ
ejpam-6598	20	10	and	and	CCONJ
ejpam-6598	20	11	intuitionistic	intuitionistic	ADJ
ejpam-6598	20	12	fuzzy	fuzzy	ADJ
ejpam-6598	20	13	topology	topology	NOUN
ejpam-6598	20	14	.	.	PUNCT
ejpam-6598	21	1	it	it	PRON
ejpam-6598	21	2	uses	use	VERB
ejpam-6598	21	3	pythagorean	pythagorean	PROPN
ejpam-6598	21	4	fuzzy	fuzzy	ADJ
ejpam-6598	21	5	sets	set	NOUN
ejpam-6598	21	6	,	,	PUNCT
ejpam-6598	21	7	which	which	PRON
ejpam-6598	21	8	provide	provide	VERB
ejpam-6598	21	9	more	more	ADJ
ejpam-6598	21	10	flexibility	flexibility	NOUN
ejpam-6598	21	11	in	in	ADP
ejpam-6598	21	12	handling	handle	VERB
ejpam-6598	21	13	uncertainty	uncertainty	NOUN
ejpam-6598	21	14	.	.	PUNCT
ejpam-6598	22	1	this	this	PRON
ejpam-6598	22	2	is	be	AUX
ejpam-6598	22	3	especially	especially	ADV
ejpam-6598	22	4	useful	useful	ADJ
ejpam-6598	22	5	in	in	ADP
ejpam-6598	22	6	situations	situation	NOUN
ejpam-6598	22	7	where	where	SCONJ
ejpam-6598	22	8	it	it	PRON
ejpam-6598	22	9	is	be	AUX
ejpam-6598	22	10	important	important	ADJ
ejpam-6598	22	11	to	to	PART
ejpam-6598	22	12	balance	balance	VERB
ejpam-6598	22	13	membership	membership	NOUN
ejpam-6598	22	14	and	and	CCONJ
ejpam-6598	22	15	non	non	ADJ
ejpam-6598	22	16	-	-	ADJ
ejpam-6598	22	17	membership	membership	ADJ
ejpam-6598	22	18	values	value	NOUN
ejpam-6598	22	19	carefully	carefully	ADV
ejpam-6598	22	20	and	and	CCONJ
ejpam-6598	22	21	where	where	SCONJ
ejpam-6598	22	22	there	there	PRON
ejpam-6598	22	23	is	be	VERB
ejpam-6598	22	24	a	a	DET
ejpam-6598	22	25	high	high	ADJ
ejpam-6598	22	26	level	level	NOUN
ejpam-6598	22	27	of	of	ADP
ejpam-6598	22	28	indeterminacy	indeterminacy	NOUN
ejpam-6598	22	29	.	.	PUNCT
ejpam-6598	23	1	motivated	motivate	VERB
ejpam-6598	23	2	by	by	ADP
ejpam-6598	23	3	this	this	DET
ejpam-6598	23	4	need	need	NOUN
ejpam-6598	23	5	,	,	PUNCT
ejpam-6598	23	6	yager	yager	PROPN
ejpam-6598	23	7	r.	r.	PROPN
ejpam-6598	23	8	r.	r.	PROPN
ejpam-6598	24	1	[	[	X
ejpam-6598	24	2	4	4	X
ejpam-6598	24	3	]	]	PUNCT
ejpam-6598	24	4	introduced	introduce	VERB
ejpam-6598	24	5	pythagorean	pythagorean	PROPN
ejpam-6598	24	6	fuzzy	fuzzy	ADJ
ejpam-6598	24	7	sets	set	NOUN
ejpam-6598	24	8	under	under	ADP
ejpam-6598	24	9	a	a	DET
ejpam-6598	24	10	specific	specific	ADJ
ejpam-6598	24	11	constraint	constraint	NOUN
ejpam-6598	24	12	µ2	µ2	NOUN
ejpam-6598	24	13	+	+	CCONJ
ejpam-6598	24	14	ν2	ν2	ADV
ejpam-6598	24	15	≤	≤	NUM
ejpam-6598	24	16	1	1	NUM
ejpam-6598	24	17	.	.	NUM
ejpam-6598	24	18	,	,	PUNCT
ejpam-6598	24	19	enabling	enable	VERB
ejpam-6598	24	20	a	a	DET
ejpam-6598	24	21	more	more	ADV
ejpam-6598	24	22	refined	refined	ADJ
ejpam-6598	24	23	mathematical	mathematical	ADJ
ejpam-6598	24	24	framework	framework	NOUN
ejpam-6598	24	25	for	for	ADP
ejpam-6598	24	26	addressing	address	VERB
ejpam-6598	24	27	uncertainty	uncertainty	NOUN
ejpam-6598	24	28	.	.	PUNCT
ejpam-6598	25	1	as	as	ADP
ejpam-6598	25	2	a	a	DET
ejpam-6598	25	3	result	result	NOUN
ejpam-6598	25	4	,	,	PUNCT
ejpam-6598	25	5	pythagorean	pythagorean	PROPN
ejpam-6598	25	6	fuzzy	fuzzy	ADJ
ejpam-6598	25	7	topology	topology	NOUN
ejpam-6598	25	8	paves	pave	VERB
ejpam-6598	25	9	the	the	DET
ejpam-6598	25	10	way	way	NOUN
ejpam-6598	25	11	for	for	ADP
ejpam-6598	25	12	new	new	ADJ
ejpam-6598	25	13	research	research	NOUN
ejpam-6598	25	14	directions	direction	NOUN
ejpam-6598	25	15	and	and	CCONJ
ejpam-6598	25	16	practical	practical	ADJ
ejpam-6598	25	17	applications	application	NOUN
ejpam-6598	25	18	in	in	ADP
ejpam-6598	25	19	areas	area	NOUN
ejpam-6598	25	20	where	where	SCONJ
ejpam-6598	25	21	classical	classical	ADJ
ejpam-6598	25	22	or	or	CCONJ
ejpam-6598	25	23	even	even	ADV
ejpam-6598	25	24	intuitionistic	intuitionistic	ADJ
ejpam-6598	25	25	methods	method	NOUN
ejpam-6598	25	26	may	may	AUX
ejpam-6598	25	27	be	be	AUX
ejpam-6598	25	28	inadequate	inadequate	ADJ
ejpam-6598	25	29	.	.	PUNCT
ejpam-6598	26	1	fuzzy	fuzzy	ADJ
ejpam-6598	26	2	digital	digital	ADJ
ejpam-6598	26	3	topology	topology	NOUN
ejpam-6598	26	4	[	[	X
ejpam-6598	26	5	5	5	NUM
ejpam-6598	26	6	]	]	PUNCT
ejpam-6598	26	7	integrates	integrate	NOUN
ejpam-6598	26	8	fuzzy	fuzzy	ADJ
ejpam-6598	26	9	set	set	NOUN
ejpam-6598	26	10	theory	theory	NOUN
ejpam-6598	26	11	with	with	ADP
ejpam-6598	26	12	digital	digital	ADJ
ejpam-6598	26	13	topology	topology	NOUN
ejpam-6598	27	1	[	[	X
ejpam-6598	27	2	6	6	NUM
ejpam-6598	27	3	]	]	PUNCT
ejpam-6598	27	4	.	.	PUNCT
ejpam-6598	28	1	it	it	PRON
ejpam-6598	28	2	employs	employ	VERB
ejpam-6598	28	3	fuzzy	fuzzy	ADJ
ejpam-6598	28	4	sets	set	NOUN
ejpam-6598	28	5	to	to	PART
ejpam-6598	28	6	represent	represent	VERB
ejpam-6598	28	7	uncertainty	uncertainty	NOUN
ejpam-6598	28	8	in	in	ADP
ejpam-6598	28	9	digital	digital	ADJ
ejpam-6598	28	10	images	image	NOUN
ejpam-6598	28	11	and	and	CCONJ
ejpam-6598	28	12	utilizes	utilize	VERB
ejpam-6598	28	13	topological	topological	ADJ
ejpam-6598	28	14	principles	principle	NOUN
ejpam-6598	28	15	to	to	PART
ejpam-6598	28	16	analyze	analyze	VERB
ejpam-6598	28	17	and	and	CCONJ
ejpam-6598	28	18	process	process	VERB
ejpam-6598	28	19	them	they	PRON
ejpam-6598	28	20	.	.	PUNCT
ejpam-6598	29	1	the	the	DET
ejpam-6598	29	2	main	main	ADJ
ejpam-6598	29	3	objective	objective	NOUN
ejpam-6598	29	4	is	be	AUX
ejpam-6598	29	5	to	to	PART
ejpam-6598	29	6	develop	develop	VERB
ejpam-6598	29	7	techniques	technique	NOUN
ejpam-6598	29	8	capable	capable	ADJ
ejpam-6598	29	9	of	of	ADP
ejpam-6598	29	10	effectively	effectively	ADV
ejpam-6598	29	11	managing	manage	VERB
ejpam-6598	29	12	the	the	DET
ejpam-6598	29	13	inherent	inherent	ADJ
ejpam-6598	29	14	fuzziness	fuzziness	NOUN
ejpam-6598	29	15	present	present	ADJ
ejpam-6598	29	16	in	in	ADP
ejpam-6598	29	17	digital	digital	ADJ
ejpam-6598	29	18	imagery	imagery	NOUN
ejpam-6598	29	19	.	.	PUNCT
ejpam-6598	30	1	this	this	PRON
ejpam-6598	30	2	includes	include	VERB
ejpam-6598	30	3	defining	define	VERB
ejpam-6598	30	4	fuzzy	fuzzy	ADJ
ejpam-6598	30	5	topological	topological	ADJ
ejpam-6598	30	6	spaces	space	NOUN
ejpam-6598	30	7	,	,	PUNCT
ejpam-6598	30	8	fuzzy	fuzzy	ADJ
ejpam-6598	30	9	connectedness	connectedness	NOUN
ejpam-6598	30	10	,	,	PUNCT
ejpam-6598	30	11	and	and	CCONJ
ejpam-6598	30	12	fuzzy	fuzzy	ADJ
ejpam-6598	30	13	boundaries	boundary	NOUN
ejpam-6598	30	14	within	within	ADP
ejpam-6598	30	15	digital	digital	ADJ
ejpam-6598	30	16	grid	grid	NOUN
ejpam-6598	30	17	structures	structure	NOUN
ejpam-6598	30	18	.	.	PUNCT
ejpam-6598	31	1	to	to	PART
ejpam-6598	31	2	improve	improve	VERB
ejpam-6598	31	3	the	the	DET
ejpam-6598	31	4	recognition	recognition	NOUN
ejpam-6598	31	5	and	and	CCONJ
ejpam-6598	31	6	categorization	categorization	NOUN
ejpam-6598	31	7	of	of	ADP
ejpam-6598	31	8	objects	object	NOUN
ejpam-6598	31	9	with	with	ADP
ejpam-6598	31	10	partially	partially	ADV
ejpam-6598	31	11	hidden	hidden	ADJ
ejpam-6598	31	12	or	or	CCONJ
ejpam-6598	31	13	ambiguous	ambiguous	ADJ
ejpam-6598	31	14	borders	border	NOUN
ejpam-6598	31	15	,	,	PUNCT
ejpam-6598	31	16	digital	digital	ADJ
ejpam-6598	31	17	fuzzy	fuzzy	ADJ
ejpam-6598	31	18	topology	topology	NOUN
ejpam-6598	31	19	incorporates	incorporate	VERB
ejpam-6598	31	20	fuzziness	fuzziness	NOUN
ejpam-6598	31	21	into	into	ADP
ejpam-6598	31	22	the	the	DET
ejpam-6598	31	23	topological	topological	ADJ
ejpam-6598	31	24	modelling	modelling	NOUN
ejpam-6598	31	25	of	of	ADP
ejpam-6598	31	26	digital	digital	ADJ
ejpam-6598	31	27	images	image	NOUN
ejpam-6598	31	28	.	.	PUNCT
ejpam-6598	32	1	this	this	DET
ejpam-6598	32	2	method	method	NOUN
ejpam-6598	32	3	works	work	VERB
ejpam-6598	32	4	especially	especially	ADV
ejpam-6598	32	5	well	well	ADV
ejpam-6598	32	6	in	in	ADP
ejpam-6598	32	7	real	real	ADJ
ejpam-6598	32	8	-	-	PUNCT
ejpam-6598	32	9	world	world	NOUN
ejpam-6598	32	10	applications	application	NOUN
ejpam-6598	32	11	,	,	PUNCT
ejpam-6598	32	12	including	include	VERB
ejpam-6598	32	13	biometric	biometric	ADJ
ejpam-6598	32	14	verification	verification	NOUN
ejpam-6598	32	15	,	,	PUNCT
ejpam-6598	32	16	automated	automate	VERB
ejpam-6598	32	17	visual	visual	ADJ
ejpam-6598	32	18	inspection	inspection	NOUN
ejpam-6598	32	19	,	,	PUNCT
ejpam-6598	32	20	and	and	CCONJ
ejpam-6598	32	21	autonomous	autonomous	ADJ
ejpam-6598	32	22	vehicle	vehicle	NOUN
ejpam-6598	32	23	navigation	navigation	NOUN
ejpam-6598	32	24	systems	system	NOUN
ejpam-6598	32	25	.	.	PUNCT
ejpam-6598	33	1	there	there	PRON
ejpam-6598	33	2	are	be	VERB
ejpam-6598	33	3	numerous	numerous	ADJ
ejpam-6598	33	4	uses	use	NOUN
ejpam-6598	33	5	for	for	ADP
ejpam-6598	33	6	the	the	DET
ejpam-6598	33	7	pythagorean	pythagorean	PROPN
ejpam-6598	33	8	fuzzy	fuzzy	ADJ
ejpam-6598	33	9	topological	topological	ADJ
ejpam-6598	33	10	space	space	NOUN
ejpam-6598	33	11	[	[	X
ejpam-6598	33	12	7	7	NUM
ejpam-6598	33	13	]	]	PUNCT
ejpam-6598	33	14	,	,	PUNCT
ejpam-6598	33	15	which	which	PRON
ejpam-6598	33	16	was	be	AUX
ejpam-6598	33	17	created	create	VERB
ejpam-6598	33	18	with	with	ADP
ejpam-6598	33	19	pythagorean	pythagorean	PROPN
ejpam-6598	33	20	fuzzy	fuzzy	ADJ
ejpam-6598	33	21	sets	set	NOUN
ejpam-6598	33	22	,	,	PUNCT
ejpam-6598	33	23	in	in	ADP
ejpam-6598	33	24	decision	decision	NOUN
ejpam-6598	33	25	-	-	PUNCT
ejpam-6598	33	26	making	making	NOUN
ejpam-6598	33	27	.	.	PUNCT
ejpam-6598	34	1	fuzzy	fuzzy	ADJ
ejpam-6598	34	2	door	door	NOUN
ejpam-6598	34	3	space	space	NOUN
ejpam-6598	34	4	was	be	AUX
ejpam-6598	34	5	first	first	ADV
ejpam-6598	34	6	proposed	propose	VERB
ejpam-6598	34	7	by	by	ADP
ejpam-6598	34	8	anjalmose	anjalmose	PROPN
ejpam-6598	34	9	s.	s.	PROPN
ejpam-6598	34	10	and	and	CCONJ
ejpam-6598	34	11	thangaraj	thangaraj	PROPN
ejpam-6598	34	12	g.	g.	PROPN
ejpam-6598	35	1	[	[	X
ejpam-6598	35	2	8	8	NUM
ejpam-6598	35	3	]	]	PUNCT
ejpam-6598	35	4	,	,	PUNCT
ejpam-6598	35	5	who	who	PRON
ejpam-6598	35	6	also	also	ADV
ejpam-6598	35	7	looked	look	VERB
ejpam-6598	35	8	into	into	ADP
ejpam-6598	35	9	the	the	DET
ejpam-6598	35	10	connections	connection	NOUN
ejpam-6598	35	11	between	between	ADP
ejpam-6598	35	12	fuzzy	fuzzy	ADJ
ejpam-6598	35	13	door	door	NOUN
ejpam-6598	35	14	space	space	NOUN
ejpam-6598	35	15	and	and	CCONJ
ejpam-6598	35	16	some	some	DET
ejpam-6598	35	17	fuzzy	fuzzy	ADJ
ejpam-6598	35	18	topological	topological	ADJ
ejpam-6598	35	19	space	space	NOUN
ejpam-6598	35	20	.	.	PUNCT
ejpam-6598	36	1	the	the	DET
ejpam-6598	36	2	notion	notion	NOUN
ejpam-6598	36	3	of	of	ADP
ejpam-6598	36	4	b	b	NOUN
ejpam-6598	36	5	-	-	PUNCT
ejpam-6598	36	6	open	open	ADJ
ejpam-6598	36	7	sets	set	NOUN
ejpam-6598	36	8	was	be	AUX
ejpam-6598	36	9	presented	present	VERB
ejpam-6598	36	10	and	and	CCONJ
ejpam-6598	36	11	examined	examine	VERB
ejpam-6598	36	12	by	by	ADP
ejpam-6598	36	13	andrijivic	andrijivic	PROPN
ejpam-6598	36	14	[	[	X
ejpam-6598	36	15	9	9	NUM
ejpam-6598	36	16	]	]	PUNCT
ejpam-6598	36	17	.	.	PUNCT
ejpam-6598	37	1	additionally	additionally	ADV
ejpam-6598	37	2	,	,	PUNCT
ejpam-6598	37	3	parameswari	parameswari	PROPN
ejpam-6598	37	4	r.u	r.u	PROPN
ejpam-6598	37	5	.	.	PROPN
ejpam-6598	37	6	and	and	CCONJ
ejpam-6598	37	7	thangavelu	thangavelu	NOUN
ejpam-6598	37	8	p.	p.	NOUN
ejpam-6598	38	1	[	[	X
ejpam-6598	38	2	10	10	NUM
ejpam-6598	38	3	]	]	PUNCT
ejpam-6598	38	4	,	,	PUNCT
ejpam-6598	38	5	presented	present	VERB
ejpam-6598	38	6	on	on	ADP
ejpam-6598	38	7	the	the	DET
ejpam-6598	38	8	idea	idea	NOUN
ejpam-6598	38	9	of	of	ADP
ejpam-6598	38	10	a	a	DET
ejpam-6598	38	11	b#-open	b#-open	ADJ
ejpam-6598	38	12	set	set	NOUN
ejpam-6598	38	13	and	and	CCONJ
ejpam-6598	38	14	its	its	PRON
ejpam-6598	38	15	fundamental	fundamental	ADJ
ejpam-6598	38	16	characteristics	characteristic	NOUN
ejpam-6598	38	17	.	.	PUNCT
ejpam-6598	39	1	using	use	VERB
ejpam-6598	39	2	the	the	DET
ejpam-6598	39	3	intuitionistic	intuitionistic	ADJ
ejpam-6598	39	4	fuzzy	fuzzy	ADJ
ejpam-6598	39	5	b	b	NOUN
ejpam-6598	39	6	-	-	PUNCT
ejpam-6598	39	7	set	set	NOUN
ejpam-6598	39	8	as	as	ADP
ejpam-6598	39	9	a	a	DET
ejpam-6598	39	10	basis	basis	NOUN
ejpam-6598	39	11	,	,	PUNCT
ejpam-6598	39	12	abdulgawad	abdulgawad	NOUN
ejpam-6598	39	13	,	,	PUNCT
ejpam-6598	39	14	a.	a.	PROPN
ejpam-6598	39	15	al	al	PROPN
ejpam-6598	39	16	-	-	PUNCT
ejpam-6598	39	17	qubati	qubati	PROPN
ejpam-6598	39	18	,	,	PUNCT
ejpam-6598	39	19	and	and	CCONJ
ejpam-6598	39	20	mohamed	mohamed	PROPN
ejpam-6598	39	21	el	el	PROPN
ejpam-6598	39	22	sayed	say	VERB
ejpam-6598	40	1	[	[	X
ejpam-6598	40	2	11	11	NUM
ejpam-6598	40	3	]	]	PUNCT
ejpam-6598	40	4	developed	develop	VERB
ejpam-6598	40	5	the	the	DET
ejpam-6598	40	6	concept	concept	NOUN
ejpam-6598	40	7	of	of	ADP
ejpam-6598	40	8	intuitionistic	intuitionistic	ADJ
ejpam-6598	40	9	fuzzy	fuzzy	ADJ
ejpam-6598	40	10	b	b	NOUN
ejpam-6598	40	11	-	-	PUNCT
ejpam-6598	40	12	door	door	NOUN
ejpam-6598	40	13	space	space	NOUN
ejpam-6598	40	14	and	and	CCONJ
ejpam-6598	40	15	investigated	investigate	VERB
ejpam-6598	40	16	its	its	PRON
ejpam-6598	40	17	properties	property	NOUN
ejpam-6598	40	18	.	.	PUNCT
ejpam-6598	41	1	harish	harish	PROPN
ejpam-6598	41	2	garg	garg	PROPN
ejpam-6598	42	1	[	[	X
ejpam-6598	42	2	12	12	NUM
ejpam-6598	42	3	]	]	PUNCT
ejpam-6598	42	4	explored	explore	VERB
ejpam-6598	42	5	confidence	confidence	NOUN
ejpam-6598	42	6	pythagorean	pythagorean	PROPN
ejpam-6598	42	7	fuzzy	fuzzy	PROPN
ejpam-6598	42	8	weighted	weight	VERB
ejpam-6598	42	9	and	and	CCONJ
ejpam-6598	42	10	ordered	order	VERB
ejpam-6598	42	11	weighted	weighted	ADJ
ejpam-6598	42	12	operators	operator	NOUN
ejpam-6598	42	13	,	,	PUNCT
ejpam-6598	42	14	which	which	PRON
ejpam-6598	42	15	are	be	AUX
ejpam-6598	42	16	novel	novel	ADJ
ejpam-6598	42	17	averaging	averaging	NOUN
ejpam-6598	42	18	and	and	CCONJ
ejpam-6598	42	19	geometric	geometric	ADJ
ejpam-6598	42	20	operators	operator	NOUN
ejpam-6598	42	21	.	.	PUNCT
ejpam-6598	43	1	to	to	PART
ejpam-6598	43	2	illustrate	illustrate	VERB
ejpam-6598	43	3	their	their	PRON
ejpam-6598	43	4	validity	validity	NOUN
ejpam-6598	43	5	and	and	CCONJ
ejpam-6598	43	6	effectiveness	effectiveness	NOUN
ejpam-6598	43	7	,	,	PUNCT
ejpam-6598	43	8	a	a	DET
ejpam-6598	43	9	real	real	ADJ
ejpam-6598	43	10	-	-	PUNCT
ejpam-6598	43	11	life	life	NOUN
ejpam-6598	43	12	application	application	NOUN
ejpam-6598	43	13	has	have	AUX
ejpam-6598	43	14	been	be	AUX
ejpam-6598	43	15	proposed	propose	VERB
ejpam-6598	43	16	.	.	PUNCT
ejpam-6598	44	1	the	the	DET
ejpam-6598	44	2	analysis	analysis	NOUN
ejpam-6598	44	3	of	of	ADP
ejpam-6598	44	4	door	door	NOUN
ejpam-6598	44	5	spaces	space	NOUN
ejpam-6598	44	6	is	be	AUX
ejpam-6598	44	7	a	a	DET
ejpam-6598	44	8	well	well	ADV
ejpam-6598	44	9	-	-	PUNCT
ejpam-6598	44	10	known	know	VERB
ejpam-6598	44	11	topic	topic	NOUN
ejpam-6598	44	12	in	in	ADP
ejpam-6598	44	13	fuzzy	fuzzy	ADJ
ejpam-6598	44	14	topology	topology	NOUN
ejpam-6598	44	15	and	and	CCONJ
ejpam-6598	44	16	intuitionistic	intuitionistic	ADJ
ejpam-6598	44	17	fuzzy	fuzzy	ADJ
ejpam-6598	44	18	topology	topology	NOUN
ejpam-6598	44	19	.	.	PUNCT
ejpam-6598	45	1	however	however	ADV
ejpam-6598	45	2	,	,	PUNCT
ejpam-6598	45	3	it	it	PRON
ejpam-6598	45	4	is	be	AUX
ejpam-6598	45	5	not	not	PART
ejpam-6598	45	6	yet	yet	ADV
ejpam-6598	45	7	known	know	VERB
ejpam-6598	45	8	whether	whether	SCONJ
ejpam-6598	45	9	it	it	PRON
ejpam-6598	45	10	can	can	AUX
ejpam-6598	45	11	be	be	AUX
ejpam-6598	45	12	used	use	VERB
ejpam-6598	45	13	to	to	PART
ejpam-6598	45	14	pythagorean	pythagorean	VERB
ejpam-6598	45	15	fuzzy	fuzzy	ADJ
ejpam-6598	45	16	digital	digital	PROPN
ejpam-6598	45	17	fine	fine	ADJ
ejpam-6598	45	18	topological	topological	ADJ
ejpam-6598	45	19	spaces	space	NOUN
ejpam-6598	45	20	.	.	PUNCT
ejpam-6598	46	1	in	in	ADP
ejpam-6598	46	2	an	an	DET
ejpam-6598	46	3	intuitionistic	intuitionistic	ADJ
ejpam-6598	46	4	fuzzy	fuzzy	ADJ
ejpam-6598	46	5	framework	framework	NOUN
ejpam-6598	46	6	,	,	PUNCT
ejpam-6598	46	7	a	a	DET
ejpam-6598	46	8	great	great	ADJ
ejpam-6598	46	9	deal	deal	NOUN
ejpam-6598	46	10	of	of	ADP
ejpam-6598	46	11	research	research	NOUN
ejpam-6598	46	12	has	have	AUX
ejpam-6598	46	13	been	be	AUX
ejpam-6598	46	14	done	do	VERB
ejpam-6598	46	15	to	to	PART
ejpam-6598	46	16	produce	produce	VERB
ejpam-6598	46	17	theoretical	theoretical	ADJ
ejpam-6598	46	18	findings	finding	NOUN
ejpam-6598	46	19	regarding	regard	VERB
ejpam-6598	46	20	door	door	NOUN
ejpam-6598	46	21	spaces	space	NOUN
ejpam-6598	46	22	.	.	PUNCT
ejpam-6598	47	1	the	the	DET
ejpam-6598	47	2	necessity	necessity	NOUN
ejpam-6598	47	3	for	for	ADP
ejpam-6598	47	4	a	a	DET
ejpam-6598	47	5	thorough	thorough	ADJ
ejpam-6598	47	6	investigation	investigation	NOUN
ejpam-6598	47	7	of	of	ADP
ejpam-6598	47	8	the	the	DET
ejpam-6598	47	9	function	function	NOUN
ejpam-6598	47	10	of	of	ADP
ejpam-6598	47	11	door	door	NOUN
ejpam-6598	47	12	spaces	space	NOUN
ejpam-6598	47	13	with	with	ADP
ejpam-6598	47	14	pythagorean	pythagorean	PROPN
ejpam-6598	47	15	fuzzy	fuzzy	ADJ
ejpam-6598	47	16	digital	digital	PROPN
ejpam-6598	47	17	fine	fine	ADJ
ejpam-6598	47	18	topological	topological	ADJ
ejpam-6598	47	19	space	space	NOUN
ejpam-6598	47	20	is	be	AUX
ejpam-6598	47	21	highlighted	highlight	VERB
ejpam-6598	47	22	by	by	ADP
ejpam-6598	47	23	this	this	DET
ejpam-6598	47	24	gap	gap	NOUN
ejpam-6598	47	25	.	.	PUNCT
ejpam-6598	48	1	the	the	DET
ejpam-6598	48	2	following	follow	VERB
ejpam-6598	48	3	is	be	AUX
ejpam-6598	48	4	the	the	DET
ejpam-6598	48	5	motivation	motivation	NOUN
ejpam-6598	48	6	behind	behind	ADP
ejpam-6598	48	7	this	this	DET
ejpam-6598	48	8	study	study	NOUN
ejpam-6598	48	9	:	:	PUNCT
ejpam-6598	48	10	•	•	NOUN
ejpam-6598	48	11	for	for	ADP
ejpam-6598	48	12	theoretical	theoretical	ADJ
ejpam-6598	48	13	developments	development	NOUN
ejpam-6598	48	14	,	,	PUNCT
ejpam-6598	48	15	it	it	PRON
ejpam-6598	48	16	is	be	AUX
ejpam-6598	48	17	crucial	crucial	ADJ
ejpam-6598	48	18	to	to	PART
ejpam-6598	48	19	comprehend	comprehend	VERB
ejpam-6598	48	20	how	how	SCONJ
ejpam-6598	48	21	fine	fine	ADJ
ejpam-6598	48	22	collections	collection	NOUN
ejpam-6598	48	23	behave	behave	VERB
ejpam-6598	48	24	in	in	ADP
ejpam-6598	48	25	a	a	DET
ejpam-6598	48	26	topological	topological	ADJ
ejpam-6598	48	27	space	space	NOUN
ejpam-6598	48	28	.	.	PUNCT
ejpam-6598	49	1	•	•	NOUN
ejpam-6598	49	2	to	to	PART
ejpam-6598	49	3	improve	improve	VERB
ejpam-6598	49	4	the	the	DET
ejpam-6598	49	5	study	study	NOUN
ejpam-6598	49	6	of	of	ADP
ejpam-6598	49	7	pythagorean	pythagorean	PROPN
ejpam-6598	49	8	fuzzy	fuzzy	ADJ
ejpam-6598	49	9	topology	topology	NOUN
ejpam-6598	49	10	,	,	PUNCT
ejpam-6598	49	11	the	the	DET
ejpam-6598	49	12	idea	idea	NOUN
ejpam-6598	49	13	of	of	ADP
ejpam-6598	49	14	door	door	NOUN
ejpam-6598	49	15	spaces	space	NOUN
ejpam-6598	49	16	is	be	AUX
ejpam-6598	49	17	extended	extend	VERB
ejpam-6598	49	18	to	to	PART
ejpam-6598	49	19	pythagorean	pythagorean	VERB
ejpam-6598	49	20	fuzzy	fuzzy	ADJ
ejpam-6598	49	21	digital	digital	PROPN
ejpam-6598	49	22	fine	fine	ADJ
ejpam-6598	49	23	door	door	NOUN
ejpam-6598	49	24	spaces	space	VERB
ejpam-6598	49	25	.	.	PUNCT
ejpam-6598	50	1	•	•	NUM
ejpam-6598	50	2	new	new	ADJ
ejpam-6598	50	3	insights	insight	NOUN
ejpam-6598	50	4	into	into	ADP
ejpam-6598	50	5	structural	structural	ADJ
ejpam-6598	50	6	features	feature	NOUN
ejpam-6598	50	7	are	be	AUX
ejpam-6598	50	8	obtained	obtain	VERB
ejpam-6598	50	9	by	by	ADP
ejpam-6598	50	10	connecting	connect	VERB
ejpam-6598	50	11	pythagorean	pythagorean	PROPN
ejpam-6598	50	12	fuzzy	fuzzy	PROPN
ejpam-6598	50	13	n.	n.	PROPN
ejpam-6598	50	14	preethi	preethi	PROPN
ejpam-6598	50	15	,	,	PUNCT
ejpam-6598	50	16	g.	g.	PROPN
ejpam-6598	50	17	k.	k.	PROPN
ejpam-6598	50	18	revathi	revathi	PROPN
ejpam-6598	50	19	/	/	SYM
ejpam-6598	50	20	eur	eur	PROPN
ejpam-6598	50	21	.	.	PUNCT
ejpam-6598	51	1	j.	j.	PROPN
ejpam-6598	51	2	pure	pure	PROPN
ejpam-6598	51	3	appl	appl	PROPN
ejpam-6598	51	4	.	.	PROPN
ejpam-6598	51	5	math	math	PROPN
ejpam-6598	51	6	,	,	PUNCT
ejpam-6598	51	7	18	18	NUM
ejpam-6598	51	8	(	(	PUNCT
ejpam-6598	51	9	3	3	NUM
ejpam-6598	51	10	)	)	PUNCT
ejpam-6598	51	11	(	(	PUNCT
ejpam-6598	51	12	2025	2025	NUM
ejpam-6598	51	13	)	)	PUNCT
ejpam-6598	51	14	,	,	PUNCT
ejpam-6598	51	15	6598	6598	NUM
ejpam-6598	51	16	3	3	NUM
ejpam-6598	51	17	of	of	ADP
ejpam-6598	51	18	17	17	NUM
ejpam-6598	51	19	digital	digital	ADJ
ejpam-6598	51	20	fine	fine	ADJ
ejpam-6598	51	21	topological	topological	ADJ
ejpam-6598	51	22	spaces	space	NOUN
ejpam-6598	51	23	with	with	ADP
ejpam-6598	51	24	pythagorean	pythagorean	PROPN
ejpam-6598	51	25	fuzzy	fuzzy	ADJ
ejpam-6598	51	26	digital	digital	ADJ
ejpam-6598	51	27	fine	fine	ADJ
ejpam-6598	51	28	b≈-door	b≈-door	NOUN
ejpam-6598	51	29	space	space	NOUN
ejpam-6598	51	30	.	.	PUNCT
ejpam-6598	52	1	•	•	NUM
ejpam-6598	52	2	filling	fill	VERB
ejpam-6598	52	3	this	this	DET
ejpam-6598	52	4	research	research	NOUN
ejpam-6598	52	5	void	void	NOUN
ejpam-6598	52	6	will	will	AUX
ejpam-6598	52	7	advance	advance	VERB
ejpam-6598	52	8	pythagorean	pythagorean	PROPN
ejpam-6598	52	9	fuzzy	fuzzy	ADJ
ejpam-6598	52	10	topology	topology	NOUN
ejpam-6598	52	11	and	and	CCONJ
ejpam-6598	52	12	enable	enable	VERB
ejpam-6598	52	13	its	its	PRON
ejpam-6598	52	14	application	application	NOUN
ejpam-6598	52	15	to	to	ADP
ejpam-6598	52	16	more	more	ADJ
ejpam-6598	52	17	general	general	ADJ
ejpam-6598	52	18	mathematics	mathematic	NOUN
ejpam-6598	52	19	and	and	CCONJ
ejpam-6598	52	20	practical	practical	ADJ
ejpam-6598	52	21	issues	issue	NOUN
ejpam-6598	52	22	.	.	PUNCT
ejpam-6598	53	1	this	this	DET
ejpam-6598	53	2	paper	paper	NOUN
ejpam-6598	53	3	introduces	introduce	VERB
ejpam-6598	53	4	the	the	DET
ejpam-6598	53	5	concept	concept	NOUN
ejpam-6598	53	6	of	of	ADP
ejpam-6598	53	7	door	door	NOUN
ejpam-6598	53	8	space	space	NOUN
ejpam-6598	53	9	within	within	ADP
ejpam-6598	53	10	the	the	DET
ejpam-6598	53	11	framework	framework	NOUN
ejpam-6598	53	12	of	of	ADP
ejpam-6598	53	13	pythagorean	pythagorean	PROPN
ejpam-6598	53	14	fuzzy	fuzzy	ADJ
ejpam-6598	53	15	digital	digital	PROPN
ejpam-6598	53	16	fine	fine	ADJ
ejpam-6598	53	17	topology	topology	NOUN
ejpam-6598	53	18	.	.	PUNCT
ejpam-6598	54	1	establishing	establish	VERB
ejpam-6598	54	2	and	and	CCONJ
ejpam-6598	54	3	examining	examine	VERB
ejpam-6598	54	4	a	a	DET
ejpam-6598	54	5	variety	variety	NOUN
ejpam-6598	54	6	of	of	ADP
ejpam-6598	54	7	structures	structure	NOUN
ejpam-6598	54	8	in	in	ADP
ejpam-6598	54	9	pythagorean	pythagorean	PROPN
ejpam-6598	54	10	fuzzy	fuzzy	ADJ
ejpam-6598	54	11	digital	digital	PROPN
ejpam-6598	54	12	fine	fine	ADJ
ejpam-6598	54	13	door	door	NOUN
ejpam-6598	54	14	spaces	space	NOUN
ejpam-6598	54	15	is	be	AUX
ejpam-6598	54	16	what	what	PRON
ejpam-6598	54	17	makes	make	VERB
ejpam-6598	54	18	this	this	DET
ejpam-6598	54	19	study	study	NOUN
ejpam-6598	54	20	new	new	ADJ
ejpam-6598	54	21	.	.	PUNCT
ejpam-6598	55	1	these	these	DET
ejpam-6598	55	2	structures	structure	NOUN
ejpam-6598	55	3	include	include	VERB
ejpam-6598	55	4	:	:	PUNCT
ejpam-6598	55	5	•	•	NUM
ejpam-6598	55	6	pythagorean	pythagorean	PROPN
ejpam-6598	55	7	fuzzy	fuzzy	ADJ
ejpam-6598	55	8	digital	digital	PROPN
ejpam-6598	55	9	fine	fine	ADJ
ejpam-6598	55	10	topology	topology	NOUN
ejpam-6598	56	1	•	•	NOUN
ejpam-6598	56	2	pythagorean	pythagorean	PROPN
ejpam-6598	56	3	fuzzy	fuzzy	ADJ
ejpam-6598	56	4	digital	digital	PROPN
ejpam-6598	56	5	fine	fine	ADJ
ejpam-6598	56	6	b≈door	b≈door	ADJ
ejpam-6598	56	7	space	space	NOUN
ejpam-6598	56	8	•	•	ADP
ejpam-6598	56	9	pythagorean	pythagorean	PROPN
ejpam-6598	56	10	fuzzy	fuzzy	ADJ
ejpam-6598	56	11	digital	digital	PROPN
ejpam-6598	56	12	fine	fine	ADJ
ejpam-6598	56	13	b≈first	b≈first	ADV
ejpam-6598	56	14	category	category	NOUN
ejpam-6598	56	15	space	space	NOUN
ejpam-6598	56	16	•	•	NOUN
ejpam-6598	56	17	pythagorean	pythagorean	PROPN
ejpam-6598	56	18	fuzzy	fuzzy	ADJ
ejpam-6598	56	19	digital	digital	ADJ
ejpam-6598	56	20	fine	fine	ADJ
ejpam-6598	56	21	b≈baire	b≈baire	ADJ
ejpam-6598	56	22	space	space	NOUN
ejpam-6598	56	23	•	•	ADP
ejpam-6598	56	24	pythagorean	pythagorean	PROPN
ejpam-6598	56	25	fuzzy	fuzzy	ADJ
ejpam-6598	56	26	digital	digital	ADJ
ejpam-6598	56	27	fine	fine	ADJ
ejpam-6598	56	28	b≈hausdorff	b≈hausdorff	NOUN
ejpam-6598	56	29	space	space	NOUN
ejpam-6598	56	30	a	a	DET
ejpam-6598	56	31	novel	novel	ADJ
ejpam-6598	56	32	real	real	ADJ
ejpam-6598	56	33	world	world	NOUN
ejpam-6598	56	34	application	application	NOUN
ejpam-6598	56	35	titled	title	VERB
ejpam-6598	56	36	as	as	ADP
ejpam-6598	56	37	selection	selection	NOUN
ejpam-6598	56	38	of	of	ADP
ejpam-6598	56	39	the	the	DET
ejpam-6598	56	40	most	most	ADV
ejpam-6598	56	41	suitable	suitable	ADJ
ejpam-6598	56	42	menstrual	menstrual	ADJ
ejpam-6598	56	43	hygiene	hygiene	NOUN
ejpam-6598	56	44	product	product	NOUN
ejpam-6598	56	45	for	for	ADP
ejpam-6598	56	46	rural	rural	ADJ
ejpam-6598	56	47	women	woman	NOUN
ejpam-6598	56	48	,	,	PUNCT
ejpam-6598	56	49	is	be	AUX
ejpam-6598	56	50	presented	present	VERB
ejpam-6598	56	51	along	along	ADP
ejpam-6598	56	52	with	with	ADP
ejpam-6598	56	53	supporting	support	VERB
ejpam-6598	56	54	numerical	numerical	ADJ
ejpam-6598	56	55	example	example	NOUN
ejpam-6598	56	56	.	.	PUNCT
ejpam-6598	57	1	this	this	DET
ejpam-6598	57	2	practical	practical	ADJ
ejpam-6598	57	3	case	case	NOUN
ejpam-6598	57	4	study	study	NOUN
ejpam-6598	57	5	illustrates	illustrate	VERB
ejpam-6598	57	6	how	how	SCONJ
ejpam-6598	57	7	the	the	DET
ejpam-6598	57	8	pythagorean	pythagorean	PROPN
ejpam-6598	57	9	fuzzy	fuzzy	ADJ
ejpam-6598	57	10	digital	digital	PROPN
ejpam-6598	57	11	fine	fine	ADJ
ejpam-6598	57	12	topology	topology	NOUN
ejpam-6598	57	13	can	can	AUX
ejpam-6598	57	14	effectively	effectively	ADV
ejpam-6598	57	15	guide	guide	VERB
ejpam-6598	57	16	and	and	CCONJ
ejpam-6598	57	17	influence	influence	VERB
ejpam-6598	57	18	the	the	DET
ejpam-6598	57	19	decision	decision	NOUN
ejpam-6598	57	20	-	-	PUNCT
ejpam-6598	57	21	making	make	VERB
ejpam-6598	57	22	process	process	NOUN
ejpam-6598	57	23	in	in	ADP
ejpam-6598	57	24	product	product	NOUN
ejpam-6598	57	25	selection	selection	NOUN
ejpam-6598	57	26	and	and	CCONJ
ejpam-6598	57	27	the	the	DET
ejpam-6598	57	28	complete	complete	ADJ
ejpam-6598	57	29	structure	structure	NOUN
ejpam-6598	57	30	of	of	ADP
ejpam-6598	57	31	this	this	DET
ejpam-6598	57	32	study	study	NOUN
ejpam-6598	57	33	is	be	AUX
ejpam-6598	57	34	given	give	VERB
ejpam-6598	57	35	in	in	ADP
ejpam-6598	57	36	the	the	DET
ejpam-6598	57	37	figure	figure	NOUN
ejpam-6598	57	38	1	1	NUM
ejpam-6598	57	39	.	.	PUNCT
ejpam-6598	57	40	figure	figure	NOUN
ejpam-6598	57	41	1	1	NUM
ejpam-6598	57	42	:	:	PUNCT
ejpam-6598	57	43	flow	flow	NOUN
ejpam-6598	57	44	of	of	ADP
ejpam-6598	57	45	pythagorean	pythagorean	PROPN
ejpam-6598	57	46	fuzzy	fuzzy	ADJ
ejpam-6598	57	47	digital	digital	ADJ
ejpam-6598	57	48	space	space	NOUN
ejpam-6598	57	49	concepts	concept	VERB
ejpam-6598	57	50	the	the	DET
ejpam-6598	57	51	structure	structure	NOUN
ejpam-6598	57	52	of	of	ADP
ejpam-6598	57	53	the	the	DET
ejpam-6598	57	54	paper	paper	NOUN
ejpam-6598	57	55	is	be	AUX
ejpam-6598	57	56	as	as	SCONJ
ejpam-6598	57	57	follows	follow	VERB
ejpam-6598	57	58	:	:	PUNCT
ejpam-6598	57	59	the	the	DET
ejpam-6598	57	60	fundamental	fundamental	ADJ
ejpam-6598	57	61	definitions	definition	NOUN
ejpam-6598	57	62	are	be	AUX
ejpam-6598	57	63	given	give	VERB
ejpam-6598	57	64	in	in	ADP
ejpam-6598	57	65	section	section	NOUN
ejpam-6598	57	66	2	2	NUM
ejpam-6598	57	67	.	.	PUNCT
ejpam-6598	58	1	the	the	DET
ejpam-6598	58	2	definition	definition	NOUN
ejpam-6598	58	3	of	of	ADP
ejpam-6598	58	4	pythagorean	pythagorean	PROPN
ejpam-6598	58	5	fuzzy	fuzzy	ADJ
ejpam-6598	58	6	digital	digital	PROPN
ejpam-6598	58	7	fine	fine	ADJ
ejpam-6598	58	8	b≈door	b≈door	ADJ
ejpam-6598	58	9	space	space	NOUN
ejpam-6598	58	10	and	and	CCONJ
ejpam-6598	58	11	a	a	DET
ejpam-6598	58	12	discussion	discussion	NOUN
ejpam-6598	58	13	n.	n.	NOUN
ejpam-6598	58	14	preethi	preethi	ADV
ejpam-6598	58	15	,	,	PUNCT
ejpam-6598	58	16	g.	g.	PROPN
ejpam-6598	58	17	k.	k.	PROPN
ejpam-6598	58	18	revathi	revathi	PROPN
ejpam-6598	58	19	/	/	SYM
ejpam-6598	58	20	eur	eur	PROPN
ejpam-6598	58	21	.	.	PUNCT
ejpam-6598	59	1	j.	j.	PROPN
ejpam-6598	59	2	pure	pure	PROPN
ejpam-6598	59	3	appl	appl	PROPN
ejpam-6598	59	4	.	.	PROPN
ejpam-6598	59	5	math	math	PROPN
ejpam-6598	59	6	,	,	PUNCT
ejpam-6598	59	7	18	18	NUM
ejpam-6598	59	8	(	(	PUNCT
ejpam-6598	59	9	3	3	NUM
ejpam-6598	59	10	)	)	PUNCT
ejpam-6598	59	11	(	(	PUNCT
ejpam-6598	59	12	2025	2025	NUM
ejpam-6598	59	13	)	)	PUNCT
ejpam-6598	59	14	,	,	PUNCT
ejpam-6598	59	15	6598	6598	NUM
ejpam-6598	59	16	4	4	NUM
ejpam-6598	59	17	of	of	ADP
ejpam-6598	59	18	17	17	NUM
ejpam-6598	59	19	of	of	ADP
ejpam-6598	59	20	several	several	ADJ
ejpam-6598	59	21	intriguing	intriguing	ADJ
ejpam-6598	59	22	characteristics	characteristic	NOUN
ejpam-6598	59	23	are	be	AUX
ejpam-6598	59	24	covered	cover	VERB
ejpam-6598	59	25	in	in	ADP
ejpam-6598	59	26	section	section	NOUN
ejpam-6598	59	27	3	3	NUM
ejpam-6598	59	28	.	.	PUNCT
ejpam-6598	60	1	the	the	DET
ejpam-6598	60	2	pythagorean	pythagorean	PROPN
ejpam-6598	60	3	fuzzy	fuzzy	ADJ
ejpam-6598	60	4	digital	digital	PROPN
ejpam-6598	60	5	b≈f	b≈f	PROPN
ejpam-6598	60	6	-quasi	-quasi	PROPN
ejpam-6598	60	7	compact	compact	NOUN
ejpam-6598	60	8	is	be	AUX
ejpam-6598	60	9	suggested	suggest	VERB
ejpam-6598	60	10	and	and	CCONJ
ejpam-6598	60	11	its	its	PRON
ejpam-6598	60	12	characteristics	characteristic	NOUN
ejpam-6598	60	13	are	be	AUX
ejpam-6598	60	14	examined	examine	VERB
ejpam-6598	60	15	in	in	ADP
ejpam-6598	60	16	section	section	NOUN
ejpam-6598	60	17	4	4	NUM
ejpam-6598	60	18	.	.	PUNCT
ejpam-6598	61	1	the	the	DET
ejpam-6598	61	2	pythagorean	pythagorean	PROPN
ejpam-6598	61	3	fuzzy	fuzzy	ADJ
ejpam-6598	61	4	digital	digital	PROPN
ejpam-6598	61	5	fine	fine	ADJ
ejpam-6598	61	6	topological	topological	ADJ
ejpam-6598	61	7	space	space	NOUN
ejpam-6598	61	8	selection	selection	NOUN
ejpam-6598	61	9	algorithm	algorithm	NOUN
ejpam-6598	61	10	is	be	AUX
ejpam-6598	61	11	presented	present	VERB
ejpam-6598	61	12	in	in	ADP
ejpam-6598	61	13	section	section	NOUN
ejpam-6598	61	14	5	5	NUM
ejpam-6598	61	15	.	.	PUNCT
ejpam-6598	62	1	the	the	DET
ejpam-6598	62	2	validation	validation	NOUN
ejpam-6598	62	3	of	of	ADP
ejpam-6598	62	4	the	the	DET
ejpam-6598	62	5	present	present	ADJ
ejpam-6598	62	6	study	study	NOUN
ejpam-6598	62	7	is	be	AUX
ejpam-6598	62	8	provided	provide	VERB
ejpam-6598	62	9	in	in	ADP
ejpam-6598	62	10	section	section	NOUN
ejpam-6598	62	11	6	6	NUM
ejpam-6598	62	12	.	.	PUNCT
ejpam-6598	63	1	finally	finally	ADV
ejpam-6598	63	2	,	,	PUNCT
ejpam-6598	63	3	section	section	NOUN
ejpam-6598	63	4	7	7	NUM
ejpam-6598	63	5	summarises	summarise	NOUN
ejpam-6598	63	6	the	the	DET
ejpam-6598	63	7	findings	finding	NOUN
ejpam-6598	63	8	of	of	ADP
ejpam-6598	63	9	the	the	DET
ejpam-6598	63	10	study	study	NOUN
ejpam-6598	63	11	.	.	PUNCT
ejpam-6598	64	1	2	2	X
ejpam-6598	64	2	.	.	X
ejpam-6598	64	3	preliminaries	preliminary	NOUN
ejpam-6598	64	4	the	the	DET
ejpam-6598	64	5	basic	basic	ADJ
ejpam-6598	64	6	concepts	concept	NOUN
ejpam-6598	64	7	necessary	necessary	ADJ
ejpam-6598	64	8	for	for	ADP
ejpam-6598	64	9	understanding	understand	VERB
ejpam-6598	64	10	this	this	DET
ejpam-6598	64	11	study	study	NOUN
ejpam-6598	64	12	are	be	AUX
ejpam-6598	64	13	outlined	outline	VERB
ejpam-6598	64	14	in	in	ADP
ejpam-6598	64	15	this	this	DET
ejpam-6598	64	16	section	section	NOUN
ejpam-6598	64	17	.	.	PUNCT
ejpam-6598	65	1	table	table	NOUN
ejpam-6598	65	2	1	1	NUM
ejpam-6598	65	3	lists	list	VERB
ejpam-6598	65	4	the	the	DET
ejpam-6598	65	5	abbreviations	abbreviation	NOUN
ejpam-6598	65	6	used	use	VERB
ejpam-6598	65	7	throughout	throughout	ADP
ejpam-6598	65	8	the	the	DET
ejpam-6598	65	9	work	work	NOUN
ejpam-6598	65	10	.	.	PUNCT
ejpam-6598	66	1	table	table	NOUN
ejpam-6598	66	2	1	1	NUM
ejpam-6598	66	3	:	:	PUNCT
ejpam-6598	66	4	list	list	NOUN
ejpam-6598	66	5	of	of	ADP
ejpam-6598	66	6	abbreviations	abbreviation	NOUN
ejpam-6598	66	7	and	and	CCONJ
ejpam-6598	66	8	acronyms	acronym	NOUN
ejpam-6598	66	9	abbreviations	abbreviation	NOUN
ejpam-6598	66	10	acronyms	acronym	NOUN
ejpam-6598	66	11	interior	interior	ADJ
ejpam-6598	66	12	i	i	PRON
ejpam-6598	66	13	closure	closure	VERB
ejpam-6598	66	14	c	c	PROPN
ejpam-6598	66	15	door	door	NOUN
ejpam-6598	66	16	space	space	NOUN
ejpam-6598	66	17	ds	ds	ADJ
ejpam-6598	66	18	membership	membership	NOUN
ejpam-6598	66	19	function	function	VERB
ejpam-6598	66	20	ms	ms	PROPN
ejpam-6598	66	21	function	function	PROPN
ejpam-6598	66	22	non	non	ADJ
ejpam-6598	66	23	-	-	ADJ
ejpam-6598	66	24	membership	membership	ADJ
ejpam-6598	66	25	function	function	NOUN
ejpam-6598	66	26	nms	nms	NOUN
ejpam-6598	66	27	function	function	VERB
ejpam-6598	66	28	fuzzy	fuzzy	ADJ
ejpam-6598	66	29	topological	topological	ADJ
ejpam-6598	66	30	space	space	NOUN
ejpam-6598	66	31	fts	fts	PROPN
ejpam-6598	66	32	fuzzy	fuzzy	ADJ
ejpam-6598	66	33	nowhere	nowhere	ADV
ejpam-6598	66	34	dense	dense	ADJ
ejpam-6598	66	35	set	set	VERB
ejpam-6598	66	36	fnds	fnd	NOUN
ejpam-6598	66	37	intuitionistic	intuitionistic	ADJ
ejpam-6598	66	38	fuzzy	fuzzy	ADJ
ejpam-6598	66	39	b	b	NOUN
ejpam-6598	66	40	-	-	PUNCT
ejpam-6598	66	41	set	set	VERB
ejpam-6598	66	42	if	if	SCONJ
ejpam-6598	66	43	b	b	NOUN
ejpam-6598	66	44	-	-	PUNCT
ejpam-6598	66	45	set	set	ADJ
ejpam-6598	66	46	intuitionistic	intuitionistic	ADJ
ejpam-6598	66	47	fuzzy	fuzzy	ADJ
ejpam-6598	66	48	b	b	NOUN
ejpam-6598	66	49	-	-	PUNCT
ejpam-6598	66	50	open	open	ADJ
ejpam-6598	66	51	if	if	SCONJ
ejpam-6598	66	52	b−os	b−o	NOUN
ejpam-6598	66	53	intuitionistic	intuitionistic	ADJ
ejpam-6598	66	54	fuzzy	fuzzy	ADJ
ejpam-6598	66	55	b	b	NOUN
ejpam-6598	66	56	-	-	PUNCT
ejpam-6598	66	57	closed	closed	ADJ
ejpam-6598	66	58	if	if	SCONJ
ejpam-6598	66	59	b−	b−	PROPN
ejpam-6598	66	60	cs	cs	PROPN
ejpam-6598	66	61	intuitionistic	intuitionistic	ADJ
ejpam-6598	66	62	fuzzy	fuzzy	ADJ
ejpam-6598	66	63	b	b	NOUN
ejpam-6598	66	64	-	-	PUNCT
ejpam-6598	66	65	door	door	NOUN
ejpam-6598	66	66	space	space	NOUN
ejpam-6598	66	67	if	if	SCONJ
ejpam-6598	66	68	b−ds	b−d	VERB
ejpam-6598	66	69	pythagorean	pythagorean	PROPN
ejpam-6598	66	70	fuzzy	fuzzy	PROPN
ejpam-6598	66	71	set	set	VERB
ejpam-6598	66	72	pfs	pfs	PROPN
ejpam-6598	66	73	pythagorean	pythagorean	PROPN
ejpam-6598	66	74	fuzzy	fuzzy	ADJ
ejpam-6598	66	75	topology	topology	NOUN
ejpam-6598	66	76	pft	pft	PROPN
ejpam-6598	66	77	pythagorean	pythagorean	PROPN
ejpam-6598	66	78	fuzzy	fuzzy	ADJ
ejpam-6598	66	79	topological	topological	ADJ
ejpam-6598	66	80	space	space	NOUN
ejpam-6598	66	81	pfts	pft	NOUN
ejpam-6598	66	82	pythagorean	pythagorean	VERB
ejpam-6598	66	83	fuzzy	fuzzy	PROPN
ejpam-6598	66	84	weighted	weight	VERB
ejpam-6598	66	85	average	average	ADJ
ejpam-6598	66	86	pfwa	pfwa	NOUN
ejpam-6598	66	87	pythagorean	pythagorean	PROPN
ejpam-6598	66	88	fuzzy	fuzzy	PROPN
ejpam-6598	66	89	weighted	weight	VERB
ejpam-6598	66	90	geometric	geometric	ADJ
ejpam-6598	66	91	pfwg	pfwg	NOUN
ejpam-6598	66	92	pythagorean	pythagorean	PROPN
ejpam-6598	66	93	fuzzy	fuzzy	ADJ
ejpam-6598	66	94	digital	digital	ADJ
ejpam-6598	66	95	set	set	NOUN
ejpam-6598	66	96	(	(	PUNCT
ejpam-6598	66	97	ω∼	ω∼	NOUN
ejpam-6598	66	98	)	)	PUNCT
ejpam-6598	66	99	pfds(ω∼	pfds(ω∼	NOUN
ejpam-6598	66	100	)	)	PUNCT
ejpam-6598	66	101	pythagorean	pythagorean	PROPN
ejpam-6598	66	102	fuzzy	fuzzy	ADJ
ejpam-6598	66	103	digital	digital	PROPN
ejpam-6598	66	104	fine	fine	ADJ
ejpam-6598	66	105	pfdf	pfdf	NOUN
ejpam-6598	66	106	pythagorean	pythagorean	PROPN
ejpam-6598	66	107	fuzzy	fuzzy	PROPN
ejpam-6598	66	108	digital	digital	PROPN
ejpam-6598	66	109	fine	fine	ADJ
ejpam-6598	66	110	set	set	VERB
ejpam-6598	66	111	pfdfs	pfdfs	NOUN
ejpam-6598	66	112	pythagorean	pythagorean	PROPN
ejpam-6598	66	113	fuzzy	fuzzy	ADJ
ejpam-6598	66	114	digital	digital	ADJ
ejpam-6598	66	115	fine	fine	ADJ
ejpam-6598	66	116	point	point	NOUN
ejpam-6598	66	117	pfdfp	pfdfp	PROPN
ejpam-6598	66	118	pythagorean	pythagorean	PROPN
ejpam-6598	66	119	fuzzy	fuzzy	ADJ
ejpam-6598	66	120	digital	digital	ADJ
ejpam-6598	66	121	fine	fine	ADJ
ejpam-6598	66	122	number	number	NOUN
ejpam-6598	66	123	pfdfn	pfdfn	NOUN
ejpam-6598	66	124	pythagorean	pythagorean	VERB
ejpam-6598	66	125	fuzzy	fuzzy	ADJ
ejpam-6598	66	126	digital	digital	PROPN
ejpam-6598	66	127	fine	fine	ADJ
ejpam-6598	66	128	topology	topology	NOUN
ejpam-6598	66	129	pfdft	pfdft	PROPN
ejpam-6598	66	130	pythagorean	pythagorean	PROPN
ejpam-6598	66	131	fuzzy	fuzzy	PROPN
ejpam-6598	66	132	digital	digital	PROPN
ejpam-6598	66	133	fine	fine	ADJ
ejpam-6598	66	134	topological	topological	ADJ
ejpam-6598	66	135	space	space	NOUN
ejpam-6598	66	136	pfdfts	pfdft	NOUN
ejpam-6598	66	137	pythagorean	pythagorean	VERB
ejpam-6598	66	138	fuzzy	fuzzy	ADJ
ejpam-6598	66	139	digital	digital	ADJ
ejpam-6598	66	140	fine	fine	ADJ
ejpam-6598	66	141	b≈-topological	b≈-topological	ADJ
ejpam-6598	66	142	space	space	NOUN
ejpam-6598	66	143	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	66	144	−ds	−ds	NOUN
ejpam-6598	66	145	pythagorean	pythagorean	PROPN
ejpam-6598	66	146	fuzzy	fuzzy	ADJ
ejpam-6598	66	147	digital	digital	ADJ
ejpam-6598	66	148	fine	fine	ADJ
ejpam-6598	66	149	b≈	b≈	NOUN
ejpam-6598	66	150	open	open	ADJ
ejpam-6598	66	151	set	set	VERB
ejpam-6598	67	1	pfdb≈f	pfdb≈f	PRON
ejpam-6598	67	2	−os	−os	NOUN
ejpam-6598	67	3	pythagorean	pythagorean	VERB
ejpam-6598	67	4	fuzzy	fuzzy	ADJ
ejpam-6598	67	5	digital	digital	ADJ
ejpam-6598	67	6	fine	fine	ADJ
ejpam-6598	67	7	b≈	b≈	NOUN
ejpam-6598	67	8	closed	close	VERB
ejpam-6598	67	9	set	set	VERB
ejpam-6598	67	10	pfdb≈f	pfdb≈f	PRON
ejpam-6598	67	11	−	−	NOUN
ejpam-6598	67	12	cs	cs	PROPN
ejpam-6598	67	13	pythagorean	pythagorean	PROPN
ejpam-6598	67	14	fuzzy	fuzzy	ADJ
ejpam-6598	67	15	digital	digital	ADJ
ejpam-6598	67	16	fine	fine	ADJ
ejpam-6598	67	17	b≈	b≈	NOUN
ejpam-6598	67	18	closure	closure	NOUN
ejpam-6598	67	19	pfdb≈f	pfdb≈f	NUM
ejpam-6598	67	20	−c	−c	NOUN
ejpam-6598	67	21	pythagorean	pythagorean	PROPN
ejpam-6598	67	22	fuzzy	fuzzy	ADJ
ejpam-6598	67	23	digital	digital	PROPN
ejpam-6598	67	24	fine	fine	ADJ
ejpam-6598	67	25	b≈−	b≈−	NOUN
ejpam-6598	67	26	interior	interior	ADJ
ejpam-6598	67	27	pfdb≈f	pfdb≈f	NUM
ejpam-6598	67	28	−i	−i	PROPN
ejpam-6598	67	29	n.	n.	PROPN
ejpam-6598	67	30	preethi	preethi	ADV
ejpam-6598	67	31	,	,	PUNCT
ejpam-6598	67	32	g.	g.	PROPN
ejpam-6598	67	33	k.	k.	PROPN
ejpam-6598	67	34	revathi	revathi	PROPN
ejpam-6598	67	35	/	/	SYM
ejpam-6598	67	36	eur	eur	PROPN
ejpam-6598	67	37	.	.	PUNCT
ejpam-6598	68	1	j.	j.	PROPN
ejpam-6598	68	2	pure	pure	PROPN
ejpam-6598	68	3	appl	appl	PROPN
ejpam-6598	68	4	.	.	PROPN
ejpam-6598	68	5	math	math	PROPN
ejpam-6598	68	6	,	,	PUNCT
ejpam-6598	68	7	18	18	NUM
ejpam-6598	68	8	(	(	PUNCT
ejpam-6598	68	9	3	3	NUM
ejpam-6598	68	10	)	)	PUNCT
ejpam-6598	68	11	(	(	PUNCT
ejpam-6598	68	12	2025	2025	NUM
ejpam-6598	68	13	)	)	PUNCT
ejpam-6598	68	14	,	,	PUNCT
ejpam-6598	68	15	6598	6598	NUM
ejpam-6598	68	16	5	5	NUM
ejpam-6598	68	17	of	of	ADP
ejpam-6598	68	18	17	17	NUM
ejpam-6598	68	19	definition	definition	NOUN
ejpam-6598	68	20	1	1	NUM
ejpam-6598	68	21	.	.	PUNCT
ejpam-6598	69	1	[	[	X
ejpam-6598	69	2	7	7	X
ejpam-6598	69	3	]	]	PUNCT
ejpam-6598	69	4	let	let	VERB
ejpam-6598	69	5	ξ	ξ	X
ejpam-6598	69	6	be	be	AUX
ejpam-6598	69	7	an	an	DET
ejpam-6598	69	8	universal	universal	ADJ
ejpam-6598	69	9	set	set	NOUN
ejpam-6598	69	10	.	.	PUNCT
ejpam-6598	70	1	then	then	ADV
ejpam-6598	70	2	a	a	DET
ejpam-6598	70	3	pfs	pfs	PROPN
ejpam-6598	70	4	ω	ω	NUM
ejpam-6598	70	5	which	which	PRON
ejpam-6598	70	6	is	be	AUX
ejpam-6598	70	7	a	a	DET
ejpam-6598	70	8	set	set	NOUN
ejpam-6598	70	9	of	of	ADP
ejpam-6598	70	10	ordered	order	VERB
ejpam-6598	70	11	pair	pair	NOUN
ejpam-6598	70	12	over	over	ADP
ejpam-6598	70	13	ξ	ξ	PROPN
ejpam-6598	70	14	is	be	AUX
ejpam-6598	70	15	defined	define	VERB
ejpam-6598	70	16	by	by	ADP
ejpam-6598	70	17	ω	ω	PROPN
ejpam-6598	70	18	=	=	SYM
ejpam-6598	70	19	{	{	PUNCT
ejpam-6598	70	20	<	<	X
ejpam-6598	70	21	x	x	X
ejpam-6598	70	22	,	,	PUNCT
ejpam-6598	70	23	µω(x	µω(x	NUM
ejpam-6598	70	24	)	)	PUNCT
ejpam-6598	70	25	,	,	PUNCT
ejpam-6598	70	26	νω(x	νω(x	NUM
ejpam-6598	70	27	)	)	PUNCT
ejpam-6598	70	28	>	>	X
ejpam-6598	70	29	/x	/x	PUNCT
ejpam-6598	71	1	∈	∈	X
ejpam-6598	71	2	ξ	ξ	PROPN
ejpam-6598	71	3	}	}	PUNCT
ejpam-6598	71	4	where	where	SCONJ
ejpam-6598	71	5	µω(x	µω(x	NUM
ejpam-6598	71	6	)	)	PUNCT
ejpam-6598	71	7	:	:	PUNCT
ejpam-6598	72	1	ξ	ξ	X
ejpam-6598	72	2	→	→	SYM
ejpam-6598	72	3	[	[	X
ejpam-6598	72	4	0	0	NUM
ejpam-6598	72	5	,	,	PUNCT
ejpam-6598	72	6	1	1	NUM
ejpam-6598	72	7	]	]	PUNCT
ejpam-6598	72	8	and	and	CCONJ
ejpam-6598	72	9	νω(x	νω(x	NOUN
ejpam-6598	72	10	)	)	PUNCT
ejpam-6598	72	11	:	:	PUNCT
ejpam-6598	73	1	ξ	ξ	X
ejpam-6598	73	2	→	→	SYM
ejpam-6598	73	3	[	[	X
ejpam-6598	73	4	0	0	NUM
ejpam-6598	73	5	,	,	PUNCT
ejpam-6598	73	6	1	1	NUM
ejpam-6598	73	7	]	]	PUNCT
ejpam-6598	73	8	define	define	VERB
ejpam-6598	73	9	the	the	DET
ejpam-6598	73	10	degree	degree	NOUN
ejpam-6598	73	11	of	of	ADP
ejpam-6598	73	12	ms	ms	NOUN
ejpam-6598	73	13	and	and	CCONJ
ejpam-6598	73	14	the	the	DET
ejpam-6598	73	15	degree	degree	NOUN
ejpam-6598	73	16	of	of	ADP
ejpam-6598	73	17	nms	nms	NOUN
ejpam-6598	73	18	respectively	respectively	ADV
ejpam-6598	73	19	such	such	ADJ
ejpam-6598	73	20	that	that	SCONJ
ejpam-6598	73	21	0	0	NUM
ejpam-6598	73	22	≤	≤	NUM
ejpam-6598	73	23	µ2ω(x	µ2ω(x	PROPN
ejpam-6598	73	24	)	)	PUNCT
ejpam-6598	74	1	+	+	CCONJ
ejpam-6598	74	2	νω2(x	νω2(x	PROPN
ejpam-6598	74	3	)	)	PUNCT
ejpam-6598	74	4	≤	≤	NOUN
ejpam-6598	74	5	1	1	NUM
ejpam-6598	74	6	.	.	PUNCT
ejpam-6598	75	1	definition	definition	NOUN
ejpam-6598	75	2	2	2	NUM
ejpam-6598	75	3	.	.	PUNCT
ejpam-6598	76	1	[	[	X
ejpam-6598	76	2	7	7	X
ejpam-6598	76	3	]	]	PUNCT
ejpam-6598	76	4	suppose	suppose	VERB
ejpam-6598	76	5	that	that	SCONJ
ejpam-6598	76	6	ω	ω	PROPN
ejpam-6598	76	7	=	=	SYM
ejpam-6598	76	8	(	(	PUNCT
ejpam-6598	76	9	µω	µω	PROPN
ejpam-6598	76	10	,	,	PUNCT
ejpam-6598	76	11	vω	vω	ADJ
ejpam-6598	76	12	)	)	PUNCT
ejpam-6598	76	13	and	and	CCONJ
ejpam-6598	76	14	ς	ς	PROPN
ejpam-6598	76	15	=	=	PUNCT
ejpam-6598	76	16	(	(	PUNCT
ejpam-6598	76	17	µς	µς	X
ejpam-6598	76	18	,	,	PUNCT
ejpam-6598	76	19	vς	vς	PROPN
ejpam-6598	76	20	)	)	PUNCT
ejpam-6598	76	21	can	can	AUX
ejpam-6598	76	22	be	be	AUX
ejpam-6598	76	23	any	any	DET
ejpam-6598	76	24	two	two	NUM
ejpam-6598	76	25	pfs	pf	NOUN
ejpam-6598	76	26	of	of	ADP
ejpam-6598	76	27	ξ	ξ	PROPN
ejpam-6598	76	28	.	.	PUNCT
ejpam-6598	77	1	then	then	ADV
ejpam-6598	77	2	•	•	INTJ
ejpam-6598	77	3	ωc	ωc	INTJ
ejpam-6598	77	4	=	=	SYM
ejpam-6598	77	5	(	(	PUNCT
ejpam-6598	77	6	vω	vω	INTJ
ejpam-6598	77	7	,	,	PUNCT
ejpam-6598	77	8	µω	µω	ADJ
ejpam-6598	77	9	)	)	PUNCT
ejpam-6598	77	10	yields	yield	VERB
ejpam-6598	77	11	the	the	DET
ejpam-6598	77	12	complement	complement	NOUN
ejpam-6598	77	13	of	of	ADP
ejpam-6598	77	14	ω	ω	PROPN
ejpam-6598	77	15	.	.	PROPN
ejpam-6598	77	16	•	•	NUM
ejpam-6598	77	17	ω	ω	PROPN
ejpam-6598	77	18	∩	∩	PROPN
ejpam-6598	77	19	ς	ς	PROPN
ejpam-6598	77	20	=	=	PUNCT
ejpam-6598	77	21	{	{	PUNCT
ejpam-6598	77	22	min	min	NOUN
ejpam-6598	77	23	(	(	PUNCT
ejpam-6598	77	24	µω	µω	PROPN
ejpam-6598	77	25	,	,	PUNCT
ejpam-6598	77	26	µς	µς	NOUN
ejpam-6598	77	27	)	)	PUNCT
ejpam-6598	77	28	,	,	PUNCT
ejpam-6598	77	29	max	max	PROPN
ejpam-6598	77	30	(	(	PUNCT
ejpam-6598	77	31	(	(	PUNCT
ejpam-6598	77	32	vω	vω	INTJ
ejpam-6598	77	33	,	,	PUNCT
ejpam-6598	77	34	vς	vς	NOUN
ejpam-6598	77	35	)	)	PUNCT
ejpam-6598	77	36	}	}	PUNCT
ejpam-6598	77	37	yields	yield	VERB
ejpam-6598	77	38	the	the	DET
ejpam-6598	77	39	intersection	intersection	NOUN
ejpam-6598	77	40	of	of	ADP
ejpam-6598	77	41	ω	ω	PROPN
ejpam-6598	77	42	and	and	CCONJ
ejpam-6598	77	43	ς	ς	PROPN
ejpam-6598	77	44	.	.	PROPN
ejpam-6598	77	45	•	•	NUM
ejpam-6598	77	46	ω	ω	NOUN
ejpam-6598	77	47	∪	∪	ADP
ejpam-6598	77	48	ς	ς	PROPN
ejpam-6598	77	49	=	=	PUNCT
ejpam-6598	77	50	{	{	PUNCT
ejpam-6598	77	51	max	max	PROPN
ejpam-6598	77	52	(	(	PUNCT
ejpam-6598	77	53	µω	µω	PROPN
ejpam-6598	77	54	,	,	PUNCT
ejpam-6598	77	55	µς	µς	NOUN
ejpam-6598	77	56	)	)	PUNCT
ejpam-6598	77	57	,	,	PUNCT
ejpam-6598	77	58	min(vω	min(vω	NOUN
ejpam-6598	77	59	,	,	PUNCT
ejpam-6598	77	60	vς	vς	PROPN
ejpam-6598	77	61	)	)	PUNCT
ejpam-6598	77	62	}	}	PUNCT
ejpam-6598	77	63	yields	yield	VERB
ejpam-6598	77	64	the	the	DET
ejpam-6598	77	65	union	union	NOUN
ejpam-6598	77	66	of	of	ADP
ejpam-6598	77	67	ω	ω	PROPN
ejpam-6598	77	68	and	and	CCONJ
ejpam-6598	77	69	ς	ς	PROPN
ejpam-6598	77	70	.	.	PROPN
ejpam-6598	77	71	•	•	NOUN
ejpam-6598	77	72	if	if	SCONJ
ejpam-6598	77	73	µω	µω	PROPN
ejpam-6598	77	74	≤	≤	X
ejpam-6598	77	75	µς	µς	X
ejpam-6598	77	76	and	and	CCONJ
ejpam-6598	77	77	vω	vω	INTJ
ejpam-6598	77	78	≥	≥	NOUN
ejpam-6598	77	79	vς	vς	ADP
ejpam-6598	77	80	then	then	ADV
ejpam-6598	77	81	ω	ω	PROPN
ejpam-6598	77	82	is	be	AUX
ejpam-6598	77	83	a	a	DET
ejpam-6598	77	84	subset	subset	NOUN
ejpam-6598	77	85	of	of	ADP
ejpam-6598	77	86	ς(ω	ς(ω	PROPN
ejpam-6598	77	87	⊆	⊆	NUM
ejpam-6598	77	88	ς	ς	NOUN
ejpam-6598	77	89	)	)	PUNCT
ejpam-6598	77	90	or	or	CCONJ
ejpam-6598	77	91	ς	ς	PROPN
ejpam-6598	77	92	contains	contain	VERB
ejpam-6598	77	93	ω(ς	ω(ς	PROPN
ejpam-6598	77	94	⊇	⊇	PROPN
ejpam-6598	77	95	ω	ω	NUM
ejpam-6598	77	96	)	)	PUNCT
ejpam-6598	77	97	.	.	PUNCT
ejpam-6598	78	1	definition	definition	NOUN
ejpam-6598	78	2	3	3	NUM
ejpam-6598	78	3	.	.	PUNCT
ejpam-6598	79	1	[	[	X
ejpam-6598	79	2	7	7	X
ejpam-6598	79	3	]	]	PUNCT
ejpam-6598	79	4	consider	consider	VERB
ejpam-6598	79	5	ξ	ξ	PROPN
ejpam-6598	79	6	is	be	AUX
ejpam-6598	79	7	a	a	DET
ejpam-6598	79	8	set	set	NOUN
ejpam-6598	79	9	and	and	CCONJ
ejpam-6598	79	10	τ	τ	PROPN
ejpam-6598	79	11	is	be	AUX
ejpam-6598	79	12	a	a	DET
ejpam-6598	79	13	family	family	NOUN
ejpam-6598	79	14	of	of	ADP
ejpam-6598	79	15	pfs	pfs	PROPN
ejpam-6598	79	16	of	of	ADP
ejpam-6598	79	17	ξ	ξ	PROPN
ejpam-6598	79	18	.	.	PROPN
ejpam-6598	79	19	•	•	NUM
ejpam-6598	79	20	0∼	0∼	NUM
ejpam-6598	79	21	,	,	PUNCT
ejpam-6598	79	22	1∼	1∼	NUM
ejpam-6598	79	23	∈	∈	NOUN
ejpam-6598	79	24	τ	τ	X
ejpam-6598	79	25	•	•	NUM
ejpam-6598	79	26	for	for	ADP
ejpam-6598	79	27	any	any	DET
ejpam-6598	79	28	{	{	PUNCT
ejpam-6598	79	29	ωj	ωj	NOUN
ejpam-6598	79	30	/	/	SYM
ejpam-6598	79	31	j	j	NOUN
ejpam-6598	79	32	∈	∈	PROPN
ejpam-6598	80	1	i	i	PRON
ejpam-6598	80	2	,	,	PUNCT
ejpam-6598	80	3	ωj	ωj	ADP
ejpam-6598	80	4	∈	∈	PROPN
ejpam-6598	80	5	τ	τ	PROPN
ejpam-6598	80	6	}	}	PUNCT
ejpam-6598	80	7	,	,	PUNCT
ejpam-6598	80	8	⋂n	⋂n	PROPN
ejpam-6598	80	9	j=1	j=1	PROPN
ejpam-6598	80	10	ωj	ωj	ADP
ejpam-6598	80	11	∈	∈	PROPN
ejpam-6598	80	12	τ	τ	X
ejpam-6598	80	13	•	•	NOUN
ejpam-6598	80	14	∪j=1ωj	∪j=1ωj	PROPN
ejpam-6598	80	15	∈	∈	PROPN
ejpam-6598	80	16	τ	τ	PROPN
ejpam-6598	80	17	for	for	ADP
ejpam-6598	80	18	any	any	DET
ejpam-6598	80	19	{	{	PUNCT
ejpam-6598	80	20	ωj	ωj	NOUN
ejpam-6598	80	21	/	/	SYM
ejpam-6598	80	22	j	j	NOUN
ejpam-6598	80	23	∈	∈	PROPN
ejpam-6598	81	1	i	i	PRON
ejpam-6598	81	2	,	,	PUNCT
ejpam-6598	81	3	ωj	ωj	ADP
ejpam-6598	81	4	∈	∈	PROPN
ejpam-6598	81	5	τ	τ	PROPN
ejpam-6598	81	6	}	}	PUNCT
ejpam-6598	81	7	,	,	PUNCT
ejpam-6598	81	8	the	the	DET
ejpam-6598	81	9	notation	notation	NOUN
ejpam-6598	81	10	τ	τ	PROPN
ejpam-6598	81	11	is	be	AUX
ejpam-6598	81	12	a	a	DET
ejpam-6598	81	13	pft	pft	PROPN
ejpam-6598	81	14	on	on	ADP
ejpam-6598	81	15	ξ	ξ	PROPN
ejpam-6598	81	16	when	when	SCONJ
ejpam-6598	81	17	i	i	PRON
ejpam-6598	81	18	is	be	AUX
ejpam-6598	81	19	any	any	DET
ejpam-6598	81	20	arbitrary	arbitrary	ADJ
ejpam-6598	81	21	index	index	NOUN
ejpam-6598	81	22	set	set	NOUN
ejpam-6598	81	23	.	.	PUNCT
ejpam-6598	82	1	this	this	DET
ejpam-6598	82	2	pair	pair	NOUN
ejpam-6598	82	3	(	(	PUNCT
ejpam-6598	82	4	ξ	ξ	PROPN
ejpam-6598	82	5	,	,	PUNCT
ejpam-6598	82	6	τ	τ	X
ejpam-6598	82	7	)	)	PUNCT
ejpam-6598	82	8	is	be	AUX
ejpam-6598	82	9	referred	refer	VERB
ejpam-6598	82	10	to	to	ADP
ejpam-6598	82	11	in	in	ADP
ejpam-6598	82	12	this	this	DET
ejpam-6598	82	13	context	context	NOUN
ejpam-6598	82	14	as	as	ADP
ejpam-6598	82	15	a	a	DET
ejpam-6598	82	16	pfts	pft	NOUN
ejpam-6598	82	17	.	.	PUNCT
ejpam-6598	83	1	an	an	DET
ejpam-6598	83	2	open	open	ADJ
ejpam-6598	83	3	pfs	pfs	NOUN
ejpam-6598	83	4	is	be	AUX
ejpam-6598	83	5	any	any	DET
ejpam-6598	83	6	member	member	NOUN
ejpam-6598	83	7	of	of	ADP
ejpam-6598	83	8	τ	τ	PROPN
ejpam-6598	83	9	,	,	PUNCT
ejpam-6598	83	10	and	and	CCONJ
ejpam-6598	83	11	the	the	DET
ejpam-6598	83	12	complement	complement	NOUN
ejpam-6598	83	13	of	of	ADP
ejpam-6598	83	14	an	an	DET
ejpam-6598	83	15	open	open	ADJ
ejpam-6598	83	16	pfs	pfs	NOUN
ejpam-6598	83	17	is	be	AUX
ejpam-6598	83	18	a	a	DET
ejpam-6598	83	19	closed	close	VERB
ejpam-6598	83	20	pfs	pf	NOUN
ejpam-6598	83	21	.	.	PUNCT
ejpam-6598	84	1	the	the	DET
ejpam-6598	84	2	topology	topology	NOUN
ejpam-6598	84	3	containing	contain	VERB
ejpam-6598	84	4	all	all	DET
ejpam-6598	84	5	pfs	pfs	PROPN
ejpam-6598	84	6	is	be	AUX
ejpam-6598	84	7	called	call	VERB
ejpam-6598	84	8	a	a	DET
ejpam-6598	84	9	discrete	discrete	ADJ
ejpam-6598	84	10	pfts	pft	NOUN
ejpam-6598	84	11	.	.	PUNCT
ejpam-6598	85	1	definition	definition	NOUN
ejpam-6598	85	2	4	4	NUM
ejpam-6598	85	3	.	.	PUNCT
ejpam-6598	86	1	[	[	X
ejpam-6598	86	2	7	7	X
ejpam-6598	86	3	]	]	PUNCT
ejpam-6598	86	4	in	in	ADP
ejpam-6598	86	5	a	a	DET
ejpam-6598	86	6	pfts	pft	NOUN
ejpam-6598	86	7	(	(	PUNCT
ejpam-6598	86	8	ξ	ξ	X
ejpam-6598	86	9	,	,	PUNCT
ejpam-6598	86	10	τ	τ	PROPN
ejpam-6598	86	11	)	)	PUNCT
ejpam-6598	86	12	,	,	PUNCT
ejpam-6598	86	13	let	let	VERB
ejpam-6598	86	14	ω	ω	NOUN
ejpam-6598	86	15	and	and	CCONJ
ejpam-6598	86	16	ς	ς	PROPN
ejpam-6598	86	17	be	be	AUX
ejpam-6598	86	18	any	any	DET
ejpam-6598	86	19	two	two	NUM
ejpam-6598	86	20	pfs	pf	NOUN
ejpam-6598	86	21	.	.	PUNCT
ejpam-6598	87	1	if	if	SCONJ
ejpam-6598	87	2	there	there	PRON
ejpam-6598	87	3	is	be	VERB
ejpam-6598	87	4	an	an	DET
ejpam-6598	87	5	open	open	ADJ
ejpam-6598	87	6	pfs	pfs	PROPN
ejpam-6598	87	7	η	η	PROPN
ejpam-6598	87	8	in	in	ADP
ejpam-6598	87	9	which	which	PRON
ejpam-6598	87	10	ω	ω	PROPN
ejpam-6598	87	11	⊆	⊆	NUM
ejpam-6598	87	12	η	η	X
ejpam-6598	87	13	⊆	⊆	NUM
ejpam-6598	87	14	ς	ς	PROPN
ejpam-6598	87	15	,	,	PUNCT
ejpam-6598	87	16	then	then	ADV
ejpam-6598	87	17	ς	ς	PROPN
ejpam-6598	87	18	is	be	AUX
ejpam-6598	87	19	regarded	regard	VERB
ejpam-6598	87	20	as	as	ADP
ejpam-6598	87	21	a	a	DET
ejpam-6598	87	22	neighborhood	neighborhood	NOUN
ejpam-6598	87	23	of	of	ADP
ejpam-6598	87	24	ω	ω	PROPN
ejpam-6598	87	25	.	.	PUNCT
ejpam-6598	88	1	definition	definition	NOUN
ejpam-6598	88	2	5	5	NUM
ejpam-6598	88	3	.	.	PUNCT
ejpam-6598	89	1	[	[	X
ejpam-6598	89	2	6	6	NUM
ejpam-6598	89	3	,	,	PUNCT
ejpam-6598	89	4	13	13	NUM
ejpam-6598	89	5	]	]	PUNCT
ejpam-6598	89	6	let	let	VERB
ejpam-6598	89	7	x	x	PRON
ejpam-6598	89	8	and	and	CCONJ
ejpam-6598	89	9	y	y	PROPN
ejpam-6598	89	10	be	be	AUX
ejpam-6598	89	11	points	point	NOUN
ejpam-6598	89	12	in	in	ADP
ejpam-6598	89	13	ξ	ξ	PROPN
ejpam-6598	89	14	,	,	PUNCT
ejpam-6598	89	15	the	the	DET
ejpam-6598	89	16	set	set	NOUN
ejpam-6598	89	17	of	of	ADP
ejpam-6598	89	18	integer	integer	NOUN
ejpam-6598	89	19	-	-	PUNCT
ejpam-6598	89	20	coordinate	coordinate	NOUN
ejpam-6598	89	21	points	point	NOUN
ejpam-6598	89	22	arranged	arrange	VERB
ejpam-6598	89	23	in	in	ADP
ejpam-6598	89	24	a	a	DET
ejpam-6598	89	25	rectangular	rectangular	ADJ
ejpam-6598	89	26	grid	grid	NOUN
ejpam-6598	89	27	.	.	PUNCT
ejpam-6598	90	1	a	a	DET
ejpam-6598	90	2	path	path	NOUN
ejpam-6598	90	3	γ	γ	X
ejpam-6598	90	4	from	from	ADP
ejpam-6598	90	5	x	x	PUNCT
ejpam-6598	90	6	to	to	ADP
ejpam-6598	90	7	y	y	PROPN
ejpam-6598	90	8	is	be	AUX
ejpam-6598	90	9	defined	define	VERB
ejpam-6598	90	10	as	as	ADP
ejpam-6598	90	11	a	a	DET
ejpam-6598	90	12	sequence	sequence	NOUN
ejpam-6598	90	13	x	x	NOUN
ejpam-6598	90	14	=	=	SYM
ejpam-6598	90	15	x0	x0	PROPN
ejpam-6598	90	16	,	,	PUNCT
ejpam-6598	90	17	x1	x1	PROPN
ejpam-6598	90	18	,	,	PUNCT
ejpam-6598	90	19	x2	x2	PROPN
ejpam-6598	90	20	,	,	PUNCT
ejpam-6598	90	21	.	.	PUNCT
ejpam-6598	90	22	.	.	PUNCT
ejpam-6598	91	1	.	.	PUNCT
ejpam-6598	92	1	,	,	PUNCT
ejpam-6598	92	2	xn	xn	PUNCT
ejpam-6598	92	3	=	=	SYM
ejpam-6598	92	4	y	y	PROPN
ejpam-6598	92	5	,	,	PUNCT
ejpam-6598	92	6	such	such	ADJ
ejpam-6598	92	7	that	that	PRON
ejpam-6598	92	8	for	for	ADP
ejpam-6598	92	9	each	each	DET
ejpam-6598	92	10	i	i	PRON
ejpam-6598	92	11	from	from	ADP
ejpam-6598	92	12	1	1	NUM
ejpam-6598	92	13	to	to	ADP
ejpam-6598	92	14	n	n	CCONJ
ejpam-6598	92	15	,	,	PUNCT
ejpam-6598	92	16	the	the	DET
ejpam-6598	92	17	point	point	NOUN
ejpam-6598	92	18	xi	xi	INTJ
ejpam-6598	92	19	is	be	AUX
ejpam-6598	92	20	adjacent	adjacent	ADJ
ejpam-6598	92	21	to	to	ADP
ejpam-6598	92	22	xi−1	xi−1	PROPN
ejpam-6598	92	23	,	,	PUNCT
ejpam-6598	92	24	with	with	ADP
ejpam-6598	92	25	adjacency	adjacency	NOUN
ejpam-6598	92	26	being	be	AUX
ejpam-6598	92	27	either	either	CCONJ
ejpam-6598	92	28	4	4	NUM
ejpam-6598	92	29	-adjacent	-adjacent	ADJ
ejpam-6598	92	30	or	or	CCONJ
ejpam-6598	92	31	8	8	NUM
ejpam-6598	92	32	-adjacent	-adjacent	NOUN
ejpam-6598	92	33	.	.	PUNCT
ejpam-6598	93	1	definition	definition	NOUN
ejpam-6598	93	2	6	6	NUM
ejpam-6598	93	3	.	.	PUNCT
ejpam-6598	94	1	[	[	X
ejpam-6598	94	2	6	6	NUM
ejpam-6598	94	3	,	,	PUNCT
ejpam-6598	94	4	13	13	NUM
ejpam-6598	94	5	]	]	PUNCT
ejpam-6598	94	6	in	in	ADP
ejpam-6598	94	7	the	the	DET
ejpam-6598	94	8	set	set	PROPN
ejpam-6598	94	9	ξ	ξ	PROPN
ejpam-6598	94	10	,	,	PUNCT
ejpam-6598	94	11	points	point	NOUN
ejpam-6598	94	12	x	x	PUNCT
ejpam-6598	94	13	and	and	CCONJ
ejpam-6598	94	14	y	y	PROPN
ejpam-6598	94	15	are	be	AUX
ejpam-6598	94	16	said	say	VERB
ejpam-6598	94	17	to	to	PART
ejpam-6598	94	18	be	be	AUX
ejpam-6598	94	19	connected	connect	VERB
ejpam-6598	94	20	when	when	SCONJ
ejpam-6598	94	21	a	a	DET
ejpam-6598	94	22	path	path	NOUN
ejpam-6598	94	23	from	from	ADP
ejpam-6598	94	24	x	x	PUNCT
ejpam-6598	94	25	to	to	ADP
ejpam-6598	94	26	y	y	PROPN
ejpam-6598	94	27	includes	include	VERB
ejpam-6598	94	28	all	all	DET
ejpam-6598	94	29	points	point	NOUN
ejpam-6598	94	30	of	of	ADP
ejpam-6598	94	31	a	a	DET
ejpam-6598	94	32	subset	subset	ADJ
ejpam-6598	94	33	p∗	p∗	NOUN
ejpam-6598	94	34	of	of	ADP
ejpam-6598	94	35	ξ	ξ	PROPN
ejpam-6598	94	36	.	.	PUNCT
ejpam-6598	95	1	definition	definition	NOUN
ejpam-6598	95	2	7	7	NUM
ejpam-6598	95	3	.	.	PUNCT
ejpam-6598	96	1	[	[	X
ejpam-6598	96	2	14	14	NUM
ejpam-6598	96	3	]	]	PUNCT
ejpam-6598	96	4	consider	consider	VERB
ejpam-6598	96	5	ξ	ξ	PROPN
ejpam-6598	96	6	as	as	ADP
ejpam-6598	96	7	a	a	DET
ejpam-6598	96	8	rectangular	rectangular	ADJ
ejpam-6598	96	9	grid	grid	NOUN
ejpam-6598	96	10	of	of	ADP
ejpam-6598	96	11	points	point	NOUN
ejpam-6598	96	12	with	with	ADP
ejpam-6598	96	13	integer	integer	NOUN
ejpam-6598	96	14	coordinates	coordinate	NOUN
ejpam-6598	96	15	in	in	ADP
ejpam-6598	96	16	the	the	DET
ejpam-6598	96	17	euclidean	euclidean	ADJ
ejpam-6598	96	18	plane	plane	NOUN
ejpam-6598	96	19	σ	σ	PROPN
ejpam-6598	96	20	,	,	PUNCT
ejpam-6598	96	21	and	and	CCONJ
ejpam-6598	96	22	let	let	VERB
ejpam-6598	96	23	ω	ω	NOUN
ejpam-6598	96	24	=	=	SYM
ejpam-6598	96	25	(	(	PUNCT
ejpam-6598	96	26	µω	µω	PROPN
ejpam-6598	96	27	,	,	PUNCT
ejpam-6598	96	28	vω	vω	AUX
ejpam-6598	96	29	)	)	PUNCT
ejpam-6598	96	30	be	be	AUX
ejpam-6598	96	31	a	a	DET
ejpam-6598	96	32	pfs	pfs	NOUN
ejpam-6598	96	33	of	of	ADP
ejpam-6598	96	34	σ	σ	PROPN
ejpam-6598	96	35	.	.	PUNCT
ejpam-6598	97	1	the	the	DET
ejpam-6598	97	2	pfds	pfds	NOUN
ejpam-6598	97	3	of	of	ADP
ejpam-6598	97	4	ξ	ξ	PROPN
ejpam-6598	97	5	,	,	PUNCT
ejpam-6598	97	6	denoted	denote	VERB
ejpam-6598	97	7	by	by	ADP
ejpam-6598	97	8	ω	ω	NUM
ejpam-6598	97	9	∼	∼	NOUN
ejpam-6598	97	10	,	,	PUNCT
ejpam-6598	97	11	assigns	assign	NOUN
ejpam-6598	97	12	to	to	ADP
ejpam-6598	97	13	each	each	DET
ejpam-6598	97	14	point	point	NOUN
ejpam-6598	97	15	x	x	X
ejpam-6598	97	16	∈	∈	ADP
ejpam-6598	97	17	ξ	ξ	X
ejpam-6598	97	18	a	a	DET
ejpam-6598	97	19	ms	ms	NOUN
ejpam-6598	97	20	degree	degree	NOUN
ejpam-6598	97	21	µω∼(x	µω∼(x	NOUN
ejpam-6598	97	22	)	)	PUNCT
ejpam-6598	97	23	and	and	CCONJ
ejpam-6598	97	24	a	a	DET
ejpam-6598	97	25	nms	nms	NOUN
ejpam-6598	97	26	degree	degree	NOUN
ejpam-6598	97	27	vω∼(x	vω∼(x	PROPN
ejpam-6598	97	28	)	)	PUNCT
ejpam-6598	97	29	defined	define	VERB
ejpam-6598	97	30	as	as	ADP
ejpam-6598	97	31	follows	follow	VERB
ejpam-6598	97	32	:	:	PUNCT
ejpam-6598	97	33	µω∼(x	µω∼(x	NUM
ejpam-6598	97	34	)	)	PUNCT
ejpam-6598	97	35	=	=	SYM
ejpam-6598	97	36	max	max	PROPN
ejpam-6598	97	37	{	{	PUNCT
ejpam-6598	97	38	µω(s	µω(s	NOUN
ejpam-6598	97	39	)	)	PUNCT
ejpam-6598	98	1	|	|	ADV
ejpam-6598	98	2	s	s	VERB
ejpam-6598	98	3	∈	∈	PROPN
ejpam-6598	98	4	p	p	NOUN
ejpam-6598	98	5	∗	∗	NOUN
ejpam-6598	98	6	}	}	PUNCT
ejpam-6598	98	7	and	and	CCONJ
ejpam-6598	98	8	vω∼(x	vω∼(x	PROPN
ejpam-6598	98	9	)	)	PUNCT
ejpam-6598	98	10	=	=	SYM
ejpam-6598	98	11	max	max	PROPN
ejpam-6598	98	12	{	{	PUNCT
ejpam-6598	98	13	vω(s	vω(s	NOUN
ejpam-6598	98	14	)	)	PUNCT
ejpam-6598	98	15	|	|	ADV
ejpam-6598	98	16	s	s	AUX
ejpam-6598	98	17	∈	∈	PROPN
ejpam-6598	98	18	p	p	NOUN
ejpam-6598	98	19	∗	∗	NOUN
ejpam-6598	98	20	}	}	PUNCT
ejpam-6598	98	21	.	.	PUNCT
ejpam-6598	99	1	here	here	ADV
ejpam-6598	99	2	s	s	VERB
ejpam-6598	99	3	is	be	AUX
ejpam-6598	99	4	the	the	DET
ejpam-6598	99	5	subset	subset	NOUN
ejpam-6598	99	6	of	of	ADP
ejpam-6598	99	7	the	the	DET
ejpam-6598	99	8	plane	plane	NOUN
ejpam-6598	99	9	and	and	CCONJ
ejpam-6598	99	10	p∗	p∗	NOUN
ejpam-6598	99	11	is	be	AUX
ejpam-6598	99	12	the	the	DET
ejpam-6598	99	13	open	open	ADJ
ejpam-6598	99	14	unit	unit	NOUN
ejpam-6598	99	15	square	square	NOUN
ejpam-6598	99	16	has	have	VERB
ejpam-6598	99	17	the	the	DET
ejpam-6598	99	18	center	center	NOUN
ejpam-6598	99	19	x	x	PUNCT
ejpam-6598	99	20	.	.	PUNCT
ejpam-6598	100	1	definition	definition	NOUN
ejpam-6598	100	2	8	8	NUM
ejpam-6598	100	3	.	.	PUNCT
ejpam-6598	101	1	[	[	X
ejpam-6598	101	2	8	8	NUM
ejpam-6598	101	3	]	]	PUNCT
ejpam-6598	101	4	in	in	ADP
ejpam-6598	101	5	a	a	DET
ejpam-6598	101	6	fts	fts	PROPN
ejpam-6598	101	7	(	(	PUNCT
ejpam-6598	101	8	ξ	ξ	PROPN
ejpam-6598	101	9	,	,	PUNCT
ejpam-6598	101	10	τ	τ	PROPN
ejpam-6598	101	11	)	)	PUNCT
ejpam-6598	101	12	,	,	PUNCT
ejpam-6598	101	13	a	a	DET
ejpam-6598	101	14	fuzzy	fuzzy	ADJ
ejpam-6598	101	15	set	set	VERB
ejpam-6598	101	16	ω	ω	PROPN
ejpam-6598	101	17	is	be	AUX
ejpam-6598	101	18	termed	term	VERB
ejpam-6598	101	19	as	as	ADV
ejpam-6598	101	20	fuzzy	fuzzy	ADJ
ejpam-6598	101	21	dense	dense	ADJ
ejpam-6598	101	22	if	if	SCONJ
ejpam-6598	101	23	c(ω	c(ω	NOUN
ejpam-6598	101	24	)	)	PUNCT
ejpam-6598	101	25	=	=	SYM
ejpam-6598	101	26	1∼.	1∼.	NOUN
ejpam-6598	101	27	this	this	PRON
ejpam-6598	101	28	implies	imply	VERB
ejpam-6598	101	29	there	there	PRON
ejpam-6598	101	30	is	be	VERB
ejpam-6598	101	31	no	no	DET
ejpam-6598	101	32	fuzzy	fuzzy	ADJ
ejpam-6598	101	33	closed	close	VERB
ejpam-6598	101	34	set	set	VERB
ejpam-6598	101	35	η	η	PROPN
ejpam-6598	101	36	in	in	ADP
ejpam-6598	101	37	(	(	PUNCT
ejpam-6598	101	38	ξ	ξ	PROPN
ejpam-6598	101	39	,	,	PUNCT
ejpam-6598	101	40	τ	τ	X
ejpam-6598	101	41	)	)	PUNCT
ejpam-6598	101	42	such	such	ADJ
ejpam-6598	101	43	that	that	SCONJ
ejpam-6598	101	44	ω	ω	PROPN
ejpam-6598	101	45	<	<	X
ejpam-6598	101	46	η	η	X
ejpam-6598	101	47	<	<	X
ejpam-6598	101	48	1	1	NUM
ejpam-6598	101	49	.	.	PUNCT
ejpam-6598	101	50	n.	n.	PROPN
ejpam-6598	101	51	preethi	preethi	PROPN
ejpam-6598	101	52	,	,	PUNCT
ejpam-6598	101	53	g.	g.	PROPN
ejpam-6598	101	54	k.	k.	PROPN
ejpam-6598	101	55	revathi	revathi	PROPN
ejpam-6598	101	56	/	/	SYM
ejpam-6598	101	57	eur	eur	PROPN
ejpam-6598	101	58	.	.	PUNCT
ejpam-6598	102	1	j.	j.	PROPN
ejpam-6598	102	2	pure	pure	PROPN
ejpam-6598	102	3	appl	appl	PROPN
ejpam-6598	102	4	.	.	PROPN
ejpam-6598	102	5	math	math	PROPN
ejpam-6598	102	6	,	,	PUNCT
ejpam-6598	102	7	18	18	NUM
ejpam-6598	102	8	(	(	PUNCT
ejpam-6598	102	9	3	3	NUM
ejpam-6598	102	10	)	)	PUNCT
ejpam-6598	102	11	(	(	PUNCT
ejpam-6598	102	12	2025	2025	NUM
ejpam-6598	102	13	)	)	PUNCT
ejpam-6598	102	14	,	,	PUNCT
ejpam-6598	102	15	6598	6598	NUM
ejpam-6598	102	16	6	6	NUM
ejpam-6598	102	17	of	of	ADP
ejpam-6598	102	18	17	17	NUM
ejpam-6598	102	19	definition	definition	NOUN
ejpam-6598	102	20	9	9	NUM
ejpam-6598	102	21	.	.	PUNCT
ejpam-6598	103	1	[	[	X
ejpam-6598	103	2	8	8	NUM
ejpam-6598	103	3	]	]	X
ejpam-6598	103	4	if	if	SCONJ
ejpam-6598	103	5	there	there	PRON
ejpam-6598	103	6	is	be	VERB
ejpam-6598	103	7	no	no	DET
ejpam-6598	103	8	non	non	ADJ
ejpam-6598	103	9	-	-	ADJ
ejpam-6598	103	10	zero	zero	ADJ
ejpam-6598	103	11	fuzzy	fuzzy	ADJ
ejpam-6598	103	12	open	open	ADJ
ejpam-6598	103	13	set	set	VERB
ejpam-6598	103	14	ς	ς	PROPN
ejpam-6598	103	15	in	in	ADP
ejpam-6598	103	16	(	(	PUNCT
ejpam-6598	103	17	ξ	ξ	PROPN
ejpam-6598	103	18	,	,	PUNCT
ejpam-6598	103	19	τ	τ	X
ejpam-6598	103	20	)	)	PUNCT
ejpam-6598	103	21	such	such	ADJ
ejpam-6598	103	22	that	that	SCONJ
ejpam-6598	103	23	ς	ς	PROPN
ejpam-6598	103	24	<	<	X
ejpam-6598	103	25	c(ω	c(ω	PROPN
ejpam-6598	103	26	)	)	PUNCT
ejpam-6598	103	27	,	,	PUNCT
ejpam-6598	103	28	i.e.	i.e.	X
ejpam-6598	103	29	,	,	PUNCT
ejpam-6598	103	30	i(c(ω	i(c(ω	NOUN
ejpam-6598	103	31	)	)	PUNCT
ejpam-6598	103	32	)	)	PUNCT
ejpam-6598	104	1	=	=	PUNCT
ejpam-6598	104	2	0∼	0∼	NUM
ejpam-6598	104	3	,	,	PUNCT
ejpam-6598	104	4	then	then	ADV
ejpam-6598	104	5	a	a	DET
ejpam-6598	104	6	fuzzy	fuzzy	ADJ
ejpam-6598	104	7	set	set	VERB
ejpam-6598	104	8	ω	ω	PROPN
ejpam-6598	104	9	in	in	ADP
ejpam-6598	104	10	a	a	DET
ejpam-6598	104	11	fts	fts	PROPN
ejpam-6598	104	12	(	(	PUNCT
ejpam-6598	104	13	ξ	ξ	PROPN
ejpam-6598	104	14	,	,	PUNCT
ejpam-6598	104	15	τ	τ	X
ejpam-6598	104	16	)	)	PUNCT
ejpam-6598	104	17	is	be	AUX
ejpam-6598	104	18	said	say	VERB
ejpam-6598	104	19	to	to	PART
ejpam-6598	104	20	be	be	AUX
ejpam-6598	104	21	a	a	DET
ejpam-6598	104	22	fnds	fnd	NOUN
ejpam-6598	104	23	.	.	PUNCT
ejpam-6598	105	1	definition	definition	NOUN
ejpam-6598	105	2	10	10	NUM
ejpam-6598	105	3	.	.	PUNCT
ejpam-6598	106	1	[	[	X
ejpam-6598	106	2	8	8	NUM
ejpam-6598	106	3	]	]	PUNCT
ejpam-6598	106	4	consider	consider	VERB
ejpam-6598	106	5	the	the	DET
ejpam-6598	106	6	fts	fts	PROPN
ejpam-6598	106	7	(	(	PUNCT
ejpam-6598	106	8	ξ	ξ	PROPN
ejpam-6598	106	9	,	,	PUNCT
ejpam-6598	106	10	τ	τ	PROPN
ejpam-6598	106	11	)	)	PUNCT
ejpam-6598	106	12	.	.	PUNCT
ejpam-6598	107	1	the	the	DET
ejpam-6598	107	2	fuzzy	fuzzy	ADJ
ejpam-6598	107	3	first	first	ADJ
ejpam-6598	107	4	category	category	NOUN
ejpam-6598	107	5	set	set	VERB
ejpam-6598	107	6	is	be	AUX
ejpam-6598	107	7	a	a	DET
ejpam-6598	107	8	fuzzy	fuzzy	ADJ
ejpam-6598	107	9	set	set	VERB
ejpam-6598	107	10	ω	ω	PROPN
ejpam-6598	107	11	in	in	ADP
ejpam-6598	107	12	(	(	PUNCT
ejpam-6598	107	13	ξ	ξ	PROPN
ejpam-6598	107	14	,	,	PUNCT
ejpam-6598	107	15	τ	τ	PROPN
ejpam-6598	107	16	)	)	PUNCT
ejpam-6598	107	17	if	if	SCONJ
ejpam-6598	107	18	ω	ω	PROPN
ejpam-6598	107	19	=	=	SYM
ejpam-6598	107	20	∨∞	∨∞	PROPN
ejpam-6598	107	21	n=1	n=1	NUM
ejpam-6598	107	22	ωn	ωn	PROPN
ejpam-6598	107	23	,	,	PUNCT
ejpam-6598	107	24	where	where	SCONJ
ejpam-6598	107	25	n	n	X
ejpam-6598	107	26	’s	’	VERB
ejpam-6598	107	27	are	be	AUX
ejpam-6598	107	28	fnds	fnd	NOUN
ejpam-6598	107	29	’s	’s	NOUN
ejpam-6598	107	30	in	in	ADP
ejpam-6598	107	31	(	(	PUNCT
ejpam-6598	107	32	ξ	ξ	PROPN
ejpam-6598	107	33	,	,	PUNCT
ejpam-6598	107	34	τ	τ	X
ejpam-6598	107	35	)	)	PUNCT
ejpam-6598	107	36	.	.	PUNCT
ejpam-6598	108	1	in	in	ADP
ejpam-6598	108	2	(	(	PUNCT
ejpam-6598	108	3	ξ	ξ	PROPN
ejpam-6598	108	4	,	,	PUNCT
ejpam-6598	108	5	τ	τ	PROPN
ejpam-6598	108	6	)	)	PUNCT
ejpam-6598	108	7	,	,	PUNCT
ejpam-6598	108	8	a	a	DET
ejpam-6598	108	9	fuzzy	fuzzy	ADJ
ejpam-6598	108	10	set	set	NOUN
ejpam-6598	108	11	that	that	PRON
ejpam-6598	108	12	is	be	AUX
ejpam-6598	108	13	not	not	PART
ejpam-6598	108	14	a	a	DET
ejpam-6598	108	15	fuzzy	fuzzy	ADJ
ejpam-6598	108	16	first	first	ADJ
ejpam-6598	108	17	category	category	NOUN
ejpam-6598	108	18	set	set	NOUN
ejpam-6598	108	19	is	be	AUX
ejpam-6598	108	20	referred	refer	VERB
ejpam-6598	108	21	to	to	ADP
ejpam-6598	108	22	as	as	ADP
ejpam-6598	108	23	a	a	DET
ejpam-6598	108	24	fuzzy	fuzzy	ADJ
ejpam-6598	108	25	second	second	ADJ
ejpam-6598	108	26	category	category	NOUN
ejpam-6598	108	27	set	set	NOUN
ejpam-6598	108	28	.	.	PUNCT
ejpam-6598	109	1	definition	definition	NOUN
ejpam-6598	109	2	11	11	NUM
ejpam-6598	109	3	.	.	PUNCT
ejpam-6598	110	1	[	[	X
ejpam-6598	110	2	8	8	NUM
ejpam-6598	110	3	]	]	X
ejpam-6598	110	4	the	the	DET
ejpam-6598	110	5	fuzzy	fuzzy	ADJ
ejpam-6598	110	6	first	first	ADJ
ejpam-6598	110	7	category	category	NOUN
ejpam-6598	110	8	space	space	NOUN
ejpam-6598	110	9	is	be	AUX
ejpam-6598	110	10	a	a	DET
ejpam-6598	110	11	fts	fts	PROPN
ejpam-6598	110	12	(	(	PUNCT
ejpam-6598	110	13	ξ	ξ	PROPN
ejpam-6598	110	14	,	,	PUNCT
ejpam-6598	110	15	τ	τ	X
ejpam-6598	110	16	)	)	PUNCT
ejpam-6598	110	17	where	where	SCONJ
ejpam-6598	110	18	1	1	NUM
ejpam-6598	110	19	=	=	SYM
ejpam-6598	110	20	∨∞	∨∞	PROPN
ejpam-6598	110	21	n=1	n=1	PROPN
ejpam-6598	110	22	ωn	ωn	ADP
ejpam-6598	110	23	where	where	SCONJ
ejpam-6598	110	24	n	n	X
ejpam-6598	110	25	’s	’	VERB
ejpam-6598	110	26	are	be	AUX
ejpam-6598	110	27	fnds	fnd	NOUN
ejpam-6598	110	28	’s	’s	NOUN
ejpam-6598	110	29	in	in	ADP
ejpam-6598	110	30	(	(	PUNCT
ejpam-6598	110	31	ξ	ξ	PROPN
ejpam-6598	110	32	,	,	PUNCT
ejpam-6598	110	33	τ	τ	PROPN
ejpam-6598	110	34	)	)	PUNCT
ejpam-6598	110	35	.	.	PUNCT
ejpam-6598	111	1	a	a	DET
ejpam-6598	111	2	topological	topological	ADJ
ejpam-6598	111	3	space	space	NOUN
ejpam-6598	111	4	is	be	AUX
ejpam-6598	111	5	considered	consider	VERB
ejpam-6598	111	6	to	to	PART
ejpam-6598	111	7	be	be	AUX
ejpam-6598	111	8	of	of	ADP
ejpam-6598	111	9	fuzzy	fuzzy	ADJ
ejpam-6598	111	10	second	second	ADJ
ejpam-6598	111	11	category	category	NOUN
ejpam-6598	111	12	space	space	NOUN
ejpam-6598	111	13	if	if	SCONJ
ejpam-6598	111	14	it	it	PRON
ejpam-6598	111	15	is	be	AUX
ejpam-6598	111	16	not	not	PART
ejpam-6598	111	17	of	of	ADP
ejpam-6598	111	18	fuzzy	fuzzy	ADJ
ejpam-6598	111	19	first	first	ADJ
ejpam-6598	111	20	category	category	NOUN
ejpam-6598	111	21	space	space	NOUN
ejpam-6598	111	22	.	.	PUNCT
ejpam-6598	112	1	definition	definition	NOUN
ejpam-6598	112	2	12	12	NUM
ejpam-6598	112	3	.	.	PUNCT
ejpam-6598	113	1	[	[	X
ejpam-6598	113	2	8	8	NUM
ejpam-6598	113	3	]	]	PUNCT
ejpam-6598	113	4	assume	assume	VERB
ejpam-6598	113	5	that	that	SCONJ
ejpam-6598	113	6	the	the	DET
ejpam-6598	113	7	fts	fts	PROPN
ejpam-6598	113	8	is	be	AUX
ejpam-6598	113	9	(	(	PUNCT
ejpam-6598	113	10	ξ	ξ	PROPN
ejpam-6598	113	11	,	,	PUNCT
ejpam-6598	113	12	τ	τ	PROPN
ejpam-6598	113	13	)	)	PUNCT
ejpam-6598	113	14	.	.	PUNCT
ejpam-6598	114	1	if	if	SCONJ
ejpam-6598	114	2	i	i	PRON
ejpam-6598	114	3	(	(	PUNCT
ejpam-6598	114	4	v∞	v∞	X
ejpam-6598	114	5	n=1ωn	n=1ωn	NUM
ejpam-6598	114	6	)	)	PUNCT
ejpam-6598	114	7	=	=	SYM
ejpam-6598	114	8	0∼	0∼	NOUN
ejpam-6598	114	9	,	,	PUNCT
ejpam-6598	114	10	then	then	ADV
ejpam-6598	114	11	(	(	PUNCT
ejpam-6598	114	12	ξ	ξ	PROPN
ejpam-6598	114	13	,	,	PUNCT
ejpam-6598	114	14	τ	τ	PROPN
ejpam-6598	114	15	)	)	PUNCT
ejpam-6598	114	16	is	be	AUX
ejpam-6598	114	17	a	a	DET
ejpam-6598	114	18	fuzzy	fuzzy	ADJ
ejpam-6598	114	19	baire	baire	NOUN
ejpam-6598	114	20	space	space	NOUN
ejpam-6598	114	21	.	.	PUNCT
ejpam-6598	115	1	here	here	ADV
ejpam-6598	115	2	ωn	ωn	PRON
ejpam-6598	115	3	’s	’	VERB
ejpam-6598	115	4	are	be	AUX
ejpam-6598	115	5	fnds	fnd	NOUN
ejpam-6598	115	6	’s	’s	NOUN
ejpam-6598	115	7	in	in	ADP
ejpam-6598	115	8	(	(	PUNCT
ejpam-6598	115	9	ξ	ξ	PROPN
ejpam-6598	115	10	,	,	PUNCT
ejpam-6598	115	11	τ	τ	PROPN
ejpam-6598	115	12	)	)	PUNCT
ejpam-6598	115	13	.	.	PUNCT
ejpam-6598	116	1	definition	definition	NOUN
ejpam-6598	116	2	13	13	NUM
ejpam-6598	116	3	.	.	PUNCT
ejpam-6598	117	1	[	[	X
ejpam-6598	117	2	8	8	X
ejpam-6598	117	3	]	]	X
ejpam-6598	117	4	if	if	SCONJ
ejpam-6598	117	5	every	every	DET
ejpam-6598	117	6	fuzzy	fuzzy	ADJ
ejpam-6598	117	7	first	first	ADJ
ejpam-6598	117	8	category	category	NOUN
ejpam-6598	117	9	set	set	VERB
ejpam-6598	117	10	in	in	ADP
ejpam-6598	117	11	(	(	PUNCT
ejpam-6598	117	12	ξ	ξ	PROPN
ejpam-6598	117	13	,	,	PUNCT
ejpam-6598	117	14	τ	τ	X
ejpam-6598	117	15	)	)	PUNCT
ejpam-6598	117	16	is	be	AUX
ejpam-6598	117	17	a	a	DET
ejpam-6598	117	18	fnds	fnd	NOUN
ejpam-6598	117	19	in	in	ADP
ejpam-6598	117	20	(	(	PUNCT
ejpam-6598	117	21	ξ	ξ	PROPN
ejpam-6598	117	22	,	,	PUNCT
ejpam-6598	117	23	τ	τ	PROPN
ejpam-6598	117	24	)	)	PUNCT
ejpam-6598	117	25	,	,	PUNCT
ejpam-6598	117	26	then	then	ADV
ejpam-6598	117	27	the	the	DET
ejpam-6598	117	28	fts	fts	PROPN
ejpam-6598	117	29	(	(	PUNCT
ejpam-6598	117	30	ξ	ξ	PROPN
ejpam-6598	117	31	,	,	PUNCT
ejpam-6598	117	32	τ	τ	X
ejpam-6598	117	33	)	)	PUNCT
ejpam-6598	117	34	is	be	AUX
ejpam-6598	117	35	referred	refer	VERB
ejpam-6598	117	36	to	to	ADP
ejpam-6598	117	37	as	as	ADP
ejpam-6598	117	38	a	a	DET
ejpam-6598	117	39	fuzzy	fuzzy	ADJ
ejpam-6598	117	40	d	d	NOUN
ejpam-6598	117	41	-	-	PUNCT
ejpam-6598	117	42	baire	baire	NOUN
ejpam-6598	117	43	space	space	NOUN
ejpam-6598	117	44	.	.	PUNCT
ejpam-6598	118	1	definition	definition	NOUN
ejpam-6598	118	2	14	14	NUM
ejpam-6598	118	3	.	.	PUNCT
ejpam-6598	119	1	[	[	X
ejpam-6598	119	2	8	8	X
ejpam-6598	119	3	]	]	X
ejpam-6598	119	4	if	if	SCONJ
ejpam-6598	119	5	i(ω	i(ω	NOUN
ejpam-6598	119	6	)	)	PUNCT
ejpam-6598	119	7	is	be	AUX
ejpam-6598	119	8	fuzzy	fuzzy	ADJ
ejpam-6598	119	9	dense	dense	ADJ
ejpam-6598	119	10	in	in	ADP
ejpam-6598	119	11	(	(	PUNCT
ejpam-6598	119	12	ξ	ξ	PROPN
ejpam-6598	119	13	,	,	PUNCT
ejpam-6598	119	14	τ	τ	X
ejpam-6598	119	15	)	)	PUNCT
ejpam-6598	119	16	for	for	ADP
ejpam-6598	119	17	any	any	DET
ejpam-6598	119	18	fuzzy	fuzzy	ADJ
ejpam-6598	119	19	dense	dense	ADJ
ejpam-6598	119	20	set	set	NOUN
ejpam-6598	119	21	ω	ω	PROPN
ejpam-6598	119	22	in	in	ADP
ejpam-6598	119	23	(	(	PUNCT
ejpam-6598	119	24	ξ	ξ	PROPN
ejpam-6598	119	25	,	,	PUNCT
ejpam-6598	119	26	τ	τ	X
ejpam-6598	119	27	)	)	PUNCT
ejpam-6598	119	28	with	with	ADP
ejpam-6598	119	29	i(ω	i(ω	NOUN
ejpam-6598	119	30	)	)	PUNCT
ejpam-6598	119	31	̸=	̸=	PROPN
ejpam-6598	119	32	0∼	0∼	NUM
ejpam-6598	119	33	(	(	PUNCT
ejpam-6598	119	34	the	the	DET
ejpam-6598	119	35	null	null	ADJ
ejpam-6598	119	36	set	set	NOUN
ejpam-6598	119	37	)	)	PUNCT
ejpam-6598	119	38	,	,	PUNCT
ejpam-6598	119	39	then	then	ADV
ejpam-6598	119	40	the	the	DET
ejpam-6598	119	41	fts	fts	PROPN
ejpam-6598	119	42	(	(	PUNCT
ejpam-6598	119	43	ξ	ξ	PROPN
ejpam-6598	119	44	,	,	PUNCT
ejpam-6598	119	45	τ	τ	X
ejpam-6598	119	46	)	)	PUNCT
ejpam-6598	119	47	is	be	AUX
ejpam-6598	119	48	a	a	DET
ejpam-6598	119	49	fuzzy	fuzzy	ADJ
ejpam-6598	119	50	quasi	quasi	ADJ
ejpam-6598	119	51	-	-	ADJ
ejpam-6598	119	52	maximal	maximal	ADJ
ejpam-6598	119	53	space	space	NOUN
ejpam-6598	119	54	.	.	PUNCT
ejpam-6598	120	1	definition	definition	NOUN
ejpam-6598	120	2	15	15	NUM
ejpam-6598	120	3	.	.	PUNCT
ejpam-6598	121	1	[	[	X
ejpam-6598	121	2	8	8	NUM
ejpam-6598	121	3	]	]	X
ejpam-6598	121	4	fuzzy	fuzzy	ADJ
ejpam-6598	121	5	hausdorff	hausdorff	NOUN
ejpam-6598	121	6	spaces	space	NOUN
ejpam-6598	121	7	are	be	AUX
ejpam-6598	121	8	fts	fts	PROPN
ejpam-6598	121	9	s	s	X
ejpam-6598	121	10	(	(	PUNCT
ejpam-6598	121	11	ξ	ξ	PROPN
ejpam-6598	121	12	,	,	PUNCT
ejpam-6598	121	13	τ	τ	X
ejpam-6598	121	14	)	)	PUNCT
ejpam-6598	121	15	if	if	SCONJ
ejpam-6598	121	16	,	,	PUNCT
ejpam-6598	121	17	for	for	ADP
ejpam-6598	121	18	every	every	DET
ejpam-6598	121	19	ω	ω	PROPN
ejpam-6598	121	20	,	,	PUNCT
ejpam-6598	121	21	ς	ς	PROPN
ejpam-6598	121	22	in	in	ADP
ejpam-6598	121	23	(	(	PUNCT
ejpam-6598	121	24	ξ	ξ	PROPN
ejpam-6598	121	25	,	,	PUNCT
ejpam-6598	121	26	τ	τ	X
ejpam-6598	121	27	)	)	PUNCT
ejpam-6598	121	28	and	and	CCONJ
ejpam-6598	121	29	ω	ω	NUM
ejpam-6598	121	30	̸=	̸=	PROPN
ejpam-6598	121	31	ς	ς	NOUN
ejpam-6598	121	32	,	,	PUNCT
ejpam-6598	121	33	we	we	PRON
ejpam-6598	121	34	identify	identify	VERB
ejpam-6598	121	35	the	the	DET
ejpam-6598	121	36	fuzzy	fuzzy	ADJ
ejpam-6598	121	37	open	open	ADJ
ejpam-6598	121	38	sets	set	NOUN
ejpam-6598	121	39	η	η	PROPN
ejpam-6598	121	40	and	and	CCONJ
ejpam-6598	121	41	δ	δ	PROPN
ejpam-6598	121	42	such	such	ADJ
ejpam-6598	121	43	that	that	SCONJ
ejpam-6598	121	44	that	that	SCONJ
ejpam-6598	121	45	ω	ω	PROPN
ejpam-6598	121	46	≤	≤	PROPN
ejpam-6598	121	47	η	η	PROPN
ejpam-6598	121	48	,	,	PUNCT
ejpam-6598	121	49	ς	ς	PROPN
ejpam-6598	121	50	≤	≤	PROPN
ejpam-6598	121	51	δ	δ	PROPN
ejpam-6598	121	52	and	and	CCONJ
ejpam-6598	121	53	η	η	PROPN
ejpam-6598	121	54	∧	∧	PROPN
ejpam-6598	121	55	δ	δ	NOUN
ejpam-6598	121	56	=	=	SYM
ejpam-6598	121	57	0∼.	0∼.	NOUN
ejpam-6598	121	58	definition	definition	NOUN
ejpam-6598	121	59	16	16	NUM
ejpam-6598	121	60	.	.	PUNCT
ejpam-6598	122	1	[	[	X
ejpam-6598	122	2	8	8	NUM
ejpam-6598	122	3	]	]	PUNCT
ejpam-6598	122	4	any	any	DET
ejpam-6598	122	5	fuzzy	fuzzy	ADJ
ejpam-6598	122	6	subset	subset	NOUN
ejpam-6598	122	7	of	of	ADP
ejpam-6598	122	8	a	a	DET
ejpam-6598	122	9	fts	fts	PROPN
ejpam-6598	122	10	(	(	PUNCT
ejpam-6598	122	11	ξ	ξ	PROPN
ejpam-6598	122	12	,	,	PUNCT
ejpam-6598	122	13	τ	τ	X
ejpam-6598	122	14	)	)	PUNCT
ejpam-6598	122	15	that	that	PRON
ejpam-6598	122	16	is	be	AUX
ejpam-6598	122	17	either	either	CCONJ
ejpam-6598	122	18	fuzzy	fuzzy	ADJ
ejpam-6598	122	19	open	open	ADJ
ejpam-6598	122	20	or	or	CCONJ
ejpam-6598	122	21	fuzzy	fuzzy	ADJ
ejpam-6598	122	22	closed	close	VERB
ejpam-6598	122	23	is	be	AUX
ejpam-6598	122	24	referred	refer	VERB
ejpam-6598	122	25	to	to	ADP
ejpam-6598	122	26	as	as	ADP
ejpam-6598	122	27	a	a	DET
ejpam-6598	122	28	fuzzy	fuzzy	ADJ
ejpam-6598	122	29	door	door	NOUN
ejpam-6598	122	30	space	space	NOUN
ejpam-6598	122	31	.	.	PUNCT
ejpam-6598	123	1	definition	definition	NOUN
ejpam-6598	123	2	17	17	NUM
ejpam-6598	123	3	.	.	PUNCT
ejpam-6598	124	1	[	[	X
ejpam-6598	124	2	9	9	NUM
ejpam-6598	124	3	,	,	PUNCT
ejpam-6598	124	4	10	10	NUM
ejpam-6598	124	5	]	]	PUNCT
ejpam-6598	124	6	if	if	SCONJ
ejpam-6598	124	7	ω	ω	NOUN
ejpam-6598	124	8	=	=	SYM
ejpam-6598	124	9	c(i(ω))∪i(c(ω	c(i(ω))∪i(c(ω	NOUN
ejpam-6598	124	10	)	)	PUNCT
ejpam-6598	124	11	)	)	PUNCT
ejpam-6598	124	12	,	,	PUNCT
ejpam-6598	124	13	then	then	ADV
ejpam-6598	124	14	a	a	DET
ejpam-6598	124	15	subset	subset	NOUN
ejpam-6598	124	16	ω	ω	NOUN
ejpam-6598	124	17	of	of	ADP
ejpam-6598	124	18	a	a	DET
ejpam-6598	124	19	space	space	NOUN
ejpam-6598	124	20	ξ	ξ	PROPN
ejpam-6598	124	21	is	be	AUX
ejpam-6598	124	22	b#-open	b#-open	ADJ
ejpam-6598	124	23	.	.	PUNCT
ejpam-6598	125	1	definition	definition	NOUN
ejpam-6598	125	2	18	18	NUM
ejpam-6598	125	3	.	.	PUNCT
ejpam-6598	126	1	[	[	X
ejpam-6598	126	2	11	11	NUM
ejpam-6598	126	3	]	]	PUNCT
ejpam-6598	126	4	(	(	PUNCT
ejpam-6598	126	5	i	i	NOUN
ejpam-6598	126	6	)	)	PUNCT
ejpam-6598	126	7	if	if	SCONJ
ejpam-6598	126	8	ω	ω	NUM
ejpam-6598	126	9	=	=	SYM
ejpam-6598	126	10	(	(	PUNCT
ejpam-6598	126	11	c(i(ω	c(i(ω	PROPN
ejpam-6598	126	12	)	)	PUNCT
ejpam-6598	126	13	∪	∪	NOUN
ejpam-6598	126	14	(	(	PUNCT
ejpam-6598	126	15	i(c(ω	i(c(ω	NOUN
ejpam-6598	126	16	)	)	PUNCT
ejpam-6598	126	17	)	)	PUNCT
ejpam-6598	126	18	)	)	PUNCT
ejpam-6598	126	19	,	,	PUNCT
ejpam-6598	126	20	then	then	ADV
ejpam-6598	126	21	an	an	DET
ejpam-6598	126	22	ifs	ifs	PROPN
ejpam-6598	126	23	ω	ω	PROPN
ejpam-6598	126	24	of	of	ADP
ejpam-6598	126	25	an	an	DET
ejpam-6598	126	26	ifts	ift	NOUN
ejpam-6598	126	27	(	(	PUNCT
ejpam-6598	126	28	ξ	ξ	PROPN
ejpam-6598	126	29	,	,	PUNCT
ejpam-6598	126	30	τ	τ	X
ejpam-6598	126	31	)	)	PUNCT
ejpam-6598	126	32	is	be	AUX
ejpam-6598	126	33	if	if	SCONJ
ejpam-6598	126	34	b	b	X
ejpam-6598	126	35	-	-	PUNCT
ejpam-6598	126	36	os	os	NOUN
ejpam-6598	126	37	and	and	CCONJ
ejpam-6598	126	38	(	(	PUNCT
ejpam-6598	126	39	ii	ii	NOUN
ejpam-6598	126	40	)	)	PUNCT
ejpam-6598	126	41	if	if	SCONJ
ejpam-6598	126	42	ω	ω	NUM
ejpam-6598	126	43	=	=	SYM
ejpam-6598	126	44	(	(	PUNCT
ejpam-6598	126	45	c(i(ω))∩	c(i(ω))∩	X
ejpam-6598	126	46	(	(	PUNCT
ejpam-6598	126	47	i(c(ω	i(c(ω	NOUN
ejpam-6598	126	48	)	)	PUNCT
ejpam-6598	126	49	)	)	PUNCT
ejpam-6598	126	50	)	)	PUNCT
ejpam-6598	126	51	,	,	PUNCT
ejpam-6598	126	52	then	then	ADV
ejpam-6598	126	53	an	an	DET
ejpam-6598	126	54	ifs	ifs	PROPN
ejpam-6598	126	55	ω	ω	PROPN
ejpam-6598	126	56	of	of	ADP
ejpam-6598	126	57	an	an	DET
ejpam-6598	126	58	ifts	ift	NOUN
ejpam-6598	126	59	(	(	PUNCT
ejpam-6598	126	60	ξ	ξ	PROPN
ejpam-6598	126	61	,	,	PUNCT
ejpam-6598	126	62	τ	τ	X
ejpam-6598	126	63	)	)	PUNCT
ejpam-6598	126	64	is	be	AUX
ejpam-6598	126	65	ifb	ifb	PROPN
ejpam-6598	126	66	-	-	PUNCT
ejpam-6598	126	67	cs	cs	PROPN
ejpam-6598	126	68	.	.	PROPN
ejpam-6598	126	69	definition	definition	NOUN
ejpam-6598	126	70	19	19	NUM
ejpam-6598	126	71	.	.	PUNCT
ejpam-6598	127	1	[	[	X
ejpam-6598	127	2	15	15	NUM
ejpam-6598	127	3	]	]	X
ejpam-6598	127	4	let	let	VERB
ejpam-6598	127	5	(	(	PUNCT
ejpam-6598	127	6	ξ	ξ	PROPN
ejpam-6598	127	7	,	,	PUNCT
ejpam-6598	127	8	τ	τ	X
ejpam-6598	127	9	)	)	PUNCT
ejpam-6598	127	10	be	be	VERB
ejpam-6598	127	11	a	a	DET
ejpam-6598	127	12	ts	ts	NOUN
ejpam-6598	127	13	and	and	CCONJ
ejpam-6598	127	14	τ	τ	PROPN
ejpam-6598	127	15	(	(	PUNCT
ejpam-6598	127	16	aα	aα	NOUN
ejpam-6598	127	17	)	)	PUNCT
ejpam-6598	127	18	=	=	SYM
ejpam-6598	128	1	τα	τα	NOUN
ejpam-6598	128	2	=	=	PRON
ejpam-6598	128	3	{	{	PUNCT
ejpam-6598	128	4	gα	gα	NOUN
ejpam-6598	128	5	(	(	PUNCT
ejpam-6598	128	6	̸=	̸=	PROPN
ejpam-6598	128	7	ξ);gα	ξ);gα	NOUN
ejpam-6598	128	8	∩	∩	PROPN
ejpam-6598	128	9	aα	aα	PROPN
ejpam-6598	128	10	̸=	̸=	PROPN
ejpam-6598	128	11	ϕ	ϕ	NOUN
ejpam-6598	128	12	,	,	PUNCT
ejpam-6598	128	13	for	for	ADP
ejpam-6598	128	14	aα	aα	NOUN
ejpam-6598	128	15	∈	∈	PROPN
ejpam-6598	128	16	τ	τ	PROPN
ejpam-6598	128	17	aα	aα	NOUN
ejpam-6598	128	18	̸=	̸=	PROPN
ejpam-6598	128	19	ϕ	ϕ	NOUN
ejpam-6598	128	20	for	for	ADP
ejpam-6598	128	21	some	some	DET
ejpam-6598	128	22	α	α	PROPN
ejpam-6598	128	23	∈	∈	PROPN
ejpam-6598	128	24	j	j	PROPN
ejpam-6598	128	25	,	,	PUNCT
ejpam-6598	128	26	j	j	PROPN
ejpam-6598	128	27	is	be	AUX
ejpam-6598	128	28	an	an	DET
ejpam-6598	128	29	index	index	NOUN
ejpam-6598	128	30	set	set	NOUN
ejpam-6598	128	31	.	.	PUNCT
ejpam-6598	129	1	and	and	CCONJ
ejpam-6598	129	2	also	also	ADV
ejpam-6598	129	3	define	define	VERB
ejpam-6598	129	4	τf	τf	ADP
ejpam-6598	130	1	=	=	PUNCT
ejpam-6598	130	2	{	{	PUNCT
ejpam-6598	130	3	ϕ	ϕ	NOUN
ejpam-6598	130	4	,	,	PUNCT
ejpam-6598	130	5	ξ	ξ	PROPN
ejpam-6598	130	6	,	,	PUNCT
ejpam-6598	130	7	⋃	⋃	PROPN
ejpam-6598	130	8	α∈j	α∈j	NOUN
ejpam-6598	130	9	{	{	PUNCT
ejpam-6598	130	10	τα	τα	NOUN
ejpam-6598	130	11	}	}	PUNCT
ejpam-6598	130	12	}	}	PUNCT
ejpam-6598	130	13	.	.	PUNCT
ejpam-6598	131	1	the	the	DET
ejpam-6598	131	2	fine	fine	ADJ
ejpam-6598	131	3	topological	topological	ADJ
ejpam-6598	131	4	space	space	NOUN
ejpam-6598	131	5	formed	form	VERB
ejpam-6598	131	6	by	by	ADP
ejpam-6598	131	7	the	the	DET
ejpam-6598	131	8	topology	topology	NOUN
ejpam-6598	131	9	τ	τ	PROPN
ejpam-6598	131	10	on	on	ADP
ejpam-6598	131	11	ξ	ξ	PROPN
ejpam-6598	131	12	is	be	AUX
ejpam-6598	131	13	denoted	denote	VERB
ejpam-6598	131	14	by	by	ADP
ejpam-6598	131	15	(	(	PUNCT
ejpam-6598	131	16	ξ	ξ	PROPN
ejpam-6598	131	17	,	,	PUNCT
ejpam-6598	131	18	τ	τ	PROPN
ejpam-6598	131	19	,	,	PUNCT
ejpam-6598	131	20	τf	τf	NUM
ejpam-6598	131	21	)	)	PUNCT
ejpam-6598	131	22	and	and	CCONJ
ejpam-6598	131	23	this	this	DET
ejpam-6598	131	24	collection	collection	NOUN
ejpam-6598	131	25	of	of	ADP
ejpam-6598	131	26	τf	τf	ADP
ejpam-6598	131	27	subsets	subset	NOUN
ejpam-6598	131	28	of	of	ADP
ejpam-6598	131	29	ξ	ξ	PROPN
ejpam-6598	131	30	,	,	PUNCT
ejpam-6598	131	31	which	which	PRON
ejpam-6598	131	32	is	be	AUX
ejpam-6598	131	33	known	know	VERB
ejpam-6598	131	34	as	as	ADP
ejpam-6598	131	35	the	the	DET
ejpam-6598	131	36	fine	fine	ADJ
ejpam-6598	131	37	collections	collection	NOUN
ejpam-6598	131	38	of	of	ADP
ejpam-6598	131	39	subsets	subset	NOUN
ejpam-6598	131	40	of	of	ADP
ejpam-6598	131	41	ξ	ξ	PROPN
ejpam-6598	131	42	.	.	PUNCT
ejpam-6598	131	43	fine	fine	ADJ
ejpam-6598	131	44	open	open	ADJ
ejpam-6598	131	45	sets	set	NOUN
ejpam-6598	131	46	in	in	ADP
ejpam-6598	131	47	(	(	PUNCT
ejpam-6598	131	48	ξ	ξ	PROPN
ejpam-6598	131	49	,	,	PUNCT
ejpam-6598	131	50	τ	τ	PROPN
ejpam-6598	131	51	,	,	PUNCT
ejpam-6598	131	52	τf	τf	NUM
ejpam-6598	131	53	)	)	PUNCT
ejpam-6598	131	54	are	be	AUX
ejpam-6598	131	55	the	the	DET
ejpam-6598	131	56	elements	element	NOUN
ejpam-6598	131	57	of	of	ADP
ejpam-6598	131	58	τf	τf	PRON
ejpam-6598	131	59	,	,	PUNCT
ejpam-6598	131	60	while	while	SCONJ
ejpam-6598	131	61	fine	fine	ADJ
ejpam-6598	131	62	closed	closed	ADJ
ejpam-6598	131	63	sets	set	NOUN
ejpam-6598	131	64	,	,	PUNCT
ejpam-6598	131	65	which	which	PRON
ejpam-6598	131	66	are	be	AUX
ejpam-6598	131	67	represented	represent	VERB
ejpam-6598	131	68	by	by	ADP
ejpam-6598	131	69	τcf	τcf	PROPN
ejpam-6598	131	70	,	,	PUNCT
ejpam-6598	131	71	are	be	AUX
ejpam-6598	131	72	the	the	DET
ejpam-6598	131	73	complement	complement	NOUN
ejpam-6598	131	74	of	of	ADP
ejpam-6598	131	75	fine	fine	ADJ
ejpam-6598	131	76	sets	set	NOUN
ejpam-6598	131	77	.	.	PUNCT
ejpam-6598	132	1	definition	definition	NOUN
ejpam-6598	132	2	20	20	NUM
ejpam-6598	132	3	.	.	PUNCT
ejpam-6598	133	1	[	[	X
ejpam-6598	133	2	12	12	NUM
ejpam-6598	133	3	]	]	X
ejpam-6598	133	4	pfwa	pfwa	NOUN
ejpam-6598	133	5	and	and	CCONJ
ejpam-6598	133	6	pfwg	pfwg	NOUN
ejpam-6598	133	7	are	be	AUX
ejpam-6598	133	8	two	two	NUM
ejpam-6598	133	9	averaging	averaging	NOUN
ejpam-6598	133	10	and	and	CCONJ
ejpam-6598	133	11	geometric	geometric	ADJ
ejpam-6598	133	12	aggregating	aggregating	NOUN
ejpam-6598	133	13	operators	operator	NOUN
ejpam-6598	133	14	that	that	PRON
ejpam-6598	133	15	have	have	AUX
ejpam-6598	133	16	been	be	AUX
ejpam-6598	133	17	developed	develop	VERB
ejpam-6598	133	18	for	for	ADP
ejpam-6598	133	19	a	a	DET
ejpam-6598	133	20	set	set	NOUN
ejpam-6598	133	21	of	of	ADP
ejpam-6598	133	22	pythagorean	pythagorean	ADJ
ejpam-6598	133	23	fuzzy	fuzzy	ADJ
ejpam-6598	133	24	numbers	number	NOUN
ejpam-6598	133	25	ji(1	ji(1	PROPN
ejpam-6598	133	26	≤	≤	X
ejpam-6598	133	27	i	i	NOUN
ejpam-6598	133	28	≤	≤	NOUN
ejpam-6598	133	29	n	n	CCONJ
ejpam-6598	133	30	)	)	PUNCT
ejpam-6598	133	31	as	as	SCONJ
ejpam-6598	133	32	follows	follow	VERB
ejpam-6598	133	33	pfwa	pfwa	NOUN
ejpam-6598	133	34	(	(	PUNCT
ejpam-6598	133	35	j1	j1	PROPN
ejpam-6598	133	36	,	,	PUNCT
ejpam-6598	133	37	j2	j2	PROPN
ejpam-6598	133	38	,	,	PUNCT
ejpam-6598	133	39	j3	j3	PROPN
ejpam-6598	133	40	,	,	PUNCT
ejpam-6598	133	41	.	.	PUNCT
ejpam-6598	133	42	.	.	PUNCT
ejpam-6598	133	43	.	.	PUNCT
ejpam-6598	133	44	.	.	PUNCT
ejpam-6598	133	45	.	.	PUNCT
ejpam-6598	133	46	.	.	PUNCT
ejpam-6598	134	1	..	..	PUNCT
ejpam-6598	134	2	,	,	PUNCT
ejpam-6598	134	3	jn	jn	PROPN
ejpam-6598	134	4	)	)	PUNCT
ejpam-6598	134	5	=	=	PUNCT
ejpam-6598	135	1	〈	〈	PROPN
ejpam-6598	135	2	√	√	PROPN
ejpam-6598	135	3	1−	1−	NUM
ejpam-6598	135	4	∏n	∏n	ADJ
ejpam-6598	135	5	i=1	i=1	PROPN
ejpam-6598	135	6	(	(	PUNCT
ejpam-6598	135	7	1−	1−	NUM
ejpam-6598	135	8	µ2i	µ2i	NOUN
ejpam-6598	135	9	)	)	PUNCT
ejpam-6598	135	10	wi	wi	PROPN
ejpam-6598	135	11	,	,	PUNCT
ejpam-6598	135	12	∏n	∏n	PROPN
ejpam-6598	135	13	i=1	i=1	PROPN
ejpam-6598	135	14	ϑi	ϑi	PROPN
ejpam-6598	135	15	wi	wi	PROPN
ejpam-6598	135	16	〉	〉	NOUN
ejpam-6598	135	17	and	and	CCONJ
ejpam-6598	135	18	pfwg	pfwg	NOUN
ejpam-6598	135	19	(	(	PUNCT
ejpam-6598	135	20	j1	j1	PROPN
ejpam-6598	135	21	,	,	PUNCT
ejpam-6598	135	22	j2	j2	PROPN
ejpam-6598	135	23	,	,	PUNCT
ejpam-6598	135	24	j3	j3	PROPN
ejpam-6598	135	25	,	,	PUNCT
ejpam-6598	135	26	.	.	PUNCT
ejpam-6598	135	27	.	.	PUNCT
ejpam-6598	135	28	.	.	PUNCT
ejpam-6598	135	29	.	.	PUNCT
ejpam-6598	135	30	.	.	PUNCT
ejpam-6598	135	31	.	.	PUNCT
ejpam-6598	135	32	.	.	PUNCT
ejpam-6598	135	33	.	.	PUNCT
ejpam-6598	135	34	.	.	PUNCT
ejpam-6598	136	1	.	.	PUNCT
ejpam-6598	136	2	,	,	PUNCT
ejpam-6598	136	3	jn	jn	PROPN
ejpam-6598	136	4	)	)	PUNCT
ejpam-6598	136	5	=	=	PUNCT
ejpam-6598	137	1	〈	〈	PROPN
ejpam-6598	137	2	∏n	∏n	PROPN
ejpam-6598	137	3	i=1	i=1	PROPN
ejpam-6598	137	4	µ	µ	PROPN
ejpam-6598	137	5	wi	wi	PROPN
ejpam-6598	137	6	i	i	PRON
ejpam-6598	137	7	,	,	PUNCT
ejpam-6598	137	8	√	√	PROPN
ejpam-6598	137	9	1−	1−	NUM
ejpam-6598	137	10	∏n	∏n	ADJ
ejpam-6598	137	11	i=1	i=1	PROPN
ejpam-6598	137	12	(	(	PUNCT
ejpam-6598	137	13	1−	1−	NUM
ejpam-6598	137	14	ϑ2i	ϑ2i	ADJ
ejpam-6598	137	15	)	)	PUNCT
ejpam-6598	137	16	wi	wi	PROPN
ejpam-6598	137	17	〉	〉	NOUN
ejpam-6598	138	1	where	where	SCONJ
ejpam-6598	138	2	w	w	NOUN
ejpam-6598	138	3	=	=	SYM
ejpam-6598	138	4	(	(	PUNCT
ejpam-6598	138	5	w1,w2,w3	w1,w2,w3	NOUN
ejpam-6598	138	6	,	,	PUNCT
ejpam-6598	138	7	.	.	PUNCT
ejpam-6598	138	8	.	.	PUNCT
ejpam-6598	138	9	.	.	PUNCT
ejpam-6598	138	10	.	.	PUNCT
ejpam-6598	138	11	.	.	PUNCT
ejpam-6598	138	12	.	.	PUNCT
ejpam-6598	139	1	,	,	PUNCT
ejpam-6598	139	2	wn	wn	PROPN
ejpam-6598	139	3	)	)	PUNCT
ejpam-6598	139	4	t	t	PROPN
ejpam-6598	139	5	is	be	AUX
ejpam-6598	139	6	the	the	DET
ejpam-6598	139	7	associated	associate	VERB
ejpam-6598	139	8	normalized	normalize	VERB
ejpam-6598	139	9	weight	weight	NOUN
ejpam-6598	139	10	vector	vector	NOUN
ejpam-6598	139	11	of	of	ADP
ejpam-6598	139	12	these	these	DET
ejpam-6598	139	13	pythagorean	pythagorean	ADJ
ejpam-6598	139	14	fuzzy	fuzzy	ADJ
ejpam-6598	139	15	numbers	number	NOUN
ejpam-6598	139	16	such	such	ADJ
ejpam-6598	139	17	that	that	PRON
ejpam-6598	139	18	wi(i	wi(i	NUM
ejpam-6598	139	19	=	=	SYM
ejpam-6598	139	20	1	1	NUM
ejpam-6598	139	21	,	,	PUNCT
ejpam-6598	139	22	2	2	NUM
ejpam-6598	139	23	,	,	PUNCT
ejpam-6598	139	24	3	3	NUM
ejpam-6598	139	25	,	,	PUNCT
ejpam-6598	139	26	.	.	PUNCT
ejpam-6598	139	27	.	.	PUNCT
ejpam-6598	139	28	.	.	PUNCT
ejpam-6598	140	1	.n	.n	PROPN
ejpam-6598	140	2	)	)	PUNCT
ejpam-6598	140	3	∈	∈	PROPN
ejpam-6598	141	1	[	[	X
ejpam-6598	141	2	0	0	NUM
ejpam-6598	141	3	,	,	PUNCT
ejpam-6598	141	4	1	1	NUM
ejpam-6598	141	5	]	]	PUNCT
ejpam-6598	141	6	and	and	CCONJ
ejpam-6598	141	7	∑n	∑n	PROPN
ejpam-6598	141	8	i=1wi	i=1wi	X
ejpam-6598	141	9	=	=	SYM
ejpam-6598	141	10	1	1	X
ejpam-6598	141	11	.	.	PUNCT
ejpam-6598	141	12	n.	n.	PROPN
ejpam-6598	141	13	preethi	preethi	PROPN
ejpam-6598	141	14	,	,	PUNCT
ejpam-6598	141	15	g.	g.	PROPN
ejpam-6598	141	16	k.	k.	PROPN
ejpam-6598	141	17	revathi	revathi	PROPN
ejpam-6598	141	18	/	/	SYM
ejpam-6598	141	19	eur	eur	PROPN
ejpam-6598	141	20	.	.	PUNCT
ejpam-6598	142	1	j.	j.	PROPN
ejpam-6598	142	2	pure	pure	PROPN
ejpam-6598	142	3	appl	appl	PROPN
ejpam-6598	142	4	.	.	PROPN
ejpam-6598	142	5	math	math	PROPN
ejpam-6598	142	6	,	,	PUNCT
ejpam-6598	142	7	18	18	NUM
ejpam-6598	142	8	(	(	PUNCT
ejpam-6598	142	9	3	3	NUM
ejpam-6598	142	10	)	)	PUNCT
ejpam-6598	142	11	(	(	PUNCT
ejpam-6598	142	12	2025	2025	NUM
ejpam-6598	142	13	)	)	PUNCT
ejpam-6598	142	14	,	,	PUNCT
ejpam-6598	142	15	6598	6598	NUM
ejpam-6598	142	16	7	7	NUM
ejpam-6598	142	17	of	of	ADP
ejpam-6598	142	18	17	17	NUM
ejpam-6598	142	19	3	3	NUM
ejpam-6598	142	20	.	.	PUNCT
ejpam-6598	143	1	pythagorean	pythagorean	PROPN
ejpam-6598	143	2	fuzzy	fuzzy	ADJ
ejpam-6598	143	3	digital	digital	PROPN
ejpam-6598	143	4	fine	fine	ADJ
ejpam-6598	143	5	b≈-door	b≈-door	NOUN
ejpam-6598	143	6	spaces	space	NOUN
ejpam-6598	143	7	this	this	DET
ejpam-6598	143	8	section	section	NOUN
ejpam-6598	143	9	provides	provide	VERB
ejpam-6598	143	10	an	an	DET
ejpam-6598	143	11	introduction	introduction	NOUN
ejpam-6598	143	12	to	to	ADP
ejpam-6598	143	13	pfdft	pfdft	NOUN
ejpam-6598	143	14	and	and	CCONJ
ejpam-6598	143	15	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	143	16	−	−	NOUN
ejpam-6598	143	17	ds	ds	NOUN
ejpam-6598	143	18	,	,	PUNCT
ejpam-6598	143	19	along	along	ADP
ejpam-6598	143	20	with	with	ADP
ejpam-6598	143	21	a	a	DET
ejpam-6598	143	22	detailed	detailed	ADJ
ejpam-6598	143	23	discussion	discussion	NOUN
ejpam-6598	143	24	of	of	ADP
ejpam-6598	143	25	their	their	PRON
ejpam-6598	143	26	properties	property	NOUN
ejpam-6598	143	27	.	.	PUNCT
ejpam-6598	144	1	definition	definition	NOUN
ejpam-6598	144	2	21	21	NUM
ejpam-6598	144	3	.	.	PUNCT
ejpam-6598	145	1	let	let	VERB
ejpam-6598	145	2	(	(	PUNCT
ejpam-6598	145	3	ξ	ξ	PROPN
ejpam-6598	145	4	,	,	PUNCT
ejpam-6598	145	5	τ	τ	X
ejpam-6598	145	6	)	)	PUNCT
ejpam-6598	145	7	be	be	AUX
ejpam-6598	145	8	a	a	DET
ejpam-6598	145	9	pfts	pft	NOUN
ejpam-6598	145	10	.	.	PUNCT
ejpam-6598	146	1	define	define	VERB
ejpam-6598	146	2	τ	τ	PROPN
ejpam-6598	146	3	(	(	PUNCT
ejpam-6598	146	4	aα	aα	NOUN
ejpam-6598	146	5	)	)	PUNCT
ejpam-6598	146	6	=	=	NOUN
ejpam-6598	146	7	τ̂α	τ̂α	PUNCT
ejpam-6598	146	8	=	=	NOUN
ejpam-6598	146	9	{	{	PUNCT
ejpam-6598	146	10	gα	gα	ADP
ejpam-6598	146	11	(	(	PUNCT
ejpam-6598	146	12	̸=	̸=	PROPN
ejpam-6598	146	13	1∼);gα	1∼);gα	NUM
ejpam-6598	146	14	∩aα	∩aα	NOUN
ejpam-6598	146	15	̸=	̸=	PROPN
ejpam-6598	146	16	0∼	0∼	NUM
ejpam-6598	146	17	,	,	PUNCT
ejpam-6598	146	18	for	for	ADP
ejpam-6598	146	19	aα	aα	NOUN
ejpam-6598	146	20	∈	∈	PROPN
ejpam-6598	146	21	τ	τ	PUNCT
ejpam-6598	146	22	aα	aα	NOUN
ejpam-6598	146	23	̸=	̸=	PROPN
ejpam-6598	146	24	0∼	0∼	NUM
ejpam-6598	146	25	for	for	ADP
ejpam-6598	146	26	some	some	DET
ejpam-6598	146	27	α	α	NOUN
ejpam-6598	146	28	∈	∈	PROPN
ejpam-6598	146	29	j	j	PROPN
ejpam-6598	146	30	,	,	PUNCT
ejpam-6598	146	31	j	j	PROPN
ejpam-6598	146	32	is	be	AUX
ejpam-6598	146	33	an	an	DET
ejpam-6598	146	34	index	index	NOUN
ejpam-6598	146	35	set	set	NOUN
ejpam-6598	146	36	.	.	PUNCT
ejpam-6598	147	1	and	and	CCONJ
ejpam-6598	147	2	also	also	ADV
ejpam-6598	147	3	define	define	VERB
ejpam-6598	147	4	τ̂f	τ̂f	PUNCT
ejpam-6598	148	1	=	=	SYM
ejpam-6598	148	2	{	{	PUNCT
ejpam-6598	148	3	0∼	0∼	ADP
ejpam-6598	148	4	,	,	PUNCT
ejpam-6598	148	5	1∼	1∼	NUM
ejpam-6598	148	6	,	,	PUNCT
ejpam-6598	148	7	⋃	⋃	PUNCT
ejpam-6598	148	8	α∈j	α∈j	NOUN
ejpam-6598	148	9	gα	gα	ADP
ejpam-6598	148	10	}	}	PUNCT
ejpam-6598	148	11	.	.	PUNCT
ejpam-6598	149	1	here	here	ADV
ejpam-6598	149	2	the	the	DET
ejpam-6598	149	3	operator	operator	NOUN
ejpam-6598	149	4	“	"	PUNCT
ejpam-6598	149	5	⋃	⋃	PROPN
ejpam-6598	149	6	”	"	PUNCT
ejpam-6598	149	7	denotes	denote	VERB
ejpam-6598	149	8	the	the	DET
ejpam-6598	149	9	union	union	NOUN
ejpam-6598	149	10	of	of	ADP
ejpam-6598	149	11	the	the	DET
ejpam-6598	149	12	set	set	NOUN
ejpam-6598	149	13	of	of	ADP
ejpam-6598	149	14	all	all	DET
ejpam-6598	149	15	collections	collection	NOUN
ejpam-6598	149	16	of	of	ADP
ejpam-6598	149	17	gα	gα	NOUN
ejpam-6598	149	18	.	.	PUNCT
ejpam-6598	150	1	the	the	DET
ejpam-6598	150	2	pfdfs	pfdfs	NOUN
ejpam-6598	150	3	of	of	ADP
ejpam-6598	150	4	ξ	ξ	PROPN
ejpam-6598	150	5	are	be	AUX
ejpam-6598	150	6	therefore	therefore	ADV
ejpam-6598	150	7	denoted	denote	VERB
ejpam-6598	150	8	by	by	ADP
ejpam-6598	150	9	τ̂f	τ̂f	PUNCT
ejpam-6598	150	10	,	,	PUNCT
ejpam-6598	150	11	and	and	CCONJ
ejpam-6598	150	12	the	the	DET
ejpam-6598	150	13	pfdfts	pfdft	NOUN
ejpam-6598	150	14	produced	produce	VERB
ejpam-6598	150	15	by	by	ADP
ejpam-6598	150	16	the	the	DET
ejpam-6598	150	17	topology	topology	NOUN
ejpam-6598	150	18	τ	τ	PROPN
ejpam-6598	150	19	on	on	ADP
ejpam-6598	150	20	ξ	ξ	PROPN
ejpam-6598	150	21	is	be	AUX
ejpam-6598	150	22	denoted	denote	VERB
ejpam-6598	150	23	by	by	ADP
ejpam-6598	150	24	(	(	PUNCT
ejpam-6598	150	25	ξ	ξ	PROPN
ejpam-6598	150	26	,	,	PUNCT
ejpam-6598	150	27	τ	τ	PROPN
ejpam-6598	150	28	,	,	PUNCT
ejpam-6598	150	29	τ̂f	τ̂f	NUM
ejpam-6598	150	30	)	)	PUNCT
ejpam-6598	150	31	.	.	PUNCT
ejpam-6598	151	1	all	all	PRON
ejpam-6598	151	2	of	of	ADP
ejpam-6598	151	3	the	the	DET
ejpam-6598	151	4	elements	element	NOUN
ejpam-6598	151	5	of	of	ADP
ejpam-6598	151	6	(	(	PUNCT
ejpam-6598	151	7	ξ	ξ	PROPN
ejpam-6598	151	8	,	,	PUNCT
ejpam-6598	151	9	τ	τ	PROPN
ejpam-6598	151	10	,	,	PUNCT
ejpam-6598	151	11	τ̂f	τ̂f	NUM
ejpam-6598	151	12	)	)	PUNCT
ejpam-6598	151	13	are	be	AUX
ejpam-6598	151	14	considered	consider	VERB
ejpam-6598	151	15	to	to	PART
ejpam-6598	151	16	be	be	AUX
ejpam-6598	151	17	pfd	pfd	PROPN
ejpam-6598	151	18	fine	fine	ADJ
ejpam-6598	151	19	open	open	ADJ
ejpam-6598	151	20	sets	set	NOUN
ejpam-6598	151	21	,	,	PUNCT
ejpam-6598	151	22	and	and	CCONJ
ejpam-6598	151	23	their	their	PRON
ejpam-6598	151	24	corresponding	corresponding	ADJ
ejpam-6598	151	25	complements	complement	NOUN
ejpam-6598	151	26	are	be	AUX
ejpam-6598	151	27	considered	consider	VERB
ejpam-6598	151	28	to	to	PART
ejpam-6598	151	29	be	be	AUX
ejpam-6598	151	30	pfd	pfd	PROPN
ejpam-6598	151	31	fine	fine	ADJ
ejpam-6598	151	32	closed	close	VERB
ejpam-6598	151	33	sets	set	NOUN
ejpam-6598	151	34	.	.	PUNCT
ejpam-6598	152	1	definition	definition	NOUN
ejpam-6598	152	2	22	22	NUM
ejpam-6598	152	3	.	.	PUNCT
ejpam-6598	153	1	a	a	DET
ejpam-6598	153	2	pfdfts	pfdft	NOUN
ejpam-6598	153	3	(	(	PUNCT
ejpam-6598	153	4	ξ	ξ	PROPN
ejpam-6598	153	5	,	,	PUNCT
ejpam-6598	153	6	τ	τ	X
ejpam-6598	153	7	)	)	PUNCT
ejpam-6598	153	8	and	and	CCONJ
ejpam-6598	153	9	its	its	PRON
ejpam-6598	153	10	pfdfs	pfdfs	NOUN
ejpam-6598	153	11	ω	ω	NOUN
ejpam-6598	153	12	are	be	AUX
ejpam-6598	153	13	referred	refer	VERB
ejpam-6598	153	14	to	to	ADP
ejpam-6598	153	15	as	as	ADP
ejpam-6598	153	16	•	•	NOUN
ejpam-6598	153	17	pfdb≈f	pfdb≈f	NUM
ejpam-6598	153	18	−os	−os	NOUN
ejpam-6598	153	19	if	if	SCONJ
ejpam-6598	153	20	ω	ω	PROPN
ejpam-6598	153	21	=	=	SYM
ejpam-6598	153	22	(	(	PUNCT
ejpam-6598	153	23	(	(	PUNCT
ejpam-6598	153	24	c(i(ω	c(i(ω	PROPN
ejpam-6598	153	25	)	)	PUNCT
ejpam-6598	153	26	)	)	PUNCT
ejpam-6598	153	27	∪	∪	ADP
ejpam-6598	153	28	(	(	PUNCT
ejpam-6598	153	29	i(c(ω	i(c(ω	NOUN
ejpam-6598	153	30	)	)	PUNCT
ejpam-6598	153	31	)	)	PUNCT
ejpam-6598	153	32	)	)	PUNCT
ejpam-6598	154	1	•	•	X
ejpam-6598	154	2	pfdb≈f	pfdb≈f	PRON
ejpam-6598	154	3	−	−	NOUN
ejpam-6598	154	4	cs	cs	PROPN
ejpam-6598	154	5	if	if	SCONJ
ejpam-6598	154	6	ω	ω	PROPN
ejpam-6598	154	7	=	=	SYM
ejpam-6598	154	8	(	(	PUNCT
ejpam-6598	154	9	(	(	PUNCT
ejpam-6598	154	10	c(i(ω	c(i(ω	ADJ
ejpam-6598	154	11	)	)	PUNCT
ejpam-6598	154	12	)	)	PUNCT
ejpam-6598	154	13	∩	∩	NOUN
ejpam-6598	154	14	(	(	PUNCT
ejpam-6598	154	15	i(c(ω	i(c(ω	NOUN
ejpam-6598	154	16	)	)	PUNCT
ejpam-6598	154	17	)	)	PUNCT
ejpam-6598	154	18	)	)	PUNCT
ejpam-6598	154	19	definition	definition	NOUN
ejpam-6598	154	20	23	23	NUM
ejpam-6598	154	21	.	.	PUNCT
ejpam-6598	155	1	let	let	VERB
ejpam-6598	155	2	ω	ω	NUM
ejpam-6598	155	3	be	be	AUX
ejpam-6598	155	4	any	any	DET
ejpam-6598	155	5	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	155	6	set	set	VERB
ejpam-6598	155	7	in	in	ADP
ejpam-6598	155	8	pfdfts	pfdft	NOUN
ejpam-6598	155	9	(	(	PUNCT
ejpam-6598	155	10	ξ	ξ	PROPN
ejpam-6598	155	11	,	,	PUNCT
ejpam-6598	155	12	τ	τ	PROPN
ejpam-6598	155	13	,	,	PUNCT
ejpam-6598	155	14	τ̂f	τ̂f	NUM
ejpam-6598	155	15	)	)	PUNCT
ejpam-6598	155	16	the	the	DET
ejpam-6598	155	17	pfdb≈f	pfdb≈f	NUM
ejpam-6598	155	18	−c	−c	NOUN
ejpam-6598	155	19	and	and	CCONJ
ejpam-6598	155	20	pfdb≈f	pfdb≈f	PRON
ejpam-6598	155	21	−i	−i	ADJ
ejpam-6598	155	22	of	of	ADP
ejpam-6598	155	23	ω	ω	PROPN
ejpam-6598	155	24	is	be	AUX
ejpam-6598	155	25	given	give	VERB
ejpam-6598	155	26	as	as	ADP
ejpam-6598	155	27	pfd	pfd	PROPN
ejpam-6598	155	28	b≈f	b≈f	PROPN
ejpam-6598	155	29	−	−	PROPN
ejpam-6598	155	30	c(ω	c(ω	PROPN
ejpam-6598	155	31	)	)	PUNCT
ejpam-6598	156	1	=	=	PUNCT
ejpam-6598	156	2	∩{a	∩{a	PROPN
ejpam-6598	156	3	:	:	PUNCT
ejpam-6598	157	1	ω	ω	NUM
ejpam-6598	157	2	⊆	⊆	NUM
ejpam-6598	157	3	a	a	PRON
ejpam-6598	157	4	,	,	PUNCT
ejpam-6598	157	5	a	a	PRON
ejpam-6598	157	6	is	be	AUX
ejpam-6598	157	7	pfdb≈f	pfdb≈f	NUM
ejpam-6598	157	8	−	−	NOUN
ejpam-6598	157	9	cs	cs	PROPN
ejpam-6598	157	10	in	in	ADP
ejpam-6598	157	11	(	(	PUNCT
ejpam-6598	157	12	ξ	ξ	PROPN
ejpam-6598	157	13	,	,	PUNCT
ejpam-6598	157	14	τ	τ	PROPN
ejpam-6598	157	15	,	,	PUNCT
ejpam-6598	157	16	τ̂f	τ̂f	NUM
ejpam-6598	157	17	)	)	PUNCT
ejpam-6598	157	18	}	}	PUNCT
ejpam-6598	157	19	pfdb≈f	pfdb≈f	NUM
ejpam-6598	157	20	−	−	NOUN
ejpam-6598	157	21	i(ω	i(ω	NOUN
ejpam-6598	157	22	)	)	PUNCT
ejpam-6598	157	23	=	=	PUNCT
ejpam-6598	158	1	∪{b	∪{b	NOUN
ejpam-6598	158	2	:	:	PUNCT
ejpam-6598	158	3	b	b	X
ejpam-6598	158	4	⊆	⊆	NUM
ejpam-6598	158	5	ω	ω	NUM
ejpam-6598	158	6	,	,	PUNCT
ejpam-6598	158	7	b	b	PROPN
ejpam-6598	158	8	is	be	AUX
ejpam-6598	158	9	pfdb≈f	pfdb≈f	PRON
ejpam-6598	158	10	−os	−os	ADV
ejpam-6598	158	11	in	in	ADP
ejpam-6598	158	12	(	(	PUNCT
ejpam-6598	158	13	ξ	ξ	PROPN
ejpam-6598	158	14	,	,	PUNCT
ejpam-6598	158	15	τ	τ	PROPN
ejpam-6598	158	16	,	,	PUNCT
ejpam-6598	158	17	τ̂f	τ̂f	NUM
ejpam-6598	158	18	)	)	PUNCT
ejpam-6598	158	19	}	}	PUNCT
ejpam-6598	158	20	definition	definition	NOUN
ejpam-6598	158	21	24	24	NUM
ejpam-6598	158	22	.	.	PUNCT
ejpam-6598	159	1	a	a	DET
ejpam-6598	159	2	pfdfts	pfdft	NOUN
ejpam-6598	159	3	(	(	PUNCT
ejpam-6598	159	4	ξ	ξ	PROPN
ejpam-6598	159	5	,	,	PUNCT
ejpam-6598	159	6	τ	τ	PROPN
ejpam-6598	159	7	,	,	PUNCT
ejpam-6598	159	8	τ̂f	τ̂f	NUM
ejpam-6598	159	9	)	)	PUNCT
ejpam-6598	159	10	is	be	AUX
ejpam-6598	159	11	called	call	VERB
ejpam-6598	159	12	as	as	ADP
ejpam-6598	159	13	the	the	DET
ejpam-6598	159	14	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	159	15	−	−	NOUN
ejpam-6598	159	16	ds	ds	VERB
ejpam-6598	159	17	if	if	SCONJ
ejpam-6598	159	18	every	every	DET
ejpam-6598	159	19	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	159	20	set	set	VERB
ejpam-6598	159	21	in	in	ADP
ejpam-6598	159	22	(	(	PUNCT
ejpam-6598	159	23	ξ	ξ	PROPN
ejpam-6598	159	24	,	,	PUNCT
ejpam-6598	159	25	τ	τ	PROPN
ejpam-6598	159	26	,	,	PUNCT
ejpam-6598	159	27	τ̂f	τ̂f	NUM
ejpam-6598	159	28	)	)	PUNCT
ejpam-6598	159	29	is	be	AUX
ejpam-6598	159	30	either	either	CCONJ
ejpam-6598	159	31	pfdb≈f	pfdb≈f	PRON
ejpam-6598	159	32	open	open	ADJ
ejpam-6598	159	33	or	or	CCONJ
ejpam-6598	159	34	pfdb≈f	pfdb≈f	PRON
ejpam-6598	159	35	closed	close	VERB
ejpam-6598	159	36	.	.	PUNCT
ejpam-6598	160	1	example	example	NOUN
ejpam-6598	161	1	1	1	NUM
ejpam-6598	161	2	.	.	X
ejpam-6598	161	3	consider	consider	VERB
ejpam-6598	161	4	ξ	ξ	X
ejpam-6598	161	5	=	=	SYM
ejpam-6598	161	6	{	{	PUNCT
ejpam-6598	161	7	l	l	NOUN
ejpam-6598	161	8	,	,	PUNCT
ejpam-6598	161	9	m	m	AUX
ejpam-6598	161	10	}	}	PUNCT
ejpam-6598	161	11	be	be	AUX
ejpam-6598	161	12	a	a	DET
ejpam-6598	161	13	non	non	X
ejpam-6598	161	14	empty	empty	ADJ
ejpam-6598	161	15	set	set	NOUN
ejpam-6598	161	16	and	and	CCONJ
ejpam-6598	161	17	τ	τ	PROPN
ejpam-6598	161	18	=	=	PUNCT
ejpam-6598	161	19	{	{	PUNCT
ejpam-6598	161	20	0∼	0∼	NUM
ejpam-6598	161	21	,	,	PUNCT
ejpam-6598	161	22	1∼	1∼	NUM
ejpam-6598	161	23	,	,	PUNCT
ejpam-6598	161	24	ξ	ξ	X
ejpam-6598	161	25	}	}	PUNCT
ejpam-6598	161	26	is	be	AUX
ejpam-6598	161	27	a	a	DET
ejpam-6598	161	28	pfdt	pfdt	NOUN
ejpam-6598	161	29	on	on	ADP
ejpam-6598	161	30	ξ	ξ	PROPN
ejpam-6598	161	31	where	where	SCONJ
ejpam-6598	161	32	0∼	0∼	X
ejpam-6598	161	33	=	=	PRON
ejpam-6598	161	34	{	{	PUNCT
ejpam-6598	161	35	<	<	X
ejpam-6598	161	36	0	0	NUM
ejpam-6598	161	37	,	,	PUNCT
ejpam-6598	161	38	1	1	NUM
ejpam-6598	161	39	>	>	PUNCT
ejpam-6598	161	40	,	,	PUNCT
ejpam-6598	161	41	<	<	X
ejpam-6598	161	42	0	0	NUM
ejpam-6598	161	43	,	,	PUNCT
ejpam-6598	161	44	1	1	NUM
ejpam-6598	161	45	>	>	PUNCT
ejpam-6598	161	46	}	}	PUNCT
ejpam-6598	161	47	,	,	PUNCT
ejpam-6598	161	48	1∼	1∼	X
ejpam-6598	161	49	=	=	SYM
ejpam-6598	161	50	{	{	PUNCT
ejpam-6598	161	51	<	<	X
ejpam-6598	161	52	1	1	NUM
ejpam-6598	161	53	,	,	PUNCT
ejpam-6598	161	54	0	0	NUM
ejpam-6598	161	55	>	>	PUNCT
ejpam-6598	161	56	,	,	PUNCT
ejpam-6598	161	57	<	<	X
ejpam-6598	161	58	1	1	NUM
ejpam-6598	161	59	,	,	PUNCT
ejpam-6598	161	60	0	0	NUM
ejpam-6598	161	61	>	>	PUNCT
ejpam-6598	161	62	}	}	PUNCT
ejpam-6598	161	63	,	,	PUNCT
ejpam-6598	161	64	and	and	CCONJ
ejpam-6598	161	65	ω	ω	X
ejpam-6598	161	66	=	=	X
ejpam-6598	161	67	<	<	X
ejpam-6598	161	68	x	x	X
ejpam-6598	161	69	,	,	PUNCT
ejpam-6598	161	70	(	(	PUNCT
ejpam-6598	161	71	l/0.2	l/0.2	PROPN
ejpam-6598	161	72	,	,	PUNCT
ejpam-6598	161	73	m/0.3	m/0.3	NOUN
ejpam-6598	161	74	)	)	PUNCT
ejpam-6598	161	75	,	,	PUNCT
ejpam-6598	161	76	(	(	PUNCT
ejpam-6598	161	77	l/0.9	l/0.9	ADJ
ejpam-6598	161	78	,	,	PUNCT
ejpam-6598	161	79	m/0.8	m/0.8	PROPN
ejpam-6598	161	80	)	)	PUNCT
ejpam-6598	161	81	>	>	PUNCT
ejpam-6598	161	82	.	.	PUNCT
ejpam-6598	162	1	consider	consider	VERB
ejpam-6598	162	2	g	g	NOUN
ejpam-6598	162	3	=	=	NOUN
ejpam-6598	162	4	<	<	X
ejpam-6598	162	5	x	x	X
ejpam-6598	162	6	,	,	PUNCT
ejpam-6598	162	7	(	(	PUNCT
ejpam-6598	162	8	l/0.2	l/0.2	PROPN
ejpam-6598	162	9	,	,	PUNCT
ejpam-6598	162	10	m/0.1	m/0.1	PROPN
ejpam-6598	162	11	)	)	PUNCT
ejpam-6598	162	12	,	,	PUNCT
ejpam-6598	162	13	(	(	PUNCT
ejpam-6598	162	14	l/0.9	l/0.9	ADJ
ejpam-6598	162	15	,	,	PUNCT
ejpam-6598	162	16	m/0.9	m/0.9	ADJ
ejpam-6598	162	17	)	)	PUNCT
ejpam-6598	162	18	>	>	PUNCT
ejpam-6598	162	19	.	.	PUNCT
ejpam-6598	163	1	here	here	ADV
ejpam-6598	163	2	ω	ω	NUM
ejpam-6598	163	3	∩	∩	PROPN
ejpam-6598	163	4	g	g	PROPN
ejpam-6598	163	5	̸=	̸=	PROPN
ejpam-6598	163	6	0∼.	0∼.	PROPN
ejpam-6598	163	7	thus	thus	ADV
ejpam-6598	163	8	,	,	PUNCT
ejpam-6598	163	9	(	(	PUNCT
ejpam-6598	163	10	ξ	ξ	X
ejpam-6598	163	11	,	,	PUNCT
ejpam-6598	163	12	τ	τ	PROPN
ejpam-6598	163	13	,	,	PUNCT
ejpam-6598	163	14	τ̂f	τ̂f	NUM
ejpam-6598	163	15	)	)	PUNCT
ejpam-6598	163	16	is	be	AUX
ejpam-6598	163	17	the	the	DET
ejpam-6598	163	18	pfdfts	pfdft	NOUN
ejpam-6598	163	19	produced	produce	VERB
ejpam-6598	163	20	by	by	ADP
ejpam-6598	163	21	the	the	DET
ejpam-6598	163	22	topology	topology	NOUN
ejpam-6598	163	23	τ	τ	PROPN
ejpam-6598	163	24	on	on	ADP
ejpam-6598	163	25	ξ	ξ	PROPN
ejpam-6598	163	26	,	,	PUNCT
ejpam-6598	163	27	and	and	CCONJ
ejpam-6598	163	28	τ̂f	τ̂f	PUNCT
ejpam-6598	163	29	=	=	SYM
ejpam-6598	163	30	{	{	PUNCT
ejpam-6598	163	31	0∼	0∼	NUM
ejpam-6598	163	32	,	,	PUNCT
ejpam-6598	163	33	1∼	1∼	NUM
ejpam-6598	163	34	,	,	PUNCT
ejpam-6598	163	35	g	g	NOUN
ejpam-6598	163	36	}	}	PUNCT
ejpam-6598	163	37	is	be	AUX
ejpam-6598	163	38	the	the	DET
ejpam-6598	163	39	pfdf	pfdf	ADJ
ejpam-6598	163	40	collections	collection	NOUN
ejpam-6598	163	41	of	of	ADP
ejpam-6598	163	42	subsets	subset	NOUN
ejpam-6598	163	43	of	of	ADP
ejpam-6598	163	44	ξ	ξ	PROPN
ejpam-6598	163	45	.	.	PUNCT
ejpam-6598	164	1	now	now	ADV
ejpam-6598	164	2	i(ω	i(ω	NUM
ejpam-6598	164	3	)	)	PUNCT
ejpam-6598	165	1	=	=	SYM
ejpam-6598	165	2	ω	ω	PROPN
ejpam-6598	165	3	;	;	PUNCT
ejpam-6598	165	4	c(i(ω	c(i(ω	PROPN
ejpam-6598	165	5	)	)	PUNCT
ejpam-6598	165	6	)	)	PUNCT
ejpam-6598	166	1	=	=	SYM
ejpam-6598	166	2	ωc	ωc	PROPN
ejpam-6598	166	3	and	and	CCONJ
ejpam-6598	166	4	c(ω	c(ω	NUM
ejpam-6598	166	5	)	)	PUNCT
ejpam-6598	166	6	=	=	SYM
ejpam-6598	166	7	ωc	ωc	X
ejpam-6598	166	8	;	;	PUNCT
ejpam-6598	166	9	i(c(ω	i(c(ω	NOUN
ejpam-6598	166	10	)	)	PUNCT
ejpam-6598	166	11	)	)	PUNCT
ejpam-6598	167	1	=	=	PUNCT
ejpam-6598	167	2	ω	ω	X
ejpam-6598	167	3	.	.	PUNCT
ejpam-6598	168	1	then	then	ADV
ejpam-6598	168	2	(	(	PUNCT
ejpam-6598	168	3	(	(	PUNCT
ejpam-6598	168	4	c(i(ω	c(i(ω	ADJ
ejpam-6598	168	5	)	)	PUNCT
ejpam-6598	168	6	∪	∪	NOUN
ejpam-6598	168	7	(	(	PUNCT
ejpam-6598	168	8	i(c(ω	i(c(ω	NOUN
ejpam-6598	168	9	)	)	PUNCT
ejpam-6598	168	10	)	)	PUNCT
ejpam-6598	168	11	)	)	PUNCT
ejpam-6598	169	1	=	=	SYM
ejpam-6598	169	2	ωc	ωc	INTJ
ejpam-6598	169	3	and	and	CCONJ
ejpam-6598	169	4	(	(	PUNCT
ejpam-6598	169	5	(	(	PUNCT
ejpam-6598	169	6	c(iω	c(iω	NOUN
ejpam-6598	169	7	)	)	PUNCT
ejpam-6598	169	8	)	)	PUNCT
ejpam-6598	169	9	∩	∩	NOUN
ejpam-6598	169	10	(	(	PUNCT
ejpam-6598	169	11	i(c(ω	i(c(ω	NOUN
ejpam-6598	169	12	)	)	PUNCT
ejpam-6598	169	13	)	)	PUNCT
ejpam-6598	169	14	)	)	PUNCT
ejpam-6598	170	1	=	=	PUNCT
ejpam-6598	170	2	ω	ω	X
ejpam-6598	170	3	.	.	PUNCT
ejpam-6598	171	1	so	so	ADV
ejpam-6598	171	2	ω	ω	PROPN
ejpam-6598	171	3	is	be	AUX
ejpam-6598	171	4	pfdb≈f	pfdb≈f	NUM
ejpam-6598	171	5	−	−	NOUN
ejpam-6598	171	6	cs	c	NOUN
ejpam-6598	171	7	and	and	CCONJ
ejpam-6598	171	8	ω	ω	PROPN
ejpam-6598	171	9	is	be	AUX
ejpam-6598	171	10	not	not	PART
ejpam-6598	171	11	pfdb≈f	pfdb≈f	ADJ
ejpam-6598	171	12	−os	−os	NOUN
ejpam-6598	171	13	.	.	PUNCT
ejpam-6598	172	1	hence	hence	ADV
ejpam-6598	172	2	(	(	PUNCT
ejpam-6598	172	3	ξ	ξ	PROPN
ejpam-6598	172	4	,	,	PUNCT
ejpam-6598	172	5	τ	τ	PROPN
ejpam-6598	172	6	,	,	PUNCT
ejpam-6598	172	7	τ̂f	τ̂f	NUM
ejpam-6598	172	8	)	)	PUNCT
ejpam-6598	172	9	is	be	AUX
ejpam-6598	172	10	a	a	DET
ejpam-6598	172	11	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	172	12	−ds	−ds	NOUN
ejpam-6598	172	13	.	.	PUNCT
ejpam-6598	173	1	definition	definition	NOUN
ejpam-6598	173	2	25	25	NUM
ejpam-6598	173	3	.	.	PUNCT
ejpam-6598	174	1	let	let	AUX
ejpam-6598	174	2	(	(	PUNCT
ejpam-6598	174	3	ξ	ξ	PROPN
ejpam-6598	174	4	,	,	PUNCT
ejpam-6598	174	5	τ	τ	PROPN
ejpam-6598	174	6	,	,	PUNCT
ejpam-6598	174	7	τ̂f	τ̂f	PUNCT
ejpam-6598	174	8	)	)	PUNCT
ejpam-6598	174	9	be	be	AUX
ejpam-6598	174	10	a	a	DET
ejpam-6598	174	11	pfdfts	pfdft	NOUN
ejpam-6598	174	12	and	and	CCONJ
ejpam-6598	174	13	let	let	VERB
ejpam-6598	174	14	ω	ω	NOUN
ejpam-6598	174	15	be	be	AUX
ejpam-6598	174	16	a	a	DET
ejpam-6598	174	17	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	174	18	set	set	VERB
ejpam-6598	174	19	in	in	ADP
ejpam-6598	174	20	(	(	PUNCT
ejpam-6598	174	21	ξ	ξ	PROPN
ejpam-6598	174	22	,	,	PUNCT
ejpam-6598	174	23	τ	τ	PROPN
ejpam-6598	174	24	,	,	PUNCT
ejpam-6598	174	25	τ̂f	τ̂f	NUM
ejpam-6598	174	26	)	)	PUNCT
ejpam-6598	174	27	.	.	PUNCT
ejpam-6598	175	1	if	if	SCONJ
ejpam-6598	175	2	there	there	PRON
ejpam-6598	175	3	is	be	VERB
ejpam-6598	175	4	no	no	DET
ejpam-6598	175	5	non	non	ADJ
ejpam-6598	175	6	-	-	ADJ
ejpam-6598	175	7	zero	zero	NUM
ejpam-6598	175	8	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	175	9	-os	-os	NOUN
ejpam-6598	175	10	ς	ς	PROPN
ejpam-6598	175	11	in	in	ADP
ejpam-6598	175	12	(	(	PUNCT
ejpam-6598	175	13	ξ	ξ	PROPN
ejpam-6598	175	14	,	,	PUNCT
ejpam-6598	175	15	τ	τ	PROPN
ejpam-6598	175	16	,	,	PUNCT
ejpam-6598	175	17	τ̂f	τ̂f	PUNCT
ejpam-6598	175	18	)	)	PUNCT
ejpam-6598	175	19	such	such	ADJ
ejpam-6598	175	20	that	that	SCONJ
ejpam-6598	175	21	ς	ς	PROPN
ejpam-6598	175	22	⊆	⊆	NUM
ejpam-6598	175	23	pfdb≈f	pfdb≈f	NUM
ejpam-6598	175	24	-c(ω	-c(ω	PROPN
ejpam-6598	175	25	)	)	PUNCT
ejpam-6598	175	26	,	,	PUNCT
ejpam-6598	175	27	then	then	ADV
ejpam-6598	175	28	ω	ω	PROPN
ejpam-6598	175	29	is	be	AUX
ejpam-6598	175	30	a	a	DET
ejpam-6598	175	31	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	175	32	−	−	NOUN
ejpam-6598	175	33	nowhere	nowhere	ADV
ejpam-6598	175	34	dense	dense	ADJ
ejpam-6598	175	35	set	set	NOUN
ejpam-6598	175	36	which	which	PRON
ejpam-6598	175	37	means	mean	VERB
ejpam-6598	175	38	that	that	SCONJ
ejpam-6598	176	1	pfdb≈f	pfdb≈f	PRON
ejpam-6598	176	2	−	−	NOUN
ejpam-6598	177	1	i	i	PRON
ejpam-6598	177	2	(	(	PUNCT
ejpam-6598	177	3	c(ω	c(ω	NOUN
ejpam-6598	177	4	)	)	PUNCT
ejpam-6598	177	5	)	)	PUNCT
ejpam-6598	178	1	=	=	PUNCT
ejpam-6598	178	2	0∼.	0∼.	NOUN
ejpam-6598	178	3	definition	definition	NOUN
ejpam-6598	178	4	26	26	NUM
ejpam-6598	178	5	.	.	PUNCT
ejpam-6598	179	1	if	if	SCONJ
ejpam-6598	179	2	ω	ω	PROPN
ejpam-6598	179	3	is	be	AUX
ejpam-6598	179	4	a	a	DET
ejpam-6598	179	5	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	179	6	nowhere	nowhere	ADV
ejpam-6598	179	7	dense	dense	ADJ
ejpam-6598	179	8	set	set	NOUN
ejpam-6598	179	9	in	in	ADP
ejpam-6598	179	10	a	a	DET
ejpam-6598	179	11	pfdfts	pfdft	NOUN
ejpam-6598	179	12	(	(	PUNCT
ejpam-6598	179	13	ξ	ξ	PROPN
ejpam-6598	179	14	,	,	PUNCT
ejpam-6598	179	15	τ	τ	PROPN
ejpam-6598	179	16	,	,	PUNCT
ejpam-6598	179	17	τ̂f	τ̂f	NUM
ejpam-6598	179	18	)	)	PUNCT
ejpam-6598	179	19	then	then	ADV
ejpam-6598	179	20	(	(	PUNCT
ejpam-6598	179	21	ξ	ξ	PROPN
ejpam-6598	179	22	,	,	PUNCT
ejpam-6598	179	23	τ	τ	PROPN
ejpam-6598	179	24	,	,	PUNCT
ejpam-6598	179	25	τ̂f	τ̂f	NUM
ejpam-6598	179	26	)	)	PUNCT
ejpam-6598	179	27	is	be	AUX
ejpam-6598	179	28	denoted	denote	VERB
ejpam-6598	179	29	as	as	ADP
ejpam-6598	179	30	a	a	DET
ejpam-6598	179	31	pfdb≈f	pfdb≈f	NUM
ejpam-6598	179	32	-baire	-baire	NOUN
ejpam-6598	179	33	space	space	NOUN
ejpam-6598	179	34	if	if	SCONJ
ejpam-6598	179	35	pfdb≈f	pfdb≈f	PRON
ejpam-6598	179	36	−	−	VERB
ejpam-6598	180	1	i	i	PRON
ejpam-6598	180	2	(	(	PUNCT
ejpam-6598	180	3	∪ωα	∪ωα	NOUN
ejpam-6598	180	4	)	)	PUNCT
ejpam-6598	180	5	=	=	PUNCT
ejpam-6598	181	1	0∼.	0∼.	NOUN
ejpam-6598	181	2	example	example	NOUN
ejpam-6598	181	3	2	2	X
ejpam-6598	181	4	.	.	PUNCT
ejpam-6598	182	1	let	let	VERB
ejpam-6598	182	2	ξ	ξ	X
ejpam-6598	182	3	=	=	SYM
ejpam-6598	182	4	{	{	PUNCT
ejpam-6598	182	5	l	l	NOUN
ejpam-6598	182	6	,	,	PUNCT
ejpam-6598	182	7	m	m	PROPN
ejpam-6598	182	8	,	,	PUNCT
ejpam-6598	182	9	n	n	CCONJ
ejpam-6598	182	10	}	}	PUNCT
ejpam-6598	182	11	be	be	AUX
ejpam-6598	182	12	a	a	DET
ejpam-6598	182	13	non	non	X
ejpam-6598	182	14	empty	empty	ADJ
ejpam-6598	182	15	set	set	NOUN
ejpam-6598	182	16	and	and	CCONJ
ejpam-6598	182	17	τ	τ	PROPN
ejpam-6598	182	18	=	=	PUNCT
ejpam-6598	182	19	{	{	PUNCT
ejpam-6598	182	20	0∼	0∼	NOUN
ejpam-6598	182	21	,	,	PUNCT
ejpam-6598	182	22	1∼,x	1∼,x	NUM
ejpam-6598	182	23	}	}	PUNCT
ejpam-6598	182	24	is	be	AUX
ejpam-6598	182	25	a	a	DET
ejpam-6598	182	26	pfdt	pfdt	NOUN
ejpam-6598	182	27	on	on	ADP
ejpam-6598	182	28	ξ	ξ	PROPN
ejpam-6598	183	1	where	where	SCONJ
ejpam-6598	183	2	0∼	0∼	X
ejpam-6598	183	3	=	=	PRON
ejpam-6598	183	4	{	{	PUNCT
ejpam-6598	183	5	<	<	X
ejpam-6598	183	6	0	0	NUM
ejpam-6598	183	7	,	,	PUNCT
ejpam-6598	183	8	1	1	NUM
ejpam-6598	183	9	>	>	PUNCT
ejpam-6598	183	10	,	,	PUNCT
ejpam-6598	183	11	<	<	X
ejpam-6598	183	12	0	0	NUM
ejpam-6598	183	13	,	,	PUNCT
ejpam-6598	183	14	1	1	NUM
ejpam-6598	183	15	>	>	PUNCT
ejpam-6598	183	16	,	,	PUNCT
ejpam-6598	183	17	<	<	X
ejpam-6598	183	18	0	0	NUM
ejpam-6598	183	19	,	,	PUNCT
ejpam-6598	183	20	1	1	NUM
ejpam-6598	183	21	>	>	PUNCT
ejpam-6598	183	22	}	}	PUNCT
ejpam-6598	183	23	,	,	PUNCT
ejpam-6598	183	24	1∼	1∼	X
ejpam-6598	183	25	=	=	SYM
ejpam-6598	183	26	{	{	PUNCT
ejpam-6598	183	27	<	<	X
ejpam-6598	183	28	1	1	NUM
ejpam-6598	183	29	,	,	PUNCT
ejpam-6598	183	30	0	0	NUM
ejpam-6598	183	31	>	>	PUNCT
ejpam-6598	183	32	,	,	PUNCT
ejpam-6598	183	33	<	<	X
ejpam-6598	183	34	1	1	NUM
ejpam-6598	183	35	,	,	PUNCT
ejpam-6598	183	36	0	0	NUM
ejpam-6598	183	37	>	>	PUNCT
ejpam-6598	183	38	,	,	PUNCT
ejpam-6598	183	39	<	<	X
ejpam-6598	183	40	1	1	NUM
ejpam-6598	183	41	,	,	PUNCT
ejpam-6598	183	42	0	0	NUM
ejpam-6598	183	43	>	>	PUNCT
ejpam-6598	183	44	}	}	PUNCT
ejpam-6598	183	45	,	,	PUNCT
ejpam-6598	183	46	and	and	CCONJ
ejpam-6598	183	47	ω	ω	X
ejpam-6598	183	48	=	=	X
ejpam-6598	183	49	<	<	X
ejpam-6598	183	50	n.	n.	NOUN
ejpam-6598	183	51	preethi	preethi	PROPN
ejpam-6598	183	52	,	,	PUNCT
ejpam-6598	183	53	g.	g.	PROPN
ejpam-6598	183	54	k.	k.	PROPN
ejpam-6598	183	55	revathi	revathi	PROPN
ejpam-6598	183	56	/	/	SYM
ejpam-6598	183	57	eur	eur	PROPN
ejpam-6598	183	58	.	.	PUNCT
ejpam-6598	184	1	j.	j.	PROPN
ejpam-6598	184	2	pure	pure	PROPN
ejpam-6598	184	3	appl	appl	PROPN
ejpam-6598	184	4	.	.	PROPN
ejpam-6598	184	5	math	math	PROPN
ejpam-6598	184	6	,	,	PUNCT
ejpam-6598	184	7	18	18	NUM
ejpam-6598	184	8	(	(	PUNCT
ejpam-6598	184	9	3	3	NUM
ejpam-6598	184	10	)	)	PUNCT
ejpam-6598	184	11	(	(	PUNCT
ejpam-6598	184	12	2025	2025	NUM
ejpam-6598	184	13	)	)	PUNCT
ejpam-6598	184	14	,	,	PUNCT
ejpam-6598	184	15	6598	6598	NUM
ejpam-6598	184	16	8	8	NUM
ejpam-6598	184	17	of	of	ADP
ejpam-6598	184	18	17	17	NUM
ejpam-6598	184	19	x	x	NOUN
ejpam-6598	184	20	,	,	PUNCT
ejpam-6598	184	21	(	(	PUNCT
ejpam-6598	184	22	l/0.6,m/0.6,n/0.6	l/0.6,m/0.6,n/0.6	PROPN
ejpam-6598	184	23	)	)	PUNCT
ejpam-6598	184	24	,	,	PUNCT
ejpam-6598	184	25	(	(	PUNCT
ejpam-6598	184	26	l/0.4,m/0.4,n/0.5	l/0.4,m/0.4,n/0.5	PROPN
ejpam-6598	184	27	)	)	PUNCT
ejpam-6598	184	28	>	>	PUNCT
ejpam-6598	184	29	.	.	PUNCT
ejpam-6598	185	1	consider	consider	VERB
ejpam-6598	185	2	g1	g1	NOUN
ejpam-6598	185	3	=	=	PRON
ejpam-6598	185	4	<	<	X
ejpam-6598	185	5	x	x	X
ejpam-6598	185	6	,	,	PUNCT
ejpam-6598	185	7	(	(	PUNCT
ejpam-6598	185	8	l/0.6,m/0.6,n/0.6	l/0.6,m/0.6,n/0.6	PROPN
ejpam-6598	185	9	)	)	PUNCT
ejpam-6598	185	10	,	,	PUNCT
ejpam-6598	185	11	(	(	PUNCT
ejpam-6598	185	12	l/0.5,m/0.5,n/0.5	l/0.5,m/0.5,n/0.5	NOUN
ejpam-6598	185	13	)	)	PUNCT
ejpam-6598	185	14	>	>	X
ejpam-6598	185	15	and	and	CCONJ
ejpam-6598	185	16	g2	g2	PROPN
ejpam-6598	186	1	=	=	SYM
ejpam-6598	186	2	<	<	X
ejpam-6598	186	3	x	x	X
ejpam-6598	186	4	,	,	PUNCT
ejpam-6598	186	5	(	(	PUNCT
ejpam-6598	186	6	l/0.4	l/0.4	X
ejpam-6598	186	7	,	,	PUNCT
ejpam-6598	186	8	m/0.4,n/0.5	m/0.4,n/0.5	NOUN
ejpam-6598	186	9	)	)	PUNCT
ejpam-6598	186	10	,	,	PUNCT
ejpam-6598	186	11	(	(	PUNCT
ejpam-6598	186	12	l/0.7	l/0.7	ADV
ejpam-6598	186	13	,	,	PUNCT
ejpam-6598	186	14	m/0.7	m/0.7	NOUN
ejpam-6598	186	15	,	,	PUNCT
ejpam-6598	186	16	n/0.6	n/0.6	PROPN
ejpam-6598	186	17	)	)	PUNCT
ejpam-6598	186	18	>	>	PUNCT
ejpam-6598	187	1	here	here	ADV
ejpam-6598	187	2	ω	ω	X
ejpam-6598	187	3	∩	∩	PROPN
ejpam-6598	187	4	g	g	PROPN
ejpam-6598	187	5	̸=	̸=	PROPN
ejpam-6598	187	6	0∼.	0∼.	VERB
ejpam-6598	187	7	the	the	DET
ejpam-6598	187	8	pfdf	pfdf	ADJ
ejpam-6598	187	9	collections	collection	NOUN
ejpam-6598	187	10	of	of	ADP
ejpam-6598	187	11	subsets	subset	NOUN
ejpam-6598	187	12	of	of	ADP
ejpam-6598	187	13	ξ	ξ	PROPN
ejpam-6598	187	14	are	be	AUX
ejpam-6598	187	15	thus	thus	ADV
ejpam-6598	187	16	denoted	denote	VERB
ejpam-6598	187	17	by	by	ADP
ejpam-6598	187	18	τ̂f	τ̂f	PUNCT
ejpam-6598	187	19	=	=	SYM
ejpam-6598	187	20	{	{	PUNCT
ejpam-6598	187	21	0∼	0∼	NUM
ejpam-6598	187	22	,	,	PUNCT
ejpam-6598	187	23	1∼	1∼	NUM
ejpam-6598	187	24	,	,	PUNCT
ejpam-6598	187	25	g1	g1	NOUN
ejpam-6598	187	26	∪g2	∪g2	VERB
ejpam-6598	187	27	}	}	PUNCT
ejpam-6598	187	28	,	,	PUNCT
ejpam-6598	187	29	and	and	CCONJ
ejpam-6598	187	30	the	the	DET
ejpam-6598	187	31	pfdfts	pfdft	NOUN
ejpam-6598	187	32	created	create	VERB
ejpam-6598	187	33	by	by	ADP
ejpam-6598	187	34	the	the	DET
ejpam-6598	187	35	topology	topology	NOUN
ejpam-6598	187	36	τ	τ	PROPN
ejpam-6598	187	37	on	on	ADP
ejpam-6598	187	38	ξ	ξ	PROPN
ejpam-6598	187	39	is	be	AUX
ejpam-6598	187	40	denoted	denote	VERB
ejpam-6598	187	41	by	by	ADP
ejpam-6598	187	42	(	(	PUNCT
ejpam-6598	187	43	ξ	ξ	PROPN
ejpam-6598	187	44	,	,	PUNCT
ejpam-6598	187	45	τ	τ	PROPN
ejpam-6598	187	46	,	,	PUNCT
ejpam-6598	187	47	τ̂f	τ̂f	NUM
ejpam-6598	187	48	)	)	PUNCT
ejpam-6598	187	49	.	.	PUNCT
ejpam-6598	188	1	now	now	ADV
ejpam-6598	188	2	pfdb≈f	pfdb≈f	PRON
ejpam-6598	188	3	−	−	NUM
ejpam-6598	188	4	i(c(ωc	i(c(ωc	NOUN
ejpam-6598	188	5	)	)	PUNCT
ejpam-6598	188	6	)	)	PUNCT
ejpam-6598	189	1	=	=	PUNCT
ejpam-6598	190	1	0∼	0∼	NUM
ejpam-6598	190	2	pfdb≈f	pfdb≈f	NUM
ejpam-6598	190	3	−	−	NOUN
ejpam-6598	190	4	i(c(g2	i(c(g2	NOUN
ejpam-6598	190	5	)	)	PUNCT
ejpam-6598	190	6	)	)	PUNCT
ejpam-6598	191	1	=	=	PUNCT
ejpam-6598	191	2	0∼	0∼	NUM
ejpam-6598	191	3	pfdb≈f	pfdb≈f	NUM
ejpam-6598	191	4	−	−	NOUN
ejpam-6598	191	5	i(c(g1	i(c(g1	NOUN
ejpam-6598	191	6	)	)	PUNCT
ejpam-6598	191	7	)	)	PUNCT
ejpam-6598	192	1	=	=	SYM
ejpam-6598	192	2	1∼	1∼	NUM
ejpam-6598	192	3	and	and	CCONJ
ejpam-6598	192	4	pfdb≈f	pfdb≈f	NUM
ejpam-6598	192	5	−	−	PROPN
ejpam-6598	192	6	i(c(ω	i(c(ω	NOUN
ejpam-6598	192	7	)	)	PUNCT
ejpam-6598	192	8	)	)	PUNCT
ejpam-6598	193	1	=	=	SYM
ejpam-6598	193	2	1∼.	1∼.	NOUN
ejpam-6598	193	3	so	so	ADV
ejpam-6598	193	4	here	here	ADV
ejpam-6598	193	5	ωc	ωc	INTJ
ejpam-6598	193	6	and	and	CCONJ
ejpam-6598	193	7	g2	g2	PROPN
ejpam-6598	193	8	are	be	AUX
ejpam-6598	193	9	pfdb≈f	pfdb≈f	PRON
ejpam-6598	193	10	nowhere	nowhere	ADV
ejpam-6598	193	11	dense	dense	ADJ
ejpam-6598	193	12	sets	set	NOUN
ejpam-6598	193	13	and	and	CCONJ
ejpam-6598	193	14	ω	ω	NUM
ejpam-6598	193	15	and	and	CCONJ
ejpam-6598	193	16	g1	g1	NOUN
ejpam-6598	193	17	are	be	AUX
ejpam-6598	193	18	not	not	PART
ejpam-6598	193	19	pfdb≈f	pfdb≈f	PRON
ejpam-6598	193	20	nowhere	nowhere	ADV
ejpam-6598	193	21	dense	dense	ADJ
ejpam-6598	193	22	sets	set	NOUN
ejpam-6598	193	23	.	.	PUNCT
ejpam-6598	194	1	now	now	ADV
ejpam-6598	195	1	pfdb≈f	pfdb≈f	PRON
ejpam-6598	195	2	−	−	NOUN
ejpam-6598	196	1	i	i	PRON
ejpam-6598	196	2	(	(	PUNCT
ejpam-6598	196	3	ωc	ωc	X
ejpam-6598	196	4	∪g2	∪g2	ADJ
ejpam-6598	196	5	)	)	PUNCT
ejpam-6598	196	6	=	=	SYM
ejpam-6598	197	1	0∼.	0∼.	NOUN
ejpam-6598	197	2	hence	hence	ADV
ejpam-6598	197	3	(	(	PUNCT
ejpam-6598	197	4	ξ	ξ	PROPN
ejpam-6598	197	5	,	,	PUNCT
ejpam-6598	197	6	τ	τ	PROPN
ejpam-6598	197	7	,	,	PUNCT
ejpam-6598	197	8	τ̂f	τ̂f	NUM
ejpam-6598	197	9	)	)	PUNCT
ejpam-6598	197	10	is	be	AUX
ejpam-6598	197	11	a	a	DET
ejpam-6598	197	12	pfd	pfd	NOUN
ejpam-6598	197	13	b≈f	b≈f	NOUN
ejpam-6598	197	14	-baire	-baire	PROPN
ejpam-6598	197	15	space	space	NOUN
ejpam-6598	197	16	.	.	PUNCT
ejpam-6598	198	1	definition	definition	NOUN
ejpam-6598	198	2	27	27	NUM
ejpam-6598	198	3	.	.	PUNCT
ejpam-6598	199	1	let	let	VERB
ejpam-6598	199	2	(	(	PUNCT
ejpam-6598	199	3	ξ	ξ	PROPN
ejpam-6598	199	4	,	,	PUNCT
ejpam-6598	199	5	τ	τ	PROPN
ejpam-6598	199	6	,	,	PUNCT
ejpam-6598	199	7	τ̂f	τ̂f	NUM
ejpam-6598	199	8	)	)	PUNCT
ejpam-6598	199	9	is	be	AUX
ejpam-6598	199	10	a	a	DET
ejpam-6598	199	11	pfdfts	pfdft	NOUN
ejpam-6598	199	12	,	,	PUNCT
ejpam-6598	199	13	then	then	ADV
ejpam-6598	199	14	(	(	PUNCT
ejpam-6598	199	15	ξ	ξ	PROPN
ejpam-6598	199	16	,	,	PUNCT
ejpam-6598	199	17	τ	τ	PROPN
ejpam-6598	199	18	,	,	PUNCT
ejpam-6598	199	19	τ̂f	τ̂f	NUM
ejpam-6598	199	20	)	)	PUNCT
ejpam-6598	199	21	is	be	AUX
ejpam-6598	199	22	called	call	VERB
ejpam-6598	199	23	a	a	DET
ejpam-6598	199	24	pfdb≈f	pfdb≈f	NUM
ejpam-6598	199	25	-submaximal	-submaximal	ADJ
ejpam-6598	199	26	space	space	NOUN
ejpam-6598	199	27	if	if	SCONJ
ejpam-6598	199	28	every	every	DET
ejpam-6598	199	29	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	199	30	dense	dense	ADJ
ejpam-6598	199	31	set	set	NOUN
ejpam-6598	199	32	is	be	AUX
ejpam-6598	199	33	a	a	DET
ejpam-6598	199	34	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	199	35	−os	−os	NOUN
ejpam-6598	199	36	in	in	ADP
ejpam-6598	199	37	(	(	PUNCT
ejpam-6598	199	38	ξ	ξ	PROPN
ejpam-6598	199	39	,	,	PUNCT
ejpam-6598	199	40	τ	τ	PROPN
ejpam-6598	199	41	,	,	PUNCT
ejpam-6598	199	42	τ̂f	τ̂f	NUM
ejpam-6598	199	43	)	)	PUNCT
ejpam-6598	199	44	definition	definition	NOUN
ejpam-6598	199	45	28	28	NUM
ejpam-6598	199	46	.	.	PUNCT
ejpam-6598	200	1	a	a	DET
ejpam-6598	200	2	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	200	3	set	set	VERB
ejpam-6598	200	4	ω	ω	PROPN
ejpam-6598	200	5	in	in	ADP
ejpam-6598	200	6	a	a	DET
ejpam-6598	200	7	pfdfts	pfdft	NOUN
ejpam-6598	200	8	(	(	PUNCT
ejpam-6598	200	9	ξ	ξ	PROPN
ejpam-6598	200	10	,	,	PUNCT
ejpam-6598	200	11	τ	τ	PROPN
ejpam-6598	200	12	,	,	PUNCT
ejpam-6598	200	13	τ̂f	τ̂f	NUM
ejpam-6598	200	14	)	)	PUNCT
ejpam-6598	200	15	is	be	AUX
ejpam-6598	200	16	said	say	VERB
ejpam-6598	200	17	to	to	PART
ejpam-6598	200	18	be	be	AUX
ejpam-6598	200	19	a	a	DET
ejpam-6598	200	20	pfdb≈f	pfdb≈f	NUM
ejpam-6598	200	21	-first	-first	NOUN
ejpam-6598	200	22	category	category	NOUN
ejpam-6598	200	23	if	if	SCONJ
ejpam-6598	200	24	(	(	PUNCT
ejpam-6598	200	25	∪∞	∪∞	X
ejpam-6598	200	26	n=1ωn	n=1ωn	NUM
ejpam-6598	200	27	)	)	PUNCT
ejpam-6598	200	28	=	=	SYM
ejpam-6598	200	29	ω	ω	X
ejpam-6598	200	30	.	.	PUNCT
ejpam-6598	200	31	here	here	ADV
ejpam-6598	200	32	ωn	ωn	ADP
ejpam-6598	200	33	implies	imply	VERB
ejpam-6598	200	34	that	that	SCONJ
ejpam-6598	200	35	the	the	DET
ejpam-6598	200	36	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	200	37	nowhere	nowhere	ADV
ejpam-6598	200	38	dense	dense	ADJ
ejpam-6598	200	39	set	set	NOUN
ejpam-6598	200	40	in	in	ADP
ejpam-6598	200	41	(	(	PUNCT
ejpam-6598	200	42	ξ	ξ	PROPN
ejpam-6598	200	43	,	,	PUNCT
ejpam-6598	200	44	τ	τ	PROPN
ejpam-6598	200	45	,	,	PUNCT
ejpam-6598	200	46	τ̂f	τ̂f	NUM
ejpam-6598	200	47	)	)	PUNCT
ejpam-6598	200	48	.	.	PUNCT
ejpam-6598	201	1	a	a	DET
ejpam-6598	201	2	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	201	3	set	set	VERB
ejpam-6598	201	4	ω	ω	PROPN
ejpam-6598	201	5	in	in	ADP
ejpam-6598	201	6	a	a	DET
ejpam-6598	201	7	pfdfts	pfdft	NOUN
ejpam-6598	201	8	(	(	PUNCT
ejpam-6598	201	9	ξ	ξ	PROPN
ejpam-6598	201	10	,	,	PUNCT
ejpam-6598	201	11	τ	τ	PROPN
ejpam-6598	201	12	,	,	PUNCT
ejpam-6598	201	13	τ̂f	τ̂f	PUNCT
ejpam-6598	201	14	)	)	PUNCT
ejpam-6598	201	15	which	which	PRON
ejpam-6598	201	16	is	be	AUX
ejpam-6598	201	17	not	not	PART
ejpam-6598	201	18	of	of	ADP
ejpam-6598	201	19	the	the	DET
ejpam-6598	201	20	pfdb≈f	pfdb≈f	NUM
ejpam-6598	201	21	-first	-first	NOUN
ejpam-6598	201	22	category	category	NOUN
ejpam-6598	201	23	,	,	PUNCT
ejpam-6598	201	24	is	be	AUX
ejpam-6598	201	25	said	say	VERB
ejpam-6598	201	26	to	to	PART
ejpam-6598	201	27	be	be	AUX
ejpam-6598	201	28	of	of	ADP
ejpam-6598	201	29	the	the	DET
ejpam-6598	201	30	pfdb≈f	pfdb≈f	NUM
ejpam-6598	201	31	-second	-second	NOUN
ejpam-6598	201	32	category	category	NOUN
ejpam-6598	201	33	.	.	PUNCT
ejpam-6598	202	1	definition	definition	NOUN
ejpam-6598	202	2	29	29	NUM
ejpam-6598	202	3	.	.	PUNCT
ejpam-6598	203	1	apfdfts	apfdft	NOUN
ejpam-6598	203	2	(	(	PUNCT
ejpam-6598	203	3	ξ	ξ	PROPN
ejpam-6598	203	4	,	,	PUNCT
ejpam-6598	203	5	τ	τ	PROPN
ejpam-6598	203	6	,	,	PUNCT
ejpam-6598	203	7	τ̂f	τ̂f	NUM
ejpam-6598	203	8	)	)	PUNCT
ejpam-6598	203	9	is	be	AUX
ejpam-6598	203	10	said	say	VERB
ejpam-6598	203	11	to	to	PART
ejpam-6598	203	12	be	be	AUX
ejpam-6598	203	13	a	a	DET
ejpam-6598	203	14	pfd	pfd	NOUN
ejpam-6598	203	15	b≈f	b≈f	NOUN
ejpam-6598	203	16	-first	-first	ADJ
ejpam-6598	203	17	category	category	NOUN
ejpam-6598	203	18	space	space	NOUN
ejpam-6598	203	19	if	if	SCONJ
ejpam-6598	203	20	(	(	PUNCT
ejpam-6598	203	21	∪∞	∪∞	X
ejpam-6598	203	22	n=1ωn	n=1ωn	NUM
ejpam-6598	203	23	)	)	PUNCT
ejpam-6598	203	24	=	=	SYM
ejpam-6598	203	25	1∼.	1∼.	NOUN
ejpam-6598	203	26	here	here	ADV
ejpam-6598	203	27	ωn	ωn	ADP
ejpam-6598	203	28	implies	imply	VERB
ejpam-6598	203	29	that	that	SCONJ
ejpam-6598	203	30	the	the	DET
ejpam-6598	203	31	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	203	32	−	−	PROPN
ejpam-6598	203	33	nowhere	nowhere	ADV
ejpam-6598	203	34	dense	dense	ADJ
ejpam-6598	203	35	set	set	NOUN
ejpam-6598	203	36	in	in	ADP
ejpam-6598	203	37	(	(	PUNCT
ejpam-6598	203	38	ξ	ξ	PROPN
ejpam-6598	203	39	,	,	PUNCT
ejpam-6598	203	40	τ	τ	PROPN
ejpam-6598	203	41	,	,	PUNCT
ejpam-6598	203	42	τ̂f	τ̂f	NUM
ejpam-6598	203	43	)	)	PUNCT
ejpam-6598	203	44	if	if	SCONJ
ejpam-6598	203	45	pfdfts	pfdft	NOUN
ejpam-6598	203	46	(	(	PUNCT
ejpam-6598	203	47	ξ	ξ	PROPN
ejpam-6598	203	48	,	,	PUNCT
ejpam-6598	203	49	τ	τ	PROPN
ejpam-6598	203	50	,	,	PUNCT
ejpam-6598	203	51	τ̂f	τ̂f	NUM
ejpam-6598	203	52	)	)	PUNCT
ejpam-6598	203	53	is	be	AUX
ejpam-6598	203	54	not	not	PART
ejpam-6598	203	55	the	the	DET
ejpam-6598	203	56	pfdb≈f	pfdb≈f	NUM
ejpam-6598	203	57	-first	-first	NOUN
ejpam-6598	203	58	category	category	NOUN
ejpam-6598	203	59	,	,	PUNCT
ejpam-6598	203	60	then	then	ADV
ejpam-6598	203	61	pfdfts	pfdft	NOUN
ejpam-6598	203	62	(	(	PUNCT
ejpam-6598	203	63	ξ	ξ	PROPN
ejpam-6598	203	64	,	,	PUNCT
ejpam-6598	203	65	τ	τ	PROPN
ejpam-6598	203	66	,	,	PUNCT
ejpam-6598	203	67	τ̂f	τ̂f	NUM
ejpam-6598	203	68	)	)	PUNCT
ejpam-6598	203	69	is	be	AUX
ejpam-6598	203	70	the	the	DET
ejpam-6598	203	71	pfdb≈f	pfdb≈f	NUM
ejpam-6598	203	72	−	−	NOUN
ejpam-6598	203	73	second	second	ADJ
ejpam-6598	203	74	category	category	NOUN
ejpam-6598	203	75	space	space	NOUN
ejpam-6598	203	76	.	.	PUNCT
ejpam-6598	204	1	proposition	proposition	NOUN
ejpam-6598	204	2	1	1	NUM
ejpam-6598	204	3	.	.	PUNCT
ejpam-6598	205	1	every	every	PRON
ejpam-6598	205	2	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	205	3	−ds	−ds	NOUN
ejpam-6598	205	4	(	(	PUNCT
ejpam-6598	205	5	ξ	ξ	PROPN
ejpam-6598	205	6	,	,	PUNCT
ejpam-6598	205	7	τ	τ	PROPN
ejpam-6598	205	8	,	,	PUNCT
ejpam-6598	205	9	τ̂f	τ̂f	NUM
ejpam-6598	205	10	)	)	PUNCT
ejpam-6598	205	11	is	be	AUX
ejpam-6598	205	12	a	a	DET
ejpam-6598	205	13	pfdb≈f	pfdb≈f	NUM
ejpam-6598	205	14	-submaximal	-submaximal	ADJ
ejpam-6598	205	15	space	space	NOUN
ejpam-6598	205	16	.	.	PUNCT
ejpam-6598	206	1	proof	proof	NOUN
ejpam-6598	206	2	.	.	PUNCT
ejpam-6598	207	1	consider	consider	VERB
ejpam-6598	207	2	a	a	DET
ejpam-6598	207	3	b≈f	b≈f	NOUN
ejpam-6598	207	4	-dense	-dense	NOUN
ejpam-6598	207	5	set	set	VERB
ejpam-6598	207	6	in	in	ADP
ejpam-6598	207	7	(	(	PUNCT
ejpam-6598	207	8	ξ	ξ	PROPN
ejpam-6598	207	9	,	,	PUNCT
ejpam-6598	207	10	τ	τ	PROPN
ejpam-6598	207	11	,	,	PUNCT
ejpam-6598	207	12	τ̂f	τ̂f	NUM
ejpam-6598	207	13	)	)	PUNCT
ejpam-6598	207	14	,	,	PUNCT
ejpam-6598	207	15	denoted	denote	VERB
ejpam-6598	207	16	by	by	ADP
ejpam-6598	207	17	ω	ω	PROPN
ejpam-6598	207	18	⊆	⊆	NUM
ejpam-6598	207	19	1∼.	1∼.	NUM
ejpam-6598	207	20	if	if	SCONJ
ejpam-6598	207	21	ω	ω	NOUN
ejpam-6598	207	22	is	be	AUX
ejpam-6598	207	23	not	not	PART
ejpam-6598	207	24	pfdb≈f	pfdb≈f	PRON
ejpam-6598	207	25	os	os	NOUN
ejpam-6598	207	26	then	then	ADV
ejpam-6598	207	27	ω	ω	PROPN
ejpam-6598	207	28	is	be	AUX
ejpam-6598	207	29	a	a	DET
ejpam-6598	207	30	pfdb≈f	pfdb≈f	NUM
ejpam-6598	207	31	−	−	NOUN
ejpam-6598	207	32	cs	cs	PROPN
ejpam-6598	207	33	since	since	SCONJ
ejpam-6598	207	34	(	(	PUNCT
ejpam-6598	207	35	ξ	ξ	PROPN
ejpam-6598	207	36	,	,	PUNCT
ejpam-6598	207	37	τ	τ	PROPN
ejpam-6598	207	38	,	,	PUNCT
ejpam-6598	207	39	τ̂f	τ̂f	NUM
ejpam-6598	207	40	)	)	PUNCT
ejpam-6598	207	41	is	be	AUX
ejpam-6598	207	42	a	a	DET
ejpam-6598	207	43	pfdb	pfdb	NOUN
ejpam-6598	207	44	≈	≈	PROPN
ejpam-6598	207	45	f	f	X
ejpam-6598	208	1	−ds	−ds	NOUN
ejpam-6598	208	2	.	.	PUNCT
ejpam-6598	209	1	then	then	ADV
ejpam-6598	209	2	ω	ω	X
ejpam-6598	209	3	=	=	SYM
ejpam-6598	209	4	ω̄	ω̄	ADP
ejpam-6598	209	5	=	=	NUM
ejpam-6598	209	6	1∼	1∼	NUM
ejpam-6598	209	7	and	and	CCONJ
ejpam-6598	209	8	ω	ω	PROPN
ejpam-6598	209	9	is	be	AUX
ejpam-6598	209	10	a	a	DET
ejpam-6598	209	11	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	209	12	−	−	NOUN
ejpam-6598	209	13	os	os	NOUN
ejpam-6598	209	14	(	(	PUNCT
ejpam-6598	209	15	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	209	16	−	−	PROPN
ejpam-6598	209	17	cs	cs	PROPN
ejpam-6598	209	18	)	)	PUNCT
ejpam-6598	209	19	.	.	PUNCT
ejpam-6598	210	1	therefore	therefore	ADV
ejpam-6598	210	2	(	(	PUNCT
ejpam-6598	210	3	ξ	ξ	PROPN
ejpam-6598	210	4	,	,	PUNCT
ejpam-6598	210	5	τ	τ	PROPN
ejpam-6598	210	6	,	,	PUNCT
ejpam-6598	210	7	τ̂f	τ̂f	NUM
ejpam-6598	210	8	)	)	PUNCT
ejpam-6598	210	9	is	be	AUX
ejpam-6598	210	10	a	a	DET
ejpam-6598	210	11	pfdb≈f	pfdb≈f	NUM
ejpam-6598	210	12	-submaximal	-submaximal	ADJ
ejpam-6598	210	13	space	space	NOUN
ejpam-6598	210	14	.	.	PUNCT
ejpam-6598	211	1	since	since	SCONJ
ejpam-6598	211	2	not	not	PART
ejpam-6598	211	3	all	all	PRON
ejpam-6598	211	4	pfdb≈f	pfdb≈f	PRON
ejpam-6598	211	5	−os	−os	NOUN
ejpam-6598	211	6	are	be	AUX
ejpam-6598	211	7	dense	dense	ADJ
ejpam-6598	211	8	,	,	PUNCT
ejpam-6598	211	9	with	with	ADP
ejpam-6598	211	10	the	the	DET
ejpam-6598	211	11	exception	exception	NOUN
ejpam-6598	211	12	of	of	ADP
ejpam-6598	211	13	1∼	1∼	NUM
ejpam-6598	211	14	,	,	PUNCT
ejpam-6598	211	15	the	the	DET
ejpam-6598	211	16	theorem	theorem	PROPN
ejpam-6598	211	17	’s	’s	PART
ejpam-6598	211	18	counterpart	counterpart	NOUN
ejpam-6598	211	19	need	need	AUX
ejpam-6598	211	20	not	not	PART
ejpam-6598	211	21	be	be	AUX
ejpam-6598	211	22	true	true	ADJ
ejpam-6598	211	23	.	.	PUNCT
ejpam-6598	212	1	proposition	proposition	NOUN
ejpam-6598	212	2	2	2	NUM
ejpam-6598	212	3	.	.	PUNCT
ejpam-6598	213	1	pfdb≈f	pfdb≈f	PRON
ejpam-6598	213	2	−	−	PROPN
ejpam-6598	213	3	cs	cs	PROPN
ejpam-6598	213	4	in	in	ADP
ejpam-6598	213	5	(	(	PUNCT
ejpam-6598	213	6	ξ	ξ	PROPN
ejpam-6598	213	7	,	,	PUNCT
ejpam-6598	213	8	τ	τ	PROPN
ejpam-6598	213	9	,	,	PUNCT
ejpam-6598	213	10	τ̂f	τ̂f	NUM
ejpam-6598	213	11	)	)	PUNCT
ejpam-6598	213	12	with	with	ADP
ejpam-6598	213	13	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	213	14	−	−	NOUN
ejpam-6598	213	15	i(ω	i(ω	NOUN
ejpam-6598	213	16	)	)	PUNCT
ejpam-6598	213	17	=	=	PUNCT
ejpam-6598	214	1	0∼	0∼	NUM
ejpam-6598	214	2	implies	imply	VERB
ejpam-6598	214	3	that	that	SCONJ
ejpam-6598	214	4	ω	ω	PROPN
ejpam-6598	214	5	is	be	AUX
ejpam-6598	214	6	a	a	DET
ejpam-6598	214	7	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	214	8	nowhere	nowhere	ADV
ejpam-6598	214	9	dense	dense	ADJ
ejpam-6598	214	10	set	set	NOUN
ejpam-6598	214	11	in	in	ADP
ejpam-6598	214	12	(	(	PUNCT
ejpam-6598	214	13	ξ	ξ	PROPN
ejpam-6598	214	14	,	,	PUNCT
ejpam-6598	214	15	τ	τ	PROPN
ejpam-6598	214	16	,	,	PUNCT
ejpam-6598	214	17	τ̂f	τ̂f	NUM
ejpam-6598	214	18	)	)	PUNCT
ejpam-6598	214	19	.	.	PUNCT
ejpam-6598	215	1	proof	proof	NOUN
ejpam-6598	215	2	.	.	PUNCT
ejpam-6598	216	1	if	if	SCONJ
ejpam-6598	216	2	ω	ω	PROPN
ejpam-6598	216	3	is	be	AUX
ejpam-6598	216	4	a	a	DET
ejpam-6598	216	5	pfdb≈f	pfdb≈f	NUM
ejpam-6598	216	6	−	−	NOUN
ejpam-6598	216	7	cs	cs	PROPN
ejpam-6598	216	8	in	in	ADP
ejpam-6598	216	9	(	(	PUNCT
ejpam-6598	216	10	ξ	ξ	PROPN
ejpam-6598	216	11	,	,	PUNCT
ejpam-6598	216	12	τ	τ	PROPN
ejpam-6598	216	13	,	,	PUNCT
ejpam-6598	216	14	τ̂f	τ̂f	NUM
ejpam-6598	216	15	)	)	PUNCT
ejpam-6598	216	16	with	with	ADP
ejpam-6598	216	17	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	216	18	−	−	NOUN
ejpam-6598	216	19	i(ω	i(ω	NOUN
ejpam-6598	216	20	)	)	PUNCT
ejpam-6598	216	21	=	=	SYM
ejpam-6598	216	22	0∼	0∼	NOUN
ejpam-6598	216	23	,	,	PUNCT
ejpam-6598	216	24	in	in	ADP
ejpam-6598	216	25	(	(	PUNCT
ejpam-6598	216	26	ξ	ξ	PROPN
ejpam-6598	216	27	,	,	PUNCT
ejpam-6598	216	28	τ	τ	PROPN
ejpam-6598	216	29	,	,	PUNCT
ejpam-6598	216	30	τ̂f	τ̂f	NUM
ejpam-6598	216	31	)	)	PUNCT
ejpam-6598	216	32	.	.	PUNCT
ejpam-6598	217	1	then	then	ADV
ejpam-6598	217	2	,	,	PUNCT
ejpam-6598	217	3	pfdb≈f	pfdb≈f	PRON
ejpam-6598	217	4	−	−	PROPN
ejpam-6598	217	5	c(ω	c(ω	PROPN
ejpam-6598	217	6	)	)	PUNCT
ejpam-6598	217	7	=	=	SYM
ejpam-6598	217	8	ω	ω	X
ejpam-6598	217	9	.	.	PUNCT
ejpam-6598	218	1	so	so	ADV
ejpam-6598	219	1	pfdb≈f	pfdb≈f	PRON
ejpam-6598	219	2	−	−	PROPN
ejpam-6598	220	1	i	i	PRON
ejpam-6598	220	2	(	(	PUNCT
ejpam-6598	220	3	c(ω	c(ω	NOUN
ejpam-6598	220	4	)	)	PUNCT
ejpam-6598	220	5	)	)	PUNCT
ejpam-6598	221	1	=	=	PUNCT
ejpam-6598	221	2	pfdb≈f	pfdb≈f	NUM
ejpam-6598	221	3	−	−	PROPN
ejpam-6598	221	4	i(ω	i(ω	NOUN
ejpam-6598	221	5	)	)	PUNCT
ejpam-6598	222	1	=	=	SYM
ejpam-6598	222	2	0∼	0∼	NOUN
ejpam-6598	222	3	,	,	PUNCT
ejpam-6598	222	4	in	in	ADP
ejpam-6598	222	5	(	(	PUNCT
ejpam-6598	222	6	ξ	ξ	PROPN
ejpam-6598	222	7	,	,	PUNCT
ejpam-6598	222	8	τ	τ	PROPN
ejpam-6598	222	9	,	,	PUNCT
ejpam-6598	222	10	τ̂f	τ̂f	NUM
ejpam-6598	222	11	)	)	PUNCT
ejpam-6598	222	12	.	.	PUNCT
ejpam-6598	223	1	hence	hence	ADV
ejpam-6598	223	2	ω	ω	PROPN
ejpam-6598	223	3	is	be	AUX
ejpam-6598	223	4	a	a	DET
ejpam-6598	223	5	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	223	6	nowhere	nowhere	ADV
ejpam-6598	223	7	dense	dense	ADJ
ejpam-6598	223	8	set	set	NOUN
ejpam-6598	223	9	in	in	ADP
ejpam-6598	223	10	(	(	PUNCT
ejpam-6598	223	11	ξ	ξ	PROPN
ejpam-6598	223	12	,	,	PUNCT
ejpam-6598	223	13	τ	τ	PROPN
ejpam-6598	223	14	,	,	PUNCT
ejpam-6598	223	15	τ̂f	τ̂f	NUM
ejpam-6598	223	16	)	)	PUNCT
ejpam-6598	223	17	.	.	PUNCT
ejpam-6598	224	1	the	the	DET
ejpam-6598	224	2	converse	converse	NOUN
ejpam-6598	224	3	of	of	ADP
ejpam-6598	224	4	the	the	DET
ejpam-6598	224	5	theorem	theorem	NOUN
ejpam-6598	224	6	does	do	AUX
ejpam-6598	224	7	not	not	PART
ejpam-6598	224	8	necessarily	necessarily	ADV
ejpam-6598	224	9	hold	hold	VERB
ejpam-6598	224	10	.	.	PUNCT
ejpam-6598	225	1	proposition	proposition	NOUN
ejpam-6598	225	2	3	3	NUM
ejpam-6598	225	3	.	.	PUNCT
ejpam-6598	226	1	every	every	DET
ejpam-6598	226	2	pfd	pfd	NOUN
ejpam-6598	226	3	subspace	subspace	NOUN
ejpam-6598	226	4	of	of	ADP
ejpam-6598	226	5	a	a	DET
ejpam-6598	226	6	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	226	7	−ds	−ds	NOUN
ejpam-6598	226	8	(	(	PUNCT
ejpam-6598	226	9	ξ	ξ	PROPN
ejpam-6598	226	10	,	,	PUNCT
ejpam-6598	226	11	τ	τ	PROPN
ejpam-6598	226	12	,	,	PUNCT
ejpam-6598	226	13	τ̂f	τ̂f	NUM
ejpam-6598	226	14	,	,	PUNCT
ejpam-6598	226	15	ψ	ψ	X
ejpam-6598	226	16	)	)	PUNCT
ejpam-6598	226	17	is	be	AUX
ejpam-6598	226	18	a	a	DET
ejpam-6598	226	19	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	226	20	−ds	−ds	NOUN
ejpam-6598	226	21	.	.	PUNCT
ejpam-6598	227	1	proof	proof	NOUN
ejpam-6598	227	2	.	.	PUNCT
ejpam-6598	228	1	if	if	SCONJ
ejpam-6598	228	2	(	(	PUNCT
ejpam-6598	228	3	g	g	NOUN
ejpam-6598	228	4	,	,	PUNCT
ejpam-6598	228	5	τ	τ	PROPN
ejpam-6598	228	6	,	,	PUNCT
ejpam-6598	228	7	τ̂f	τ̂f	PUNCT
ejpam-6598	228	8	,	,	PUNCT
ejpam-6598	228	9	ψg	ψg	X
ejpam-6598	228	10	)	)	PUNCT
ejpam-6598	228	11	is	be	AUX
ejpam-6598	228	12	a	a	DET
ejpam-6598	228	13	subspace	subspace	NOUN
ejpam-6598	228	14	of	of	ADP
ejpam-6598	228	15	a	a	DET
ejpam-6598	228	16	pfd	pfd	NOUN
ejpam-6598	229	1	b≈f	b≈f	PROPN
ejpam-6598	229	2	−ds	−ds	PROPN
ejpam-6598	229	3	(	(	PUNCT
ejpam-6598	229	4	ξ	ξ	PROPN
ejpam-6598	229	5	,	,	PUNCT
ejpam-6598	229	6	τ	τ	PROPN
ejpam-6598	229	7	,	,	PUNCT
ejpam-6598	229	8	τ̂f	τ̂f	NUM
ejpam-6598	229	9	,	,	PUNCT
ejpam-6598	229	10	ψ	ψ	X
ejpam-6598	229	11	)	)	PUNCT
ejpam-6598	229	12	,	,	PUNCT
ejpam-6598	229	13	implies	imply	VERB
ejpam-6598	229	14	g	g	PROPN
ejpam-6598	229	15	⊂	⊂	PROPN
ejpam-6598	229	16	ξ	ξ	PROPN
ejpam-6598	229	17	.	.	PUNCT
ejpam-6598	230	1	let	let	VERB
ejpam-6598	230	2	ω	ω	PROPN
ejpam-6598	230	3	⊂	⊂	PROPN
ejpam-6598	230	4	g	g	PROPN
ejpam-6598	230	5	,	,	PUNCT
ejpam-6598	230	6	since	since	SCONJ
ejpam-6598	230	7	(	(	PUNCT
ejpam-6598	230	8	ξ	ξ	PROPN
ejpam-6598	230	9	,	,	PUNCT
ejpam-6598	230	10	τ	τ	PROPN
ejpam-6598	230	11	,	,	PUNCT
ejpam-6598	230	12	τ̂f	τ̂f	NUM
ejpam-6598	230	13	,	,	PUNCT
ejpam-6598	230	14	ψ	ψ	X
ejpam-6598	230	15	)	)	PUNCT
ejpam-6598	230	16	is	be	AUX
ejpam-6598	230	17	a	a	DET
ejpam-6598	230	18	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	230	19	−	−	NOUN
ejpam-6598	230	20	ds	ds	NOUN
ejpam-6598	230	21	,	,	PUNCT
ejpam-6598	230	22	then	then	ADV
ejpam-6598	230	23	ω	ω	PROPN
ejpam-6598	230	24	is	be	AUX
ejpam-6598	230	25	either	either	PRON
ejpam-6598	230	26	pfdb≈f	pfdb≈f	PRON
ejpam-6598	230	27	−	−	PROPN
ejpam-6598	231	1	os	os	NOUN
ejpam-6598	232	1	or	or	CCONJ
ejpam-6598	232	2	pfdb≈f	pfdb≈f	PRON
ejpam-6598	232	3	−	−	PROPN
ejpam-6598	232	4	cs	cs	PROPN
ejpam-6598	232	5	in	in	ADP
ejpam-6598	232	6	(	(	PUNCT
ejpam-6598	232	7	ξ	ξ	PROPN
ejpam-6598	232	8	,	,	PUNCT
ejpam-6598	232	9	τ	τ	PROPN
ejpam-6598	232	10	,	,	PUNCT
ejpam-6598	232	11	τ̂f	τ̂f	NUM
ejpam-6598	232	12	,	,	PUNCT
ejpam-6598	232	13	ψ	ψ	X
ejpam-6598	232	14	)	)	PUNCT
ejpam-6598	232	15	and	and	CCONJ
ejpam-6598	232	16	hence	hence	ADV
ejpam-6598	232	17	in	in	ADV
ejpam-6598	232	18	(	(	PUNCT
ejpam-6598	232	19	g	g	PROPN
ejpam-6598	232	20	,	,	PUNCT
ejpam-6598	232	21	τ	τ	PROPN
ejpam-6598	232	22	,	,	PUNCT
ejpam-6598	232	23	τ̂f	τ̂f	PUNCT
ejpam-6598	232	24	,	,	PUNCT
ejpam-6598	232	25	ψg	ψg	PROPN
ejpam-6598	232	26	)	)	PUNCT
ejpam-6598	232	27	.	.	PUNCT
ejpam-6598	233	1	therefore	therefore	ADV
ejpam-6598	233	2	,	,	PUNCT
ejpam-6598	233	3	(	(	PUNCT
ejpam-6598	233	4	g	g	PROPN
ejpam-6598	233	5	,	,	PUNCT
ejpam-6598	233	6	τ	τ	PROPN
ejpam-6598	233	7	,	,	PUNCT
ejpam-6598	233	8	τ̂f	τ̂f	PUNCT
ejpam-6598	233	9	,	,	PUNCT
ejpam-6598	233	10	ψg	ψg	X
ejpam-6598	233	11	)	)	PUNCT
ejpam-6598	233	12	is	be	AUX
ejpam-6598	233	13	a	a	DET
ejpam-6598	233	14	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	233	15	−ds	−ds	NOUN
ejpam-6598	233	16	.	.	PUNCT
ejpam-6598	234	1	n.	n.	PROPN
ejpam-6598	234	2	preethi	preethi	PROPN
ejpam-6598	234	3	,	,	PUNCT
ejpam-6598	234	4	g.	g.	PROPN
ejpam-6598	234	5	k.	k.	PROPN
ejpam-6598	234	6	revathi	revathi	PROPN
ejpam-6598	234	7	/	/	SYM
ejpam-6598	234	8	eur	eur	PROPN
ejpam-6598	234	9	.	.	PUNCT
ejpam-6598	235	1	j.	j.	PROPN
ejpam-6598	235	2	pure	pure	PROPN
ejpam-6598	235	3	appl	appl	PROPN
ejpam-6598	235	4	.	.	PROPN
ejpam-6598	235	5	math	math	PROPN
ejpam-6598	235	6	,	,	PUNCT
ejpam-6598	235	7	18	18	NUM
ejpam-6598	235	8	(	(	PUNCT
ejpam-6598	235	9	3	3	NUM
ejpam-6598	235	10	)	)	PUNCT
ejpam-6598	235	11	(	(	PUNCT
ejpam-6598	235	12	2025	2025	NUM
ejpam-6598	235	13	)	)	PUNCT
ejpam-6598	235	14	,	,	PUNCT
ejpam-6598	235	15	6598	6598	NUM
ejpam-6598	235	16	9	9	NUM
ejpam-6598	235	17	of	of	ADP
ejpam-6598	235	18	17	17	NUM
ejpam-6598	235	19	definition	definition	NOUN
ejpam-6598	235	20	30	30	NUM
ejpam-6598	235	21	.	.	PUNCT
ejpam-6598	236	1	a	a	DET
ejpam-6598	236	2	pfd	pfd	PROPN
ejpam-6598	236	3	fts	fts	X
ejpam-6598	236	4	(	(	PUNCT
ejpam-6598	236	5	ξ	ξ	PROPN
ejpam-6598	236	6	,	,	PUNCT
ejpam-6598	236	7	τ	τ	PROPN
ejpam-6598	236	8	,	,	PUNCT
ejpam-6598	236	9	τ̂f	τ̂f	NUM
ejpam-6598	236	10	)	)	PUNCT
ejpam-6598	236	11	is	be	AUX
ejpam-6598	236	12	considered	consider	VERB
ejpam-6598	236	13	a	a	DET
ejpam-6598	236	14	pfd	pfd	NOUN
ejpam-6598	236	15	b≈f	b≈f	PROPN
ejpam-6598	236	16	d	d	NOUN
ejpam-6598	236	17	-	-	PUNCT
ejpam-6598	236	18	baire	baire	NOUN
ejpam-6598	236	19	space	space	NOUN
ejpam-6598	236	20	when	when	SCONJ
ejpam-6598	236	21	every	every	DET
ejpam-6598	236	22	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	236	23	-first	-first	NOUN
ejpam-6598	236	24	category	category	NOUN
ejpam-6598	236	25	set	set	VERB
ejpam-6598	236	26	ω	ω	PROPN
ejpam-6598	236	27	in	in	ADP
ejpam-6598	236	28	(	(	PUNCT
ejpam-6598	236	29	ξ	ξ	PROPN
ejpam-6598	236	30	,	,	PUNCT
ejpam-6598	236	31	τ	τ	PROPN
ejpam-6598	236	32	,	,	PUNCT
ejpam-6598	236	33	τ̂f	τ̂f	NUM
ejpam-6598	236	34	)	)	PUNCT
ejpam-6598	236	35	satisfies	satisfy	VERB
ejpam-6598	236	36	the	the	DET
ejpam-6598	236	37	condition	condition	NOUN
ejpam-6598	236	38	pfdb≈f	pfdb≈f	NUM
ejpam-6598	236	39	i(c(ω	i(c(ω	NOUN
ejpam-6598	236	40	)	)	PUNCT
ejpam-6598	236	41	)	)	PUNCT
ejpam-6598	237	1	=	=	PUNCT
ejpam-6598	237	2	0∼	0∼	NUM
ejpam-6598	237	3	;	;	PUNCT
ejpam-6598	237	4	that	that	PRON
ejpam-6598	237	5	is	is	ADV
ejpam-6598	237	6	,	,	PUNCT
ejpam-6598	237	7	all	all	DET
ejpam-6598	237	8	such	such	ADJ
ejpam-6598	237	9	sets	set	NOUN
ejpam-6598	237	10	are	be	AUX
ejpam-6598	237	11	pfdb≈f	pfdb≈f	PRON
ejpam-6598	237	12	nowhere	nowhere	ADV
ejpam-6598	237	13	dense	dense	ADJ
ejpam-6598	237	14	set	set	NOUN
ejpam-6598	237	15	in	in	ADP
ejpam-6598	237	16	(	(	PUNCT
ejpam-6598	237	17	ξ	ξ	PROPN
ejpam-6598	237	18	,	,	PUNCT
ejpam-6598	237	19	τ	τ	PROPN
ejpam-6598	237	20	,	,	PUNCT
ejpam-6598	237	21	τ̂f	τ̂f	NUM
ejpam-6598	237	22	)	)	PUNCT
ejpam-6598	237	23	.	.	PUNCT
ejpam-6598	238	1	proposition	proposition	NOUN
ejpam-6598	238	2	4	4	NUM
ejpam-6598	238	3	.	.	PUNCT
ejpam-6598	239	1	every	every	DET
ejpam-6598	239	2	pfdb≈f	pfdb≈f	NUM
ejpam-6598	239	3	baire	baire	NOUN
ejpam-6598	239	4	space	space	NOUN
ejpam-6598	239	5	in	in	ADP
ejpam-6598	239	6	(	(	PUNCT
ejpam-6598	239	7	ξ	ξ	PROPN
ejpam-6598	239	8	,	,	PUNCT
ejpam-6598	239	9	τ	τ	PROPN
ejpam-6598	239	10	,	,	PUNCT
ejpam-6598	239	11	τ̂f	τ̂f	NUM
ejpam-6598	239	12	)	)	PUNCT
ejpam-6598	239	13	is	be	AUX
ejpam-6598	239	14	a	a	DET
ejpam-6598	239	15	pfdb≈f	pfdb≈f	ADJ
ejpam-6598	239	16	d	d	NOUN
ejpam-6598	239	17	-	-	PUNCT
ejpam-6598	239	18	baire	baire	NOUN
ejpam-6598	239	19	space	space	NOUN
ejpam-6598	239	20	.	.	PUNCT
ejpam-6598	240	1	proof	proof	NOUN
ejpam-6598	240	2	.	.	PUNCT
ejpam-6598	241	1	suppose	suppose	VERB
ejpam-6598	241	2	that	that	SCONJ
ejpam-6598	241	3	ω	ω	PROPN
ejpam-6598	241	4	is	be	AUX
ejpam-6598	241	5	a	a	DET
ejpam-6598	241	6	pfdb≈f	pfdb≈f	NUM
ejpam-6598	241	7	first	first	ADJ
ejpam-6598	241	8	category	category	NOUN
ejpam-6598	241	9	set	set	VERB
ejpam-6598	241	10	in	in	ADP
ejpam-6598	241	11	a	a	DET
ejpam-6598	241	12	pfdb≈f	pfdb≈f	ADJ
ejpam-6598	241	13	d	d	ADJ
ejpam-6598	241	14	-	-	PUNCT
ejpam-6598	241	15	baire	baire	NOUN
ejpam-6598	241	16	space	space	NOUN
ejpam-6598	241	17	(	(	PUNCT
ejpam-6598	241	18	ξ	ξ	PROPN
ejpam-6598	241	19	,	,	PUNCT
ejpam-6598	241	20	τ	τ	PROPN
ejpam-6598	241	21	,	,	PUNCT
ejpam-6598	241	22	τ̂f	τ̂f	NUM
ejpam-6598	241	23	)	)	PUNCT
ejpam-6598	241	24	.	.	PUNCT
ejpam-6598	242	1	then	then	ADV
ejpam-6598	242	2	ω	ω	X
ejpam-6598	242	3	=	=	SYM
ejpam-6598	242	4	(	(	PUNCT
ejpam-6598	242	5	∪∞	∪∞	X
ejpam-6598	242	6	n=1ωn	n=1ωn	NUM
ejpam-6598	242	7	)	)	PUNCT
ejpam-6598	242	8	=	=	PUNCT
ejpam-6598	243	1	0∼	0∼	NUM
ejpam-6598	243	2	here	here	ADV
ejpam-6598	243	3	ω	ω	PROPN
ejpam-6598	243	4	and	and	CCONJ
ejpam-6598	243	5	ωn	ωn	PRON
ejpam-6598	243	6	are	be	AUX
ejpam-6598	243	7	pfdb≈f	pfdb≈f	PRON
ejpam-6598	243	8	-nowhere	-nowhere	ADJ
ejpam-6598	243	9	dense	dense	ADJ
ejpam-6598	243	10	sets	set	NOUN
ejpam-6598	243	11	in	in	ADP
ejpam-6598	243	12	(	(	PUNCT
ejpam-6598	243	13	ξ	ξ	PROPN
ejpam-6598	243	14	,	,	PUNCT
ejpam-6598	243	15	τ	τ	PROPN
ejpam-6598	243	16	,	,	PUNCT
ejpam-6598	243	17	τ̂f	τ̂f	NUM
ejpam-6598	243	18	)	)	PUNCT
ejpam-6598	243	19	.	.	PUNCT
ejpam-6598	244	1	so	so	ADV
ejpam-6598	244	2	,	,	PUNCT
ejpam-6598	244	3	pfdb	pfdb	NOUN
ejpam-6598	245	1	≈	≈	PROPN
ejpam-6598	245	2	f	f	PROPN
ejpam-6598	245	3	−	−	PROPN
ejpam-6598	245	4	i(c(ω	i(c(ω	NOUN
ejpam-6598	245	5	)	)	PUNCT
ejpam-6598	245	6	)	)	PUNCT
ejpam-6598	246	1	=	=	PUNCT
ejpam-6598	246	2	0∼	0∼	NOUN
ejpam-6598	246	3	,	,	PUNCT
ejpam-6598	246	4	and	and	CCONJ
ejpam-6598	246	5	pfdb	pfdb	VERB
ejpam-6598	246	6	≈	≈	PROPN
ejpam-6598	246	7	f	f	PROPN
ejpam-6598	247	1	−	−	PROPN
ejpam-6598	247	2	i(ω	i(ω	NUM
ejpam-6598	247	3	)	)	PUNCT
ejpam-6598	247	4	≤	≤	NUM
ejpam-6598	247	5	pfdb≈f	pfdb≈f	NUM
ejpam-6598	247	6	−	−	PROPN
ejpam-6598	247	7	i(c(ω	i(c(ω	NOUN
ejpam-6598	247	8	)	)	PUNCT
ejpam-6598	247	9	)	)	PUNCT
ejpam-6598	247	10	gives	give	VERB
ejpam-6598	247	11	that	that	DET
ejpam-6598	247	12	pfd	pfd	VERB
ejpam-6598	247	13	b≈f	b≈f	PROPN
ejpam-6598	247	14	−	−	PROPN
ejpam-6598	247	15	i(ω	i(ω	NOUN
ejpam-6598	247	16	)	)	PUNCT
ejpam-6598	248	1	=	=	PUNCT
ejpam-6598	248	2	0∼.	0∼.	NOUN
ejpam-6598	248	3	hence	hence	ADV
ejpam-6598	248	4	pfdb≈f	pfdb≈f	NUM
ejpam-6598	248	5	−	−	NOUN
ejpam-6598	249	1	i	i	PRON
ejpam-6598	249	2	(	(	PUNCT
ejpam-6598	249	3	∪∞	∪∞	X
ejpam-6598	249	4	n=1ωn	n=1ωn	NUM
ejpam-6598	249	5	)	)	PUNCT
ejpam-6598	249	6	=	=	PUNCT
ejpam-6598	250	1	0∼	0∼	NUM
ejpam-6598	250	2	where	where	SCONJ
ejpam-6598	250	3	ωn	ωn	PRON
ejpam-6598	250	4	implies	imply	VERB
ejpam-6598	250	5	pfdb≈f	pfdb≈f	PRON
ejpam-6598	250	6	nowhere	nowhere	ADV
ejpam-6598	250	7	dense	dense	ADJ
ejpam-6598	250	8	sets	set	NOUN
ejpam-6598	250	9	in	in	ADP
ejpam-6598	250	10	(	(	PUNCT
ejpam-6598	250	11	ξ	ξ	PROPN
ejpam-6598	250	12	,	,	PUNCT
ejpam-6598	250	13	τ	τ	PROPN
ejpam-6598	250	14	,	,	PUNCT
ejpam-6598	250	15	τ̂f	τ̂f	NUM
ejpam-6598	250	16	)	)	PUNCT
ejpam-6598	250	17	.	.	PUNCT
ejpam-6598	251	1	hence	hence	ADV
ejpam-6598	251	2	(	(	PUNCT
ejpam-6598	251	3	ξ	ξ	PROPN
ejpam-6598	251	4	,	,	PUNCT
ejpam-6598	251	5	τ	τ	PROPN
ejpam-6598	251	6	,	,	PUNCT
ejpam-6598	251	7	τ̂f	τ̂f	NUM
ejpam-6598	251	8	)	)	PUNCT
ejpam-6598	251	9	is	be	AUX
ejpam-6598	251	10	a	a	DET
ejpam-6598	251	11	pfdb≈f	pfdb≈f	NUM
ejpam-6598	251	12	baire	baire	NOUN
ejpam-6598	251	13	space	space	NOUN
ejpam-6598	251	14	.	.	PUNCT
ejpam-6598	252	1	proposition	proposition	NOUN
ejpam-6598	252	2	5	5	NUM
ejpam-6598	252	3	.	.	PUNCT
ejpam-6598	252	4	suppose	suppose	VERB
ejpam-6598	252	5	that	that	SCONJ
ejpam-6598	252	6	(	(	PUNCT
ejpam-6598	252	7	ξ	ξ	PROPN
ejpam-6598	252	8	,	,	PUNCT
ejpam-6598	252	9	τ	τ	PROPN
ejpam-6598	252	10	,	,	PUNCT
ejpam-6598	252	11	τ̂f	τ̂f	PUNCT
ejpam-6598	252	12	)	)	PUNCT
ejpam-6598	252	13	be	be	AUX
ejpam-6598	252	14	a	a	DET
ejpam-6598	252	15	pfdb≈f	pfdb≈f	NUM
ejpam-6598	252	16	-first	-first	NOUN
ejpam-6598	252	17	category	category	NOUN
ejpam-6598	252	18	space	space	NOUN
ejpam-6598	252	19	.	.	PUNCT
ejpam-6598	253	1	therefore	therefore	ADV
ejpam-6598	253	2	,	,	PUNCT
ejpam-6598	253	3	(	(	PUNCT
ejpam-6598	253	4	ξ	ξ	X
ejpam-6598	253	5	,	,	PUNCT
ejpam-6598	253	6	τ	τ	PROPN
ejpam-6598	253	7	,	,	PUNCT
ejpam-6598	253	8	τ̂f	τ̂f	NUM
ejpam-6598	253	9	)	)	PUNCT
ejpam-6598	253	10	is	be	AUX
ejpam-6598	253	11	not	not	PART
ejpam-6598	253	12	a	a	DET
ejpam-6598	253	13	pfdb≈f	pfdb≈f	ADJ
ejpam-6598	253	14	d	d	ADJ
ejpam-6598	253	15	-	-	PUNCT
ejpam-6598	253	16	baire	baire	NOUN
ejpam-6598	253	17	space	space	NOUN
ejpam-6598	253	18	.	.	PUNCT
ejpam-6598	254	1	proof	proof	NOUN
ejpam-6598	254	2	.	.	PUNCT
ejpam-6598	255	1	if	if	SCONJ
ejpam-6598	255	2	(	(	PUNCT
ejpam-6598	255	3	ξ	ξ	PROPN
ejpam-6598	255	4	,	,	PUNCT
ejpam-6598	255	5	τ	τ	PROPN
ejpam-6598	255	6	,	,	PUNCT
ejpam-6598	255	7	τ̂f	τ̂f	NUM
ejpam-6598	255	8	)	)	PUNCT
ejpam-6598	255	9	is	be	AUX
ejpam-6598	255	10	a	a	DET
ejpam-6598	255	11	pfdb≈f	pfdb≈f	NUM
ejpam-6598	255	12	-first	-first	NOUN
ejpam-6598	255	13	category	category	NOUN
ejpam-6598	255	14	space	space	NOUN
ejpam-6598	255	15	.	.	PUNCT
ejpam-6598	256	1	hence	hence	ADV
ejpam-6598	256	2	(	(	PUNCT
ejpam-6598	256	3	∪∞	∪∞	X
ejpam-6598	256	4	n=1ωn	n=1ωn	NUM
ejpam-6598	256	5	)	)	PUNCT
ejpam-6598	256	6	=	=	SYM
ejpam-6598	257	1	1∼.	1∼.	NOUN
ejpam-6598	257	2	here	here	ADV
ejpam-6598	257	3	ωn	ωn	ADP
ejpam-6598	257	4	implies	imply	VERB
ejpam-6598	257	5	pfdb≈f	pfdb≈f	NUM
ejpam-6598	257	6	-nowhere	-nowhere	ADJ
ejpam-6598	257	7	dense	dense	ADJ
ejpam-6598	257	8	sets	set	NOUN
ejpam-6598	257	9	in	in	ADP
ejpam-6598	257	10	(	(	PUNCT
ejpam-6598	257	11	ξ	ξ	PROPN
ejpam-6598	257	12	,	,	PUNCT
ejpam-6598	257	13	τ	τ	PROPN
ejpam-6598	257	14	,	,	PUNCT
ejpam-6598	257	15	τ̂f	τ̂f	NUM
ejpam-6598	257	16	)	)	PUNCT
ejpam-6598	257	17	.	.	PUNCT
ejpam-6598	258	1	we	we	PRON
ejpam-6598	258	2	obtain	obtain	VERB
ejpam-6598	258	3	pfdb≈f	pfdb≈f	PRON
ejpam-6598	258	4	-i	-i	PUNCT
ejpam-6598	259	1	(	(	PUNCT
ejpam-6598	259	2	c	c	X
ejpam-6598	259	3	(	(	PUNCT
ejpam-6598	259	4	1∼	1∼	NUM
ejpam-6598	259	5	)	)	PUNCT
ejpam-6598	259	6	)	)	PUNCT
ejpam-6598	260	1	=	=	PUNCT
ejpam-6598	260	2	0∼	0∼	NUM
ejpam-6598	260	3	for	for	ADP
ejpam-6598	260	4	the	the	DET
ejpam-6598	260	5	pfdb≈f	pfdb≈f	NUM
ejpam-6598	260	6	-first	-first	NOUN
ejpam-6598	260	7	category	category	NOUN
ejpam-6598	260	8	set	set	VERB
ejpam-6598	260	9	1∼.	1∼.	NUM
ejpam-6598	260	10	so	so	ADV
ejpam-6598	260	11	,	,	PUNCT
ejpam-6598	260	12	(	(	PUNCT
ejpam-6598	260	13	ξ	ξ	PROPN
ejpam-6598	260	14	,	,	PUNCT
ejpam-6598	260	15	τ	τ	PROPN
ejpam-6598	260	16	,	,	PUNCT
ejpam-6598	260	17	τ̂f	τ̂f	NUM
ejpam-6598	260	18	)	)	PUNCT
ejpam-6598	260	19	is	be	AUX
ejpam-6598	260	20	not	not	PART
ejpam-6598	260	21	a	a	DET
ejpam-6598	260	22	pfd	pfd	NOUN
ejpam-6598	260	23	b≈f	b≈f	PROPN
ejpam-6598	260	24	d	d	NOUN
ejpam-6598	260	25	-	-	PUNCT
ejpam-6598	260	26	baire	baire	NOUN
ejpam-6598	260	27	space	space	NOUN
ejpam-6598	260	28	.	.	PUNCT
ejpam-6598	261	1	definition	definition	NOUN
ejpam-6598	261	2	31	31	NUM
ejpam-6598	261	3	.	.	PUNCT
ejpam-6598	262	1	if	if	SCONJ
ejpam-6598	262	2	every	every	DET
ejpam-6598	262	3	pfdf	pfdf	NOUN
ejpam-6598	262	4	has	have	VERB
ejpam-6598	262	5	two	two	NUM
ejpam-6598	262	6	disjoint	disjoint	ADJ
ejpam-6598	262	7	points	point	NOUN
ejpam-6598	262	8	that	that	PRON
ejpam-6598	262	9	may	may	AUX
ejpam-6598	262	10	be	be	AUX
ejpam-6598	262	11	separated	separate	VERB
ejpam-6598	262	12	by	by	ADP
ejpam-6598	262	13	pfdb≈f	pfdb≈f	NUM
ejpam-6598	262	14	disjoint	disjoint	VERB
ejpam-6598	262	15	open	open	ADJ
ejpam-6598	262	16	sets	set	NOUN
ejpam-6598	262	17	,	,	PUNCT
ejpam-6598	262	18	then	then	ADV
ejpam-6598	262	19	a	a	DET
ejpam-6598	262	20	pfdfts	pfdft	NOUN
ejpam-6598	262	21	(	(	PUNCT
ejpam-6598	262	22	ξ	ξ	PROPN
ejpam-6598	262	23	,	,	PUNCT
ejpam-6598	262	24	τ	τ	PROPN
ejpam-6598	262	25	,	,	PUNCT
ejpam-6598	262	26	τ̂f	τ̂f	NUM
ejpam-6598	262	27	,	,	PUNCT
ejpam-6598	262	28	ψ	ψ	X
ejpam-6598	262	29	)	)	PUNCT
ejpam-6598	262	30	is	be	AUX
ejpam-6598	262	31	a	a	DET
ejpam-6598	262	32	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	262	33	-hausdorff	-hausdorff	NOUN
ejpam-6598	262	34	.	.	PUNCT
ejpam-6598	263	1	lemma	lemma	PROPN
ejpam-6598	263	2	1	1	NUM
ejpam-6598	263	3	.	.	PUNCT
ejpam-6598	263	4	given	give	VERB
ejpam-6598	263	5	k	k	PROPN
ejpam-6598	263	6	=	=	PUNCT
ejpam-6598	263	7	x(p	x(p	PROPN
ejpam-6598	263	8	,	,	PUNCT
ejpam-6598	263	9	q	q	X
ejpam-6598	263	10	)	)	PUNCT
ejpam-6598	263	11	is	be	AUX
ejpam-6598	263	12	a	a	DET
ejpam-6598	263	13	pfdfp	pfdfp	NOUN
ejpam-6598	263	14	in	in	ADP
ejpam-6598	263	15	(	(	PUNCT
ejpam-6598	263	16	e	e	NOUN
ejpam-6598	263	17	,	,	PUNCT
ejpam-6598	263	18	τ	τ	PROPN
ejpam-6598	263	19	,	,	PUNCT
ejpam-6598	263	20	τ̂f	τ̂f	NUM
ejpam-6598	263	21	,	,	PUNCT
ejpam-6598	263	22	ψ	ψ	NOUN
ejpam-6598	263	23	)	)	PUNCT
ejpam-6598	263	24	,	,	PUNCT
ejpam-6598	263	25	{	{	PUNCT
ejpam-6598	263	26	k	k	NOUN
ejpam-6598	263	27	}	}	PUNCT
ejpam-6598	263	28	will	will	AUX
ejpam-6598	263	29	only	only	ADV
ejpam-6598	263	30	be	be	AUX
ejpam-6598	263	31	considered	consider	VERB
ejpam-6598	263	32	a	a	DET
ejpam-6598	263	33	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	263	34	−os	−os	NOUN
ejpam-6598	263	35	if	if	SCONJ
ejpam-6598	263	36	it	it	PRON
ejpam-6598	263	37	is	be	AUX
ejpam-6598	263	38	a	a	DET
ejpam-6598	263	39	pfdf	pfdf	NOUN
ejpam-6598	263	40	open	open	ADJ
ejpam-6598	263	41	set	set	NOUN
ejpam-6598	263	42	.	.	PUNCT
ejpam-6598	264	1	lemma	lemma	PROPN
ejpam-6598	264	2	2	2	X
ejpam-6598	264	3	.	.	PUNCT
ejpam-6598	265	1	consider	consider	VERB
ejpam-6598	265	2	two	two	NUM
ejpam-6598	265	3	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	265	4	sets	set	VERB
ejpam-6598	265	5	f	f	PROPN
ejpam-6598	265	6	and	and	CCONJ
ejpam-6598	265	7	g	g	PROPN
ejpam-6598	265	8	in	in	ADP
ejpam-6598	265	9	(	(	PUNCT
ejpam-6598	265	10	ξ	ξ	PROPN
ejpam-6598	265	11	,	,	PUNCT
ejpam-6598	265	12	τ	τ	PROPN
ejpam-6598	265	13	,	,	PUNCT
ejpam-6598	265	14	τ̂f	τ̂f	NUM
ejpam-6598	265	15	,	,	PUNCT
ejpam-6598	265	16	ψ	ψ	NOUN
ejpam-6598	265	17	)	)	PUNCT
ejpam-6598	265	18	.	.	PUNCT
ejpam-6598	266	1	then	then	ADV
ejpam-6598	266	2	f	f	PROPN
ejpam-6598	266	3	∩g	∩g	PROPN
ejpam-6598	266	4	is	be	AUX
ejpam-6598	266	5	a	a	DET
ejpam-6598	266	6	pfdb≈f	pfdb≈f	NUM
ejpam-6598	266	7	os	os	NOUN
ejpam-6598	266	8	in	in	ADP
ejpam-6598	266	9	(	(	PUNCT
ejpam-6598	266	10	ξ	ξ	PROPN
ejpam-6598	266	11	,	,	PUNCT
ejpam-6598	266	12	τ	τ	PROPN
ejpam-6598	266	13	,	,	PUNCT
ejpam-6598	266	14	τ̂f	τ̂f	NUM
ejpam-6598	266	15	,	,	PUNCT
ejpam-6598	266	16	ψ	ψ	X
ejpam-6598	266	17	)	)	PUNCT
ejpam-6598	266	18	if	if	SCONJ
ejpam-6598	266	19	f	f	PROPN
ejpam-6598	266	20	is	be	AUX
ejpam-6598	266	21	a	a	DET
ejpam-6598	266	22	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	266	23	−os	−os	NOUN
ejpam-6598	266	24	and	and	CCONJ
ejpam-6598	266	25	f	f	PROPN
ejpam-6598	266	26	is	be	AUX
ejpam-6598	266	27	a	a	DET
ejpam-6598	266	28	pfdf	pfdf	NOUN
ejpam-6598	266	29	open	open	ADJ
ejpam-6598	266	30	set	set	NOUN
ejpam-6598	266	31	.	.	PUNCT
ejpam-6598	267	1	proposition	proposition	NOUN
ejpam-6598	267	2	6	6	NUM
ejpam-6598	267	3	.	.	PUNCT
ejpam-6598	268	1	only	only	ADV
ejpam-6598	268	2	one	one	NUM
ejpam-6598	268	3	limit	limit	NOUN
ejpam-6598	268	4	point	point	NOUN
ejpam-6598	268	5	exists	exist	VERB
ejpam-6598	268	6	for	for	ADP
ejpam-6598	268	7	a	a	DET
ejpam-6598	268	8	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	268	9	-hausdorff	-hausdorff	NOUN
ejpam-6598	268	10	ds	ds	NOUN
ejpam-6598	268	11	(	(	PUNCT
ejpam-6598	268	12	ξ	ξ	PROPN
ejpam-6598	268	13	,	,	PUNCT
ejpam-6598	268	14	τ	τ	PROPN
ejpam-6598	268	15	,	,	PUNCT
ejpam-6598	268	16	τ̂f	τ̂f	NUM
ejpam-6598	268	17	)	)	PUNCT
ejpam-6598	268	18	.	.	PUNCT
ejpam-6598	269	1	proof	proof	NOUN
ejpam-6598	269	2	.	.	PUNCT
ejpam-6598	270	1	consider	consider	VERB
ejpam-6598	270	2	two	two	NUM
ejpam-6598	270	3	pfdfps	pfdfps	NOUN
ejpam-6598	270	4	in	in	ADP
ejpam-6598	270	5	(	(	PUNCT
ejpam-6598	270	6	ξ	ξ	PROPN
ejpam-6598	270	7	,	,	PUNCT
ejpam-6598	270	8	τ	τ	PROPN
ejpam-6598	270	9	,	,	PUNCT
ejpam-6598	270	10	τ̂f	τ̂f	NUM
ejpam-6598	270	11	)	)	PUNCT
ejpam-6598	270	12	,	,	PUNCT
ejpam-6598	270	13	k	k	PROPN
ejpam-6598	270	14	=	=	SYM
ejpam-6598	270	15	x1(p	x1(p	PROPN
ejpam-6598	270	16	,	,	PUNCT
ejpam-6598	270	17	q	q	NOUN
ejpam-6598	270	18	)	)	PUNCT
ejpam-6598	270	19	and	and	CCONJ
ejpam-6598	270	20	l	l	NOUN
ejpam-6598	271	1	=	=	SYM
ejpam-6598	271	2	x2(u	x2(u	NUM
ejpam-6598	271	3	,	,	PUNCT
ejpam-6598	271	4	v	v	NOUN
ejpam-6598	271	5	)	)	PUNCT
ejpam-6598	271	6	.	.	PUNCT
ejpam-6598	272	1	since	since	SCONJ
ejpam-6598	272	2	(	(	PUNCT
ejpam-6598	272	3	ξ	ξ	PROPN
ejpam-6598	272	4	,	,	PUNCT
ejpam-6598	272	5	τ	τ	PROPN
ejpam-6598	272	6	,	,	PUNCT
ejpam-6598	272	7	τ̂f	τ̂f	NUM
ejpam-6598	272	8	)	)	PUNCT
ejpam-6598	272	9	is	be	AUX
ejpam-6598	272	10	a	a	DET
ejpam-6598	272	11	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	272	12	-hausdorff	-hausdorff	NOUN
ejpam-6598	272	13	,	,	PUNCT
ejpam-6598	272	14	two	two	NUM
ejpam-6598	272	15	pfdb≈f	pfdb≈f	PRON
ejpam-6598	272	16	−os	−os	NOUN
ejpam-6598	272	17	exist	exist	VERB
ejpam-6598	272	18	,	,	PUNCT
ejpam-6598	272	19	f	f	PROPN
ejpam-6598	272	20	and	and	CCONJ
ejpam-6598	272	21	g	g	PROPN
ejpam-6598	272	22	,	,	PUNCT
ejpam-6598	272	23	such	such	ADJ
ejpam-6598	272	24	that	that	SCONJ
ejpam-6598	272	25	k	k	PROPN
ejpam-6598	272	26	∈	∈	PROPN
ejpam-6598	272	27	f	f	X
ejpam-6598	272	28	,	,	PUNCT
ejpam-6598	272	29	l	l	PROPN
ejpam-6598	272	30	∈	∈	PROPN
ejpam-6598	272	31	g	g	NOUN
ejpam-6598	272	32	and	and	CCONJ
ejpam-6598	272	33	f∩g	f∩g	NOUN
ejpam-6598	272	34	=	=	NOUN
ejpam-6598	272	35	0∼.	0∼.	NOUN
ejpam-6598	272	36	since	since	SCONJ
ejpam-6598	272	37	(	(	PUNCT
ejpam-6598	272	38	ξ	ξ	PROPN
ejpam-6598	272	39	,	,	PUNCT
ejpam-6598	272	40	τ	τ	PROPN
ejpam-6598	272	41	,	,	PUNCT
ejpam-6598	272	42	τ̂f	τ̂f	NUM
ejpam-6598	272	43	,	,	PUNCT
ejpam-6598	272	44	ψ	ψ	X
ejpam-6598	272	45	)	)	PUNCT
ejpam-6598	272	46	is	be	AUX
ejpam-6598	272	47	a	a	DET
ejpam-6598	272	48	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	272	49	−ds	−ds	NOUN
ejpam-6598	272	50	,	,	PUNCT
ejpam-6598	272	51	ω	ω	PROPN
ejpam-6598	272	52	=	=	X
ejpam-6598	272	53	(	(	PUNCT
ejpam-6598	272	54	f\k)∪l	f\k)∪l	X
ejpam-6598	272	55	is	be	AUX
ejpam-6598	272	56	either	either	CCONJ
ejpam-6598	272	57	pfdb≈f	pfdb≈f	PRON
ejpam-6598	272	58	−os	−os	NOUN
ejpam-6598	272	59	or	or	CCONJ
ejpam-6598	272	60	pfdb≈f	pfdb≈f	PRON
ejpam-6598	272	61	−	−	PROPN
ejpam-6598	273	1	cs	cs	PROPN
ejpam-6598	273	2	.	.	PROPN
ejpam-6598	273	3	then	then	ADV
ejpam-6598	273	4	,	,	PUNCT
ejpam-6598	273	5	according	accord	VERB
ejpam-6598	273	6	to	to	ADP
ejpam-6598	273	7	lemma	lemma	PROPN
ejpam-6598	273	8	1	1	NUM
ejpam-6598	273	9	,	,	PUNCT
ejpam-6598	273	10	ω	ω	NOUN
ejpam-6598	273	11	∩	∩	ADJ
ejpam-6598	273	12	g	g	NOUN
ejpam-6598	273	13	=	=	SYM
ejpam-6598	273	14	{	{	PUNCT
ejpam-6598	273	15	l	l	NOUN
ejpam-6598	273	16	}	}	PUNCT
ejpam-6598	273	17	is	be	AUX
ejpam-6598	273	18	pfdb≈f	pfdb≈f	NUM
ejpam-6598	273	19	−	−	NOUN
ejpam-6598	273	20	os	os	NOUN
ejpam-6598	273	21	in	in	ADP
ejpam-6598	273	22	the	the	DET
ejpam-6598	273	23	preceding	precede	VERB
ejpam-6598	273	24	case	case	NOUN
ejpam-6598	273	25	,	,	PUNCT
ejpam-6598	273	26	and	and	CCONJ
ejpam-6598	273	27	according	accord	VERB
ejpam-6598	273	28	to	to	ADP
ejpam-6598	273	29	lemma	lemma	PROPN
ejpam-6598	273	30	2	2	NUM
ejpam-6598	273	31	,	,	PUNCT
ejpam-6598	273	32	it	it	PRON
ejpam-6598	273	33	is	be	AUX
ejpam-6598	273	34	pfd	pfd	NOUN
ejpam-6598	274	1	b≈f	b≈f	PROPN
ejpam-6598	274	2	−	−	PROPN
ejpam-6598	274	3	os	os	NOUN
ejpam-6598	274	4	.	.	PUNCT
ejpam-6598	275	1	in	in	ADP
ejpam-6598	275	2	the	the	DET
ejpam-6598	275	3	latter	latter	ADJ
ejpam-6598	275	4	instance	instance	NOUN
ejpam-6598	275	5	,	,	PUNCT
ejpam-6598	275	6	ωc	ωc	X
ejpam-6598	275	7	is	be	AUX
ejpam-6598	275	8	pfdb≈f	pfdb≈f	NUM
ejpam-6598	275	9	−os	−os	NUM
ejpam-6598	275	10	;	;	PUNCT
ejpam-6598	275	11	hence	hence	ADV
ejpam-6598	275	12	,	,	PUNCT
ejpam-6598	275	13	ωc	ωc	ADP
ejpam-6598	275	14	∩f	∩f	NOUN
ejpam-6598	275	15	=	=	PRON
ejpam-6598	275	16	{	{	PUNCT
ejpam-6598	275	17	k	k	NOUN
ejpam-6598	275	18	}	}	PUNCT
ejpam-6598	275	19	is	be	AUX
ejpam-6598	275	20	pfdb≈f	pfdb≈f	PRON
ejpam-6598	275	21	−os	−os	NOUN
ejpam-6598	275	22	and	and	CCONJ
ejpam-6598	275	23	consequently	consequently	ADV
ejpam-6598	275	24	,	,	PUNCT
ejpam-6598	275	25	pfdf	pfdf	NOUN
ejpam-6598	275	26	open	open	ADJ
ejpam-6598	275	27	set	set	PROPN
ejpam-6598	275	28	.	.	PUNCT
ejpam-6598	276	1	in	in	ADP
ejpam-6598	276	2	the	the	DET
ejpam-6598	276	3	second	second	ADJ
ejpam-6598	276	4	case	case	NOUN
ejpam-6598	276	5	,	,	PUNCT
ejpam-6598	276	6	ωc	ωc	X
ejpam-6598	276	7	is	be	AUX
ejpam-6598	276	8	pfd	pfd	VERB
ejpam-6598	276	9	b≈f	b≈f	PROPN
ejpam-6598	276	10	−	−	PROPN
ejpam-6598	276	11	os	os	NOUN
ejpam-6598	276	12	;	;	PUNCT
ejpam-6598	276	13	thus	thus	ADV
ejpam-6598	276	14	,	,	PUNCT
ejpam-6598	276	15	ωc	ωc	ADP
ejpam-6598	276	16	∩	∩	ADJ
ejpam-6598	276	17	f	f	X
ejpam-6598	276	18	=	=	PRON
ejpam-6598	276	19	{	{	PUNCT
ejpam-6598	276	20	k	k	NOUN
ejpam-6598	276	21	}	}	PUNCT
ejpam-6598	276	22	is	be	AUX
ejpam-6598	276	23	pfdb≈f	pfdb≈f	NUM
ejpam-6598	276	24	−	−	PROPN
ejpam-6598	277	1	os	os	NOUN
ejpam-6598	278	1	and	and	CCONJ
ejpam-6598	278	2	hence	hence	ADV
ejpam-6598	278	3	pfdf	pfdf	VERB
ejpam-6598	278	4	open	open	ADJ
ejpam-6598	278	5	set	set	NOUN
ejpam-6598	278	6	.	.	PUNCT
ejpam-6598	279	1	at	at	ADV
ejpam-6598	279	2	least	least	ADJ
ejpam-6598	279	3	one	one	NUM
ejpam-6598	279	4	of	of	ADP
ejpam-6598	279	5	the	the	DET
ejpam-6598	279	6	two	two	NUM
ejpam-6598	279	7	pfdfps	pfdfps	NOUN
ejpam-6598	279	8	in	in	ADP
ejpam-6598	279	9	(	(	PUNCT
ejpam-6598	279	10	ξ	ξ	PROPN
ejpam-6598	279	11	,	,	PUNCT
ejpam-6598	279	12	τ	τ	PROPN
ejpam-6598	279	13	,	,	PUNCT
ejpam-6598	279	14	τ̂f	τ̂f	NUM
ejpam-6598	279	15	)	)	PUNCT
ejpam-6598	279	16	is	be	AUX
ejpam-6598	279	17	therefore	therefore	ADV
ejpam-6598	279	18	an	an	DET
ejpam-6598	279	19	isolated	isolated	ADJ
ejpam-6598	279	20	pfdfp	pfdfp	NOUN
ejpam-6598	279	21	in	in	ADP
ejpam-6598	279	22	both	both	DET
ejpam-6598	279	23	situations	situation	NOUN
ejpam-6598	279	24	,	,	PUNCT
ejpam-6598	279	25	and	and	CCONJ
ejpam-6598	279	26	this	this	PRON
ejpam-6598	279	27	is	be	AUX
ejpam-6598	279	28	demonstrated	demonstrate	VERB
ejpam-6598	279	29	by	by	ADP
ejpam-6598	279	30	contradiction	contradiction	NOUN
ejpam-6598	279	31	.	.	PUNCT
ejpam-6598	280	1	definition	definition	NOUN
ejpam-6598	280	2	32	32	NUM
ejpam-6598	280	3	.	.	PUNCT
ejpam-6598	281	1	apfdfts	apfdft	NOUN
ejpam-6598	281	2	(	(	PUNCT
ejpam-6598	281	3	ξ	ξ	PROPN
ejpam-6598	281	4	,	,	PUNCT
ejpam-6598	281	5	τ	τ	PROPN
ejpam-6598	281	6	,	,	PUNCT
ejpam-6598	281	7	τ̂f	τ̂f	NUM
ejpam-6598	281	8	,	,	PUNCT
ejpam-6598	281	9	ψ	ψ	X
ejpam-6598	281	10	)	)	PUNCT
ejpam-6598	281	11	is	be	AUX
ejpam-6598	281	12	a	a	DET
ejpam-6598	281	13	pfdb≈f	pfdb≈f	NUM
ejpam-6598	281	14	−t1/2	−t1/2	NOUN
ejpam-6598	281	15	space	space	NOUN
ejpam-6598	281	16	if	if	SCONJ
ejpam-6598	281	17	every	every	DET
ejpam-6598	281	18	pfdfp	pfdfp	NOUN
ejpam-6598	281	19	{	{	PUNCT
ejpam-6598	281	20	k	k	NOUN
ejpam-6598	281	21	}	}	PUNCT
ejpam-6598	281	22	is	be	AUX
ejpam-6598	281	23	either	either	CCONJ
ejpam-6598	281	24	an	an	DET
ejpam-6598	281	25	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	281	26	−os	−os	NOUN
ejpam-6598	281	27	or	or	CCONJ
ejpam-6598	281	28	pfdb≈f	pfdb≈f	PRON
ejpam-6598	281	29	−	−	PROPN
ejpam-6598	281	30	cs	cs	PROPN
ejpam-6598	281	31	in	in	ADP
ejpam-6598	281	32	(	(	PUNCT
ejpam-6598	281	33	ξ	ξ	PROPN
ejpam-6598	281	34	,	,	PUNCT
ejpam-6598	281	35	τ	τ	PROPN
ejpam-6598	281	36	,	,	PUNCT
ejpam-6598	281	37	τ̂f	τ̂f	NUM
ejpam-6598	281	38	)	)	PUNCT
ejpam-6598	281	39	.	.	PUNCT
ejpam-6598	282	1	proposition	proposition	NOUN
ejpam-6598	282	2	7	7	NUM
ejpam-6598	282	3	.	.	PUNCT
ejpam-6598	283	1	every	every	DET
ejpam-6598	283	2	pfdfts	pfdft	NOUN
ejpam-6598	283	3	(	(	PUNCT
ejpam-6598	283	4	ξ	ξ	PROPN
ejpam-6598	283	5	,	,	PUNCT
ejpam-6598	283	6	τ	τ	PROPN
ejpam-6598	283	7	,	,	PUNCT
ejpam-6598	283	8	τ̂f	τ̂f	NUM
ejpam-6598	283	9	,	,	PUNCT
ejpam-6598	283	10	ψ	ψ	X
ejpam-6598	283	11	)	)	PUNCT
ejpam-6598	283	12	is	be	AUX
ejpam-6598	283	13	a	a	DET
ejpam-6598	283	14	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	283	15	−	−	NOUN
ejpam-6598	283	16	t1/2	t1/2	ADJ
ejpam-6598	283	17	space	space	NOUN
ejpam-6598	283	18	.	.	PUNCT
ejpam-6598	284	1	n.	n.	PROPN
ejpam-6598	284	2	preethi	preethi	PROPN
ejpam-6598	284	3	,	,	PUNCT
ejpam-6598	284	4	g.	g.	PROPN
ejpam-6598	284	5	k.	k.	PROPN
ejpam-6598	284	6	revathi	revathi	PROPN
ejpam-6598	284	7	/	/	SYM
ejpam-6598	284	8	eur	eur	PROPN
ejpam-6598	284	9	.	.	PUNCT
ejpam-6598	285	1	j.	j.	PROPN
ejpam-6598	285	2	pure	pure	PROPN
ejpam-6598	285	3	appl	appl	PROPN
ejpam-6598	285	4	.	.	PROPN
ejpam-6598	285	5	math	math	PROPN
ejpam-6598	285	6	,	,	PUNCT
ejpam-6598	285	7	18	18	NUM
ejpam-6598	285	8	(	(	PUNCT
ejpam-6598	285	9	3	3	NUM
ejpam-6598	285	10	)	)	PUNCT
ejpam-6598	285	11	(	(	PUNCT
ejpam-6598	285	12	2025	2025	NUM
ejpam-6598	285	13	)	)	PUNCT
ejpam-6598	285	14	,	,	PUNCT
ejpam-6598	285	15	6598	6598	NUM
ejpam-6598	285	16	10	10	NUM
ejpam-6598	285	17	of	of	ADP
ejpam-6598	285	18	17	17	NUM
ejpam-6598	285	19	proof	proof	NOUN
ejpam-6598	285	20	.	.	PUNCT
ejpam-6598	285	21	suppose	suppose	VERB
ejpam-6598	285	22	that	that	SCONJ
ejpam-6598	285	23	{	{	PUNCT
ejpam-6598	285	24	k	k	NOUN
ejpam-6598	285	25	}	}	PUNCT
ejpam-6598	285	26	is	be	AUX
ejpam-6598	285	27	a	a	DET
ejpam-6598	285	28	pfdfp	pfdfp	NOUN
ejpam-6598	285	29	in	in	ADP
ejpam-6598	285	30	(	(	PUNCT
ejpam-6598	285	31	ξ	ξ	PROPN
ejpam-6598	285	32	,	,	PUNCT
ejpam-6598	285	33	τ	τ	PROPN
ejpam-6598	285	34	,	,	PUNCT
ejpam-6598	285	35	τ̂f	τ̂f	NUM
ejpam-6598	285	36	)	)	PUNCT
ejpam-6598	285	37	.	.	PUNCT
ejpam-6598	286	1	given	give	VERB
ejpam-6598	286	2	that	that	SCONJ
ejpam-6598	286	3	all	all	DET
ejpam-6598	286	4	pfdf	pfdf	NOUN
ejpam-6598	286	5	-nowhere	-nowhere	ADJ
ejpam-6598	286	6	dense	dense	ADJ
ejpam-6598	286	7	sets	set	NOUN
ejpam-6598	286	8	are	be	AUX
ejpam-6598	286	9	pfdb≈f	pfdb≈f	PROPN
ejpam-6598	286	10	−cs	−cs	PROPN
ejpam-6598	286	11	,	,	PUNCT
ejpam-6598	286	12	{	{	PUNCT
ejpam-6598	286	13	k	k	X
ejpam-6598	286	14	}	}	PUNCT
ejpam-6598	286	15	is	be	AUX
ejpam-6598	286	16	either	either	CCONJ
ejpam-6598	286	17	a	a	DET
ejpam-6598	286	18	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	286	19	−os	−os	NOUN
ejpam-6598	286	20	or	or	CCONJ
ejpam-6598	286	21	a	a	DET
ejpam-6598	286	22	pfdf	pfdf	NOUN
ejpam-6598	286	23	-nowhere	-nowhere	ADJ
ejpam-6598	286	24	dense	dense	ADJ
ejpam-6598	286	25	set	set	NOUN
ejpam-6598	286	26	.	.	PUNCT
ejpam-6598	287	1	therefore	therefore	ADV
ejpam-6598	287	2	,	,	PUNCT
ejpam-6598	287	3	{	{	PUNCT
ejpam-6598	287	4	k	k	X
ejpam-6598	287	5	}	}	PUNCT
ejpam-6598	287	6	is	be	AUX
ejpam-6598	287	7	either	either	CCONJ
ejpam-6598	287	8	pfdb≈f	pfdb≈f	PRON
ejpam-6598	287	9	−os	−os	NOUN
ejpam-6598	287	10	or	or	CCONJ
ejpam-6598	287	11	pfdb≈f	pfdb≈f	NUM
ejpam-6598	287	12	−cs	−cs	PROPN
ejpam-6598	287	13	.	.	PUNCT
ejpam-6598	288	1	hence	hence	ADV
ejpam-6598	288	2	(	(	PUNCT
ejpam-6598	288	3	ξ	ξ	PROPN
ejpam-6598	288	4	,	,	PUNCT
ejpam-6598	288	5	τ	τ	PROPN
ejpam-6598	288	6	,	,	PUNCT
ejpam-6598	288	7	τ̂f	τ̂f	NUM
ejpam-6598	288	8	)	)	PUNCT
ejpam-6598	288	9	is	be	AUX
ejpam-6598	288	10	a	a	DET
ejpam-6598	288	11	pfdb≈f	pfdb≈f	NUM
ejpam-6598	288	12	−t1/2	−t1/2	NOUN
ejpam-6598	288	13	space	space	NOUN
ejpam-6598	288	14	.	.	PUNCT
ejpam-6598	289	1	proposition	proposition	NOUN
ejpam-6598	289	2	8	8	NUM
ejpam-6598	289	3	.	.	PUNCT
ejpam-6598	290	1	let	let	VERB
ejpam-6598	290	2	(	(	PUNCT
ejpam-6598	290	3	ξ	ξ	PROPN
ejpam-6598	290	4	,	,	PUNCT
ejpam-6598	290	5	τ	τ	PROPN
ejpam-6598	290	6	,	,	PUNCT
ejpam-6598	290	7	τ̂f	τ̂f	NUM
ejpam-6598	290	8	,	,	PUNCT
ejpam-6598	290	9	ψ	ψ	X
ejpam-6598	290	10	)	)	PUNCT
ejpam-6598	290	11	be	be	AUX
ejpam-6598	290	12	a	a	DET
ejpam-6598	290	13	pfdfts	pfdft	NOUN
ejpam-6598	290	14	,	,	PUNCT
ejpam-6598	290	15	the	the	DET
ejpam-6598	290	16	statements	statement	NOUN
ejpam-6598	290	17	listed	list	VERB
ejpam-6598	290	18	below	below	ADV
ejpam-6598	290	19	are	be	AUX
ejpam-6598	290	20	logically	logically	ADV
ejpam-6598	290	21	equivalent	equivalent	ADJ
ejpam-6598	290	22	.	.	PUNCT
ejpam-6598	291	1	(	(	PUNCT
ejpam-6598	291	2	i	i	NOUN
ejpam-6598	291	3	)	)	PUNCT
ejpam-6598	291	4	(	(	PUNCT
ejpam-6598	291	5	ξ	ξ	PROPN
ejpam-6598	291	6	,	,	PUNCT
ejpam-6598	291	7	τ	τ	PROPN
ejpam-6598	291	8	,	,	PUNCT
ejpam-6598	291	9	τ̂f	τ̂f	NUM
ejpam-6598	291	10	,	,	PUNCT
ejpam-6598	291	11	ψ	ψ	X
ejpam-6598	291	12	)	)	PUNCT
ejpam-6598	291	13	is	be	AUX
ejpam-6598	291	14	a	a	DET
ejpam-6598	291	15	pfdf	pfdf	NOUN
ejpam-6598	291	16	-	-	ADJ
ejpam-6598	291	17	discrete	discrete	ADJ
ejpam-6598	291	18	space	space	NOUN
ejpam-6598	291	19	.	.	PUNCT
ejpam-6598	292	1	(	(	PUNCT
ejpam-6598	292	2	ii	ii	NOUN
ejpam-6598	292	3	)	)	PUNCT
ejpam-6598	292	4	(	(	PUNCT
ejpam-6598	292	5	ξ	ξ	PROPN
ejpam-6598	292	6	,	,	PUNCT
ejpam-6598	292	7	τ	τ	PROPN
ejpam-6598	292	8	,	,	PUNCT
ejpam-6598	292	9	τ̂f	τ̂f	NUM
ejpam-6598	292	10	,	,	PUNCT
ejpam-6598	292	11	ψ	ψ	X
ejpam-6598	292	12	)	)	PUNCT
ejpam-6598	292	13	is	be	AUX
ejpam-6598	292	14	a	a	DET
ejpam-6598	292	15	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	292	16	−ds	−ds	NOUN
ejpam-6598	292	17	.	.	PUNCT
ejpam-6598	293	1	proof	proof	NOUN
ejpam-6598	293	2	.	.	PUNCT
ejpam-6598	294	1	(	(	PUNCT
ejpam-6598	294	2	i	i	NOUN
ejpam-6598	294	3	)	)	PUNCT
ejpam-6598	294	4	⇒	⇒	PROPN
ejpam-6598	294	5	(	(	PUNCT
ejpam-6598	294	6	ii	ii	NOUN
ejpam-6598	294	7	)	)	PUNCT
ejpam-6598	294	8	assume	assume	VERB
ejpam-6598	294	9	that	that	SCONJ
ejpam-6598	294	10	(	(	PUNCT
ejpam-6598	294	11	ξ	ξ	PROPN
ejpam-6598	294	12	,	,	PUNCT
ejpam-6598	294	13	τ	τ	PROPN
ejpam-6598	294	14	,	,	PUNCT
ejpam-6598	294	15	τ̂f	τ̂f	NUM
ejpam-6598	294	16	,	,	PUNCT
ejpam-6598	294	17	ψ	ψ	X
ejpam-6598	294	18	)	)	PUNCT
ejpam-6598	294	19	is	be	AUX
ejpam-6598	294	20	a	a	DET
ejpam-6598	294	21	pfdf	pfdf	NOUN
ejpam-6598	294	22	discrete	discrete	NOUN
ejpam-6598	294	23	,	,	PUNCT
ejpam-6598	294	24	then	then	ADV
ejpam-6598	294	25	every	every	DET
ejpam-6598	294	26	pfdfs	pfdfs	NOUN
ejpam-6598	294	27	is	be	AUX
ejpam-6598	294	28	a	a	DET
ejpam-6598	294	29	pfdf	pfdf	NOUN
ejpam-6598	294	30	open	open	ADJ
ejpam-6598	294	31	or	or	CCONJ
ejpam-6598	294	32	pfdf	pfdf	NOUN
ejpam-6598	294	33	closed	close	VERB
ejpam-6598	294	34	,	,	PUNCT
ejpam-6598	294	35	and	and	CCONJ
ejpam-6598	294	36	then	then	ADV
ejpam-6598	294	37	pfd	pfd	VERB
ejpam-6598	294	38	b≈f	b≈f	PRON
ejpam-6598	294	39	−os	−os	NOUN
ejpam-6598	294	40	or	or	CCONJ
ejpam-6598	294	41	pfdb≈f	pfdb≈f	NUM
ejpam-6598	294	42	−cs	−cs	PROPN
ejpam-6598	294	43	.	.	PUNCT
ejpam-6598	295	1	hence	hence	ADV
ejpam-6598	295	2	(	(	PUNCT
ejpam-6598	295	3	ξ	ξ	PROPN
ejpam-6598	295	4	,	,	PUNCT
ejpam-6598	295	5	τ	τ	PROPN
ejpam-6598	295	6	,	,	PUNCT
ejpam-6598	295	7	τ̂f	τ̂f	NUM
ejpam-6598	295	8	,	,	PUNCT
ejpam-6598	295	9	ψ	ψ	X
ejpam-6598	295	10	)	)	PUNCT
ejpam-6598	295	11	is	be	AUX
ejpam-6598	295	12	a	a	DET
ejpam-6598	295	13	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	295	14	−ds	−ds	NOUN
ejpam-6598	295	15	.	.	PUNCT
ejpam-6598	296	1	(	(	PUNCT
ejpam-6598	296	2	ii	ii	NOUN
ejpam-6598	296	3	)	)	PUNCT
ejpam-6598	296	4	⇒	⇒	NOUN
ejpam-6598	296	5	(	(	PUNCT
ejpam-6598	296	6	i	i	NOUN
ejpam-6598	296	7	)	)	PUNCT
ejpam-6598	296	8	if	if	SCONJ
ejpam-6598	296	9	k	k	PROPN
ejpam-6598	296	10	=	=	SYM
ejpam-6598	296	11	x(p	x(p	PROPN
ejpam-6598	296	12	,	,	PUNCT
ejpam-6598	296	13	q	q	X
ejpam-6598	296	14	)	)	PUNCT
ejpam-6598	296	15	is	be	AUX
ejpam-6598	296	16	a	a	DET
ejpam-6598	296	17	pfdfp	pfdfp	NOUN
ejpam-6598	296	18	in	in	ADP
ejpam-6598	296	19	(	(	PUNCT
ejpam-6598	296	20	ξ	ξ	PROPN
ejpam-6598	296	21	,	,	PUNCT
ejpam-6598	296	22	τ	τ	PROPN
ejpam-6598	296	23	,	,	PUNCT
ejpam-6598	296	24	τ̂f	τ̂f	NUM
ejpam-6598	296	25	)	)	PUNCT
ejpam-6598	296	26	.	.	PUNCT
ejpam-6598	297	1	consequently	consequently	ADV
ejpam-6598	297	2	,	,	PUNCT
ejpam-6598	297	3	k	k	PROPN
ejpam-6598	297	4	is	be	AUX
ejpam-6598	297	5	pfdb≈f	pfdb≈f	PRON
ejpam-6598	297	6	−	−	NOUN
ejpam-6598	297	7	cs	cs	PROPN
ejpam-6598	297	8	if	if	SCONJ
ejpam-6598	297	9	{	{	PUNCT
ejpam-6598	297	10	k	k	NOUN
ejpam-6598	297	11	}	}	PUNCT
ejpam-6598	297	12	is	be	AUX
ejpam-6598	297	13	not	not	PART
ejpam-6598	297	14	pfdb≈f	pfdb≈f	PRON
ejpam-6598	297	15	−	−	NOUN
ejpam-6598	298	1	os	os	NOUN
ejpam-6598	298	2	and	and	CCONJ
ejpam-6598	298	3	{	{	PUNCT
ejpam-6598	298	4	k	k	NOUN
ejpam-6598	298	5	}	}	PUNCT
ejpam-6598	298	6	=	=	SYM
ejpam-6598	298	7	(	(	PUNCT
ejpam-6598	298	8	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	298	9	−	−	NOUN
ejpam-6598	298	10	c(i(k	c(i(k	NOUN
ejpam-6598	298	11	)	)	PUNCT
ejpam-6598	298	12	)	)	PUNCT
ejpam-6598	299	1	∩	∩	NOUN
ejpam-6598	299	2	(	(	PUNCT
ejpam-6598	299	3	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	299	4	−	−	PROPN
ejpam-6598	299	5	i(c(k	i(c(k	PROPN
ejpam-6598	299	6	)	)	PUNCT
ejpam-6598	299	7	)	)	PUNCT
ejpam-6598	299	8	.	.	PUNCT
ejpam-6598	300	1	since	since	SCONJ
ejpam-6598	300	2	pfdb≈f	pfdb≈f	PRON
ejpam-6598	300	3	−	−	NOUN
ejpam-6598	300	4	i(k	i(k	PROPN
ejpam-6598	300	5	)	)	PUNCT
ejpam-6598	300	6	is	be	AUX
ejpam-6598	300	7	not	not	PART
ejpam-6598	300	8	empty	empty	ADJ
ejpam-6598	300	9	and	and	CCONJ
ejpam-6598	300	10	{	{	PUNCT
ejpam-6598	300	11	k	k	NOUN
ejpam-6598	300	12	}	}	PUNCT
ejpam-6598	300	13	=	=	SYM
ejpam-6598	300	14	(	(	PUNCT
ejpam-6598	300	15	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	300	16	−	−	NOUN
ejpam-6598	300	17	c(k	c(k	NOUN
ejpam-6598	300	18	)	)	PUNCT
ejpam-6598	300	19	)	)	PUNCT
ejpam-6598	301	1	,	,	PUNCT
ejpam-6598	301	2	then	then	ADV
ejpam-6598	301	3	{	{	PUNCT
ejpam-6598	301	4	k	k	NOUN
ejpam-6598	301	5	}	}	PUNCT
ejpam-6598	301	6	=	=	SYM
ejpam-6598	301	7	(	(	PUNCT
ejpam-6598	301	8	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	301	9	−	−	NOUN
ejpam-6598	301	10	c(i(k	c(i(k	NOUN
ejpam-6598	301	11	)	)	PUNCT
ejpam-6598	301	12	)	)	PUNCT
ejpam-6598	301	13	∩	∩	NOUN
ejpam-6598	301	14	(	(	PUNCT
ejpam-6598	301	15	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	301	16	−	−	NOUN
ejpam-6598	301	17	i(k	i(k	PROPN
ejpam-6598	301	18	)	)	PUNCT
ejpam-6598	301	19	)	)	PUNCT
ejpam-6598	302	1	=	=	PUNCT
ejpam-6598	302	2	pfdb≈f	pfdb≈f	NUM
ejpam-6598	302	3	−	−	PROPN
ejpam-6598	302	4	i({k	i({k	PROPN
ejpam-6598	302	5	}	}	PUNCT
ejpam-6598	302	6	)	)	PUNCT
ejpam-6598	302	7	.	.	PUNCT
ejpam-6598	303	1	in	in	ADP
ejpam-6598	303	2	both	both	DET
ejpam-6598	303	3	cases	case	NOUN
ejpam-6598	303	4	,	,	PUNCT
ejpam-6598	303	5	{	{	PUNCT
ejpam-6598	303	6	k	k	NOUN
ejpam-6598	303	7	}	}	PUNCT
ejpam-6598	303	8	is	be	AUX
ejpam-6598	303	9	a	a	DET
ejpam-6598	303	10	pfdf	pfdf	NOUN
ejpam-6598	303	11	open	open	ADJ
ejpam-6598	303	12	set	set	NOUN
ejpam-6598	303	13	.	.	PUNCT
ejpam-6598	304	1	therefore	therefore	ADV
ejpam-6598	304	2	,	,	PUNCT
ejpam-6598	304	3	(	(	PUNCT
ejpam-6598	304	4	ξ	ξ	X
ejpam-6598	304	5	,	,	PUNCT
ejpam-6598	304	6	τ	τ	PROPN
ejpam-6598	304	7	,	,	PUNCT
ejpam-6598	304	8	τ̂f	τ̂f	NUM
ejpam-6598	304	9	,	,	PUNCT
ejpam-6598	304	10	ψ	ψ	X
ejpam-6598	304	11	)	)	PUNCT
ejpam-6598	304	12	is	be	AUX
ejpam-6598	304	13	a	a	DET
ejpam-6598	304	14	pfdf	pfdf	ADJ
ejpam-6598	304	15	-discrete	-discrete	ADJ
ejpam-6598	304	16	space	space	NOUN
ejpam-6598	304	17	.	.	PUNCT
ejpam-6598	305	1	definition	definition	NOUN
ejpam-6598	305	2	33	33	NUM
ejpam-6598	305	3	.	.	PUNCT
ejpam-6598	306	1	a	a	DET
ejpam-6598	306	2	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	306	3	ts	ts	ADP
ejpam-6598	306	4	(	(	PUNCT
ejpam-6598	306	5	ξ	ξ	PROPN
ejpam-6598	306	6	,	,	PUNCT
ejpam-6598	306	7	τ	τ	PROPN
ejpam-6598	306	8	,	,	PUNCT
ejpam-6598	306	9	τ̂f	τ̂f	NUM
ejpam-6598	306	10	,	,	PUNCT
ejpam-6598	306	11	ψ	ψ	X
ejpam-6598	306	12	)	)	PUNCT
ejpam-6598	306	13	is	be	AUX
ejpam-6598	306	14	irreducible	irreducible	ADJ
ejpam-6598	306	15	if	if	SCONJ
ejpam-6598	306	16	every	every	DET
ejpam-6598	306	17	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	306	18	set	set	VERB
ejpam-6598	306	19	in	in	ADP
ejpam-6598	306	20	(	(	PUNCT
ejpam-6598	306	21	ξ	ξ	PROPN
ejpam-6598	306	22	,	,	PUNCT
ejpam-6598	306	23	τ	τ	PROPN
ejpam-6598	306	24	,	,	PUNCT
ejpam-6598	306	25	τ̂f	τ̂f	NUM
ejpam-6598	306	26	,	,	PUNCT
ejpam-6598	306	27	ψ	ψ	X
ejpam-6598	306	28	)	)	PUNCT
ejpam-6598	306	29	is	be	AUX
ejpam-6598	306	30	pfdb≈f	pfdb≈f	PRON
ejpam-6598	306	31	connected	connect	VERB
ejpam-6598	306	32	,	,	PUNCT
ejpam-6598	306	33	equivalent	equivalent	ADJ
ejpam-6598	306	34	to	to	ADP
ejpam-6598	306	35	every	every	DET
ejpam-6598	306	36	non	non	ADJ
ejpam-6598	306	37	-	-	ADJ
ejpam-6598	306	38	void	void	ADJ
ejpam-6598	306	39	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	306	40	−	−	NOUN
ejpam-6598	306	41	os	os	NOUN
ejpam-6598	306	42	in	in	ADP
ejpam-6598	306	43	(	(	PUNCT
ejpam-6598	306	44	ξ	ξ	PROPN
ejpam-6598	306	45	,	,	PUNCT
ejpam-6598	306	46	τ	τ	PROPN
ejpam-6598	306	47	,	,	PUNCT
ejpam-6598	306	48	τ̂f	τ̂f	NUM
ejpam-6598	306	49	,	,	PUNCT
ejpam-6598	306	50	ψ	ψ	X
ejpam-6598	306	51	)	)	PUNCT
ejpam-6598	306	52	being	be	AUX
ejpam-6598	306	53	dense	dense	ADJ
ejpam-6598	306	54	.	.	PUNCT
ejpam-6598	307	1	proposition	proposition	NOUN
ejpam-6598	307	2	9	9	NUM
ejpam-6598	307	3	.	.	PUNCT
ejpam-6598	308	1	every	every	DET
ejpam-6598	308	2	pfdf	pfdf	NOUN
ejpam-6598	308	3	irreducible	irreducible	ADJ
ejpam-6598	308	4	submaximal	submaximal	ADJ
ejpam-6598	308	5	space	space	NOUN
ejpam-6598	308	6	(	(	PUNCT
ejpam-6598	308	7	ξ	ξ	PROPN
ejpam-6598	308	8	,	,	PUNCT
ejpam-6598	308	9	τ	τ	PROPN
ejpam-6598	308	10	,	,	PUNCT
ejpam-6598	308	11	τ̂f	τ̂f	NUM
ejpam-6598	308	12	,	,	PUNCT
ejpam-6598	308	13	ψ	ψ	X
ejpam-6598	308	14	)	)	PUNCT
ejpam-6598	308	15	is	be	AUX
ejpam-6598	308	16	a	a	DET
ejpam-6598	308	17	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	308	18	−	−	NOUN
ejpam-6598	308	19	ds	ds	ADJ
ejpam-6598	308	20	.	.	NOUN
ejpam-6598	308	21	proof	proof	NOUN
ejpam-6598	308	22	.	.	PUNCT
ejpam-6598	309	1	assume	assume	VERB
ejpam-6598	309	2	that	that	SCONJ
ejpam-6598	309	3	ω	ω	PROPN
ejpam-6598	309	4	be	be	AUX
ejpam-6598	309	5	a	a	DET
ejpam-6598	309	6	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	309	7	set	set	VERB
ejpam-6598	309	8	in	in	ADP
ejpam-6598	309	9	(	(	PUNCT
ejpam-6598	309	10	ξ	ξ	PROPN
ejpam-6598	309	11	,	,	PUNCT
ejpam-6598	309	12	τ	τ	PROPN
ejpam-6598	309	13	,	,	PUNCT
ejpam-6598	309	14	τ̂f	τ̂f	NUM
ejpam-6598	309	15	,	,	PUNCT
ejpam-6598	309	16	ψ	ψ	NOUN
ejpam-6598	309	17	)	)	PUNCT
ejpam-6598	309	18	.	.	PUNCT
ejpam-6598	310	1	suppose	suppose	VERB
ejpam-6598	310	2	ω	ω	NOUN
ejpam-6598	310	3	is	be	AUX
ejpam-6598	310	4	pfdb≈f	pfdb≈f	NUM
ejpam-6598	310	5	-dense	-dense	NOUN
ejpam-6598	310	6	,	,	PUNCT
ejpam-6598	310	7	then	then	ADV
ejpam-6598	310	8	because	because	SCONJ
ejpam-6598	310	9	(	(	PUNCT
ejpam-6598	310	10	ξ	ξ	PROPN
ejpam-6598	310	11	,	,	PUNCT
ejpam-6598	310	12	τ	τ	PROPN
ejpam-6598	310	13	,	,	PUNCT
ejpam-6598	310	14	τ̂f	τ̂f	NUM
ejpam-6598	310	15	,	,	PUNCT
ejpam-6598	310	16	ψ	ψ	X
ejpam-6598	310	17	)	)	PUNCT
ejpam-6598	310	18	is	be	AUX
ejpam-6598	310	19	pfdb≈f	pfdb≈f	PRON
ejpam-6598	310	20	-submaximal	-submaximal	ADJ
ejpam-6598	310	21	,	,	PUNCT
ejpam-6598	310	22	ω	ω	PROPN
ejpam-6598	310	23	is	be	AUX
ejpam-6598	310	24	pfdb≈f	pfdb≈f	NUM
ejpam-6598	310	25	-os	-o	NOUN
ejpam-6598	310	26	,	,	PUNCT
ejpam-6598	310	27	if	if	SCONJ
ejpam-6598	310	28	ω	ω	NOUN
ejpam-6598	310	29	is	be	AUX
ejpam-6598	310	30	not	not	PART
ejpam-6598	310	31	pfdb≈f	pfdb≈f	PRON
ejpam-6598	310	32	dense	dense	ADJ
ejpam-6598	310	33	,	,	PUNCT
ejpam-6598	310	34	so	so	CCONJ
ejpam-6598	310	35	a	a	DET
ejpam-6598	310	36	non	non	ADJ
ejpam-6598	310	37	-	-	ADJ
ejpam-6598	310	38	void	void	ADJ
ejpam-6598	310	39	pfdb≈f	pfdb≈f	NUM
ejpam-6598	310	40	-os	-os	NOUN
ejpam-6598	310	41	ς	ς	PROPN
ejpam-6598	310	42	and	and	CCONJ
ejpam-6598	310	43	ωc	ωc	PROPN
ejpam-6598	310	44	can	can	AUX
ejpam-6598	310	45	be	be	AUX
ejpam-6598	310	46	found	find	VERB
ejpam-6598	310	47	.	.	PUNCT
ejpam-6598	311	1	since	since	SCONJ
ejpam-6598	311	2	(	(	PUNCT
ejpam-6598	311	3	ξ	ξ	PROPN
ejpam-6598	311	4	,	,	PUNCT
ejpam-6598	311	5	τ	τ	PROPN
ejpam-6598	311	6	,	,	PUNCT
ejpam-6598	311	7	τ̂f	τ̂f	NUM
ejpam-6598	311	8	,	,	PUNCT
ejpam-6598	311	9	ψ	ψ	X
ejpam-6598	311	10	)	)	PUNCT
ejpam-6598	311	11	is	be	AUX
ejpam-6598	311	12	irreducible	irreducible	ADJ
ejpam-6598	311	13	,	,	PUNCT
ejpam-6598	311	14	ς	ς	PROPN
ejpam-6598	311	15	and	and	CCONJ
ejpam-6598	311	16	ωc	ωc	PROPN
ejpam-6598	311	17	are	be	AUX
ejpam-6598	311	18	pfd	pfd	NOUN
ejpam-6598	311	19	b≈f	b≈f	PRON
ejpam-6598	311	20	-dense	-dense	NOUN
ejpam-6598	311	21	.	.	PUNCT
ejpam-6598	312	1	in	in	ADP
ejpam-6598	312	2	addition	addition	NOUN
ejpam-6598	312	3	,	,	PUNCT
ejpam-6598	312	4	since	since	SCONJ
ejpam-6598	312	5	(	(	PUNCT
ejpam-6598	312	6	ξ	ξ	PROPN
ejpam-6598	312	7	,	,	PUNCT
ejpam-6598	312	8	τ	τ	PROPN
ejpam-6598	312	9	,	,	PUNCT
ejpam-6598	312	10	τ̂f	τ̂f	NUM
ejpam-6598	312	11	,	,	PUNCT
ejpam-6598	312	12	ψ	ψ	X
ejpam-6598	312	13	)	)	PUNCT
ejpam-6598	312	14	is	be	AUX
ejpam-6598	312	15	pfd	pfd	PROPN
ejpam-6598	312	16	b≈f	b≈f	NOUN
ejpam-6598	312	17	-submaximal	-submaximal	PROPN
ejpam-6598	312	18	,	,	PUNCT
ejpam-6598	312	19	ωc	ωc	X
ejpam-6598	312	20	is	be	AUX
ejpam-6598	312	21	pfdb≈f	pfdb≈f	PRON
ejpam-6598	312	22	-os	-os	NOUN
ejpam-6598	312	23	or	or	CCONJ
ejpam-6598	312	24	equivalently	equivalently	ADV
ejpam-6598	312	25	,	,	PUNCT
ejpam-6598	312	26	ω	ω	PROPN
ejpam-6598	312	27	is	be	AUX
ejpam-6598	312	28	pfdb≈f	pfdb≈f	NUM
ejpam-6598	312	29	−	−	NOUN
ejpam-6598	312	30	cs	cs	PROPN
ejpam-6598	312	31	.	.	PROPN
ejpam-6598	312	32	thus	thus	ADV
ejpam-6598	312	33	,	,	PUNCT
ejpam-6598	312	34	in	in	ADP
ejpam-6598	312	35	any	any	DET
ejpam-6598	312	36	case	case	NOUN
ejpam-6598	312	37	,	,	PUNCT
ejpam-6598	312	38	ω	ω	PROPN
ejpam-6598	312	39	is	be	AUX
ejpam-6598	312	40	either	either	CCONJ
ejpam-6598	312	41	pfdb≈f	pfdb≈f	PRON
ejpam-6598	312	42	−os	−os	NOUN
ejpam-6598	312	43	or	or	CCONJ
ejpam-6598	312	44	pfdb≈f	pfdb≈f	PRON
ejpam-6598	312	45	−	−	PROPN
ejpam-6598	312	46	cs	cs	PROPN
ejpam-6598	312	47	.	.	PROPN
ejpam-6598	312	48	therefore	therefore	ADV
ejpam-6598	312	49	,	,	PUNCT
ejpam-6598	312	50	(	(	PUNCT
ejpam-6598	312	51	ξ	ξ	X
ejpam-6598	312	52	,	,	PUNCT
ejpam-6598	312	53	τ	τ	PROPN
ejpam-6598	312	54	,	,	PUNCT
ejpam-6598	312	55	τ̂f	τ̂f	NUM
ejpam-6598	312	56	,	,	PUNCT
ejpam-6598	312	57	ψ	ψ	X
ejpam-6598	312	58	)	)	PUNCT
ejpam-6598	312	59	is	be	AUX
ejpam-6598	312	60	a	a	DET
ejpam-6598	312	61	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	312	62	−ds	−ds	NOUN
ejpam-6598	312	63	.	.	PUNCT
ejpam-6598	313	1	definition	definition	NOUN
ejpam-6598	313	2	34	34	NUM
ejpam-6598	313	3	.	.	PUNCT
ejpam-6598	314	1	an	an	DET
ejpam-6598	314	2	pfdfts	pfdft	NOUN
ejpam-6598	314	3	(	(	PUNCT
ejpam-6598	314	4	ξ	ξ	PROPN
ejpam-6598	314	5	,	,	PUNCT
ejpam-6598	314	6	τ	τ	PROPN
ejpam-6598	314	7	,	,	PUNCT
ejpam-6598	314	8	τ̂f	τ̂f	NUM
ejpam-6598	314	9	)	)	PUNCT
ejpam-6598	314	10	is	be	AUX
ejpam-6598	314	11	called	call	VERB
ejpam-6598	314	12	pfdb	pfdb	NOUN
ejpam-6598	314	13	≈	≈	PROPN
ejpam-6598	314	14	f	f	NOUN
ejpam-6598	314	15	-extremely	-extremely	ADV
ejpam-6598	314	16	disconnected	disconnected	ADJ
ejpam-6598	314	17	if	if	SCONJ
ejpam-6598	314	18	the	the	DET
ejpam-6598	314	19	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	314	20	−	−	PROPN
ejpam-6598	314	21	c	c	NOUN
ejpam-6598	314	22	of	of	ADP
ejpam-6598	314	23	an	an	DET
ejpam-6598	314	24	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	314	25	-os	-os	NOUN
ejpam-6598	314	26	is	be	AUX
ejpam-6598	314	27	a	a	DET
ejpam-6598	314	28	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	314	29	−os	−os	NOUN
ejpam-6598	314	30	.	.	PUNCT
ejpam-6598	315	1	4	4	X
ejpam-6598	315	2	.	.	X
ejpam-6598	315	3	pythagorean	pythagorean	PROPN
ejpam-6598	315	4	fuzzy	fuzzy	ADJ
ejpam-6598	315	5	digital	digital	ADJ
ejpam-6598	315	6	fine	fine	ADJ
ejpam-6598	315	7	functions	function	NOUN
ejpam-6598	315	8	in	in	ADP
ejpam-6598	315	9	b≈f	b≈f	PROPN
ejpam-6598	315	10	-door	-door	NOUN
ejpam-6598	315	11	spaces	space	NOUN
ejpam-6598	315	12	this	this	DET
ejpam-6598	315	13	section	section	NOUN
ejpam-6598	315	14	explores	explore	VERB
ejpam-6598	315	15	the	the	DET
ejpam-6598	315	16	notion	notion	NOUN
ejpam-6598	315	17	of	of	ADP
ejpam-6598	315	18	pfdb≈f	pfdb≈f	NUM
ejpam-6598	315	19	-quasi	-quasi	NOUN
ejpam-6598	315	20	compactness	compactness	NOUN
ejpam-6598	315	21	and	and	CCONJ
ejpam-6598	315	22	discusses	discuss	VERB
ejpam-6598	315	23	its	its	PRON
ejpam-6598	315	24	key	key	ADJ
ejpam-6598	315	25	properties	property	NOUN
ejpam-6598	315	26	.	.	PUNCT
ejpam-6598	316	1	definition	definition	NOUN
ejpam-6598	316	2	35	35	NUM
ejpam-6598	316	3	.	.	PUNCT
ejpam-6598	317	1	let	let	VERB
ejpam-6598	317	2	σ	σ	NOUN
ejpam-6598	317	3	:	:	PUNCT
ejpam-6598	317	4	(	(	PUNCT
ejpam-6598	317	5	ξ	ξ	X
ejpam-6598	317	6	,	,	PUNCT
ejpam-6598	317	7	ψ	ψ	NOUN
ejpam-6598	317	8	)	)	PUNCT
ejpam-6598	317	9	→	→	SYM
ejpam-6598	317	10	(	(	PUNCT
ejpam-6598	317	11	g	g	PROPN
ejpam-6598	317	12	,	,	PUNCT
ejpam-6598	317	13	η	η	NOUN
ejpam-6598	317	14	)	)	PUNCT
ejpam-6598	317	15	be	be	VERB
ejpam-6598	317	16	a	a	DET
ejpam-6598	317	17	pfdf	pfdf	ADJ
ejpam-6598	317	18	function	function	NOUN
ejpam-6598	317	19	.	.	PUNCT
ejpam-6598	318	1	then	then	ADV
ejpam-6598	318	2	,	,	PUNCT
ejpam-6598	318	3	σ	σ	PROPN
ejpam-6598	318	4	is	be	AUX
ejpam-6598	318	5	pfdf	pfdf	NOUN
ejpam-6598	318	6	-quasi	-quasi	PROPN
ejpam-6598	318	7	compact	compact	ADJ
ejpam-6598	318	8	if	if	SCONJ
ejpam-6598	318	9	ω	ω	PROPN
ejpam-6598	318	10	⊆	⊆	NUM
ejpam-6598	318	11	1∼	1∼	NUM
ejpam-6598	318	12	is	be	AUX
ejpam-6598	318	13	pfdb≈f	pfdb≈f	NUM
ejpam-6598	318	14	−	−	NOUN
ejpam-6598	318	15	os	os	NOUN
ejpam-6598	318	16	in	in	ADP
ejpam-6598	318	17	(	(	PUNCT
ejpam-6598	318	18	ξ	ξ	PROPN
ejpam-6598	318	19	,	,	PUNCT
ejpam-6598	318	20	ψ	ψ	NOUN
ejpam-6598	318	21	)	)	PUNCT
ejpam-6598	318	22	such	such	ADJ
ejpam-6598	318	23	that	that	DET
ejpam-6598	318	24	σ−1(σ(ω	σ−1(σ(ω	NOUN
ejpam-6598	318	25	)	)	PUNCT
ejpam-6598	318	26	)	)	PUNCT
ejpam-6598	319	1	=	=	SYM
ejpam-6598	319	2	ω	ω	X
ejpam-6598	319	3	.	.	PUNCT
ejpam-6598	320	1	then	then	ADV
ejpam-6598	320	2	,	,	PUNCT
ejpam-6598	320	3	σ(ω	σ(ω	PROPN
ejpam-6598	320	4	)	)	PUNCT
ejpam-6598	320	5	is	be	AUX
ejpam-6598	320	6	pfdb≈f	pfdb≈f	PRON
ejpam-6598	320	7	−os	−os	ADV
ejpam-6598	320	8	in	in	ADP
ejpam-6598	320	9	(	(	PUNCT
ejpam-6598	320	10	g	g	PROPN
ejpam-6598	320	11	,	,	PUNCT
ejpam-6598	320	12	η	η	NOUN
ejpam-6598	320	13	)	)	PUNCT
ejpam-6598	320	14	.	.	PUNCT
ejpam-6598	321	1	proposition	proposition	NOUN
ejpam-6598	321	2	10	10	NUM
ejpam-6598	321	3	.	.	PUNCT
ejpam-6598	322	1	a	a	DET
ejpam-6598	322	2	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	322	3	−ds	−ds	NOUN
ejpam-6598	322	4	has	have	VERB
ejpam-6598	322	5	a	a	DET
ejpam-6598	322	6	topological	topological	ADJ
ejpam-6598	322	7	property	property	NOUN
ejpam-6598	322	8	.	.	PUNCT
ejpam-6598	323	1	n.	n.	PROPN
ejpam-6598	323	2	preethi	preethi	PROPN
ejpam-6598	323	3	,	,	PUNCT
ejpam-6598	323	4	g.	g.	PROPN
ejpam-6598	323	5	k.	k.	PROPN
ejpam-6598	323	6	revathi	revathi	PROPN
ejpam-6598	323	7	/	/	SYM
ejpam-6598	323	8	eur	eur	PROPN
ejpam-6598	323	9	.	.	PUNCT
ejpam-6598	324	1	j.	j.	PROPN
ejpam-6598	324	2	pure	pure	PROPN
ejpam-6598	324	3	appl	appl	PROPN
ejpam-6598	324	4	.	.	PROPN
ejpam-6598	324	5	math	math	PROPN
ejpam-6598	324	6	,	,	PUNCT
ejpam-6598	324	7	18	18	NUM
ejpam-6598	324	8	(	(	PUNCT
ejpam-6598	324	9	3	3	NUM
ejpam-6598	324	10	)	)	PUNCT
ejpam-6598	324	11	(	(	PUNCT
ejpam-6598	324	12	2025	2025	NUM
ejpam-6598	324	13	)	)	PUNCT
ejpam-6598	324	14	,	,	PUNCT
ejpam-6598	324	15	6598	6598	NUM
ejpam-6598	324	16	11	11	NUM
ejpam-6598	324	17	of	of	ADP
ejpam-6598	324	18	17	17	NUM
ejpam-6598	324	19	proof	proof	NOUN
ejpam-6598	324	20	.	.	PUNCT
ejpam-6598	325	1	let	let	VERB
ejpam-6598	325	2	σ	σ	NOUN
ejpam-6598	325	3	:	:	PUNCT
ejpam-6598	325	4	(	(	PUNCT
ejpam-6598	325	5	ξ	ξ	X
ejpam-6598	325	6	,	,	PUNCT
ejpam-6598	325	7	ψ	ψ	NOUN
ejpam-6598	325	8	)	)	PUNCT
ejpam-6598	325	9	→	→	SYM
ejpam-6598	325	10	(	(	PUNCT
ejpam-6598	325	11	g	g	PROPN
ejpam-6598	325	12	,	,	PUNCT
ejpam-6598	325	13	η	η	NOUN
ejpam-6598	325	14	)	)	PUNCT
ejpam-6598	325	15	be	be	VERB
ejpam-6598	325	16	an	an	DET
ejpam-6598	325	17	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	325	18	-homeomorphism	-homeomorphism	NOUN
ejpam-6598	325	19	from	from	ADP
ejpam-6598	325	20	a	a	DET
ejpam-6598	325	21	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	325	22	−ds	−ds	NOUN
ejpam-6598	325	23	(	(	PUNCT
ejpam-6598	325	24	ξ	ξ	PROPN
ejpam-6598	325	25	,	,	PUNCT
ejpam-6598	325	26	ψ	ψ	NOUN
ejpam-6598	325	27	)	)	PUNCT
ejpam-6598	325	28	into	into	ADP
ejpam-6598	325	29	another	another	DET
ejpam-6598	325	30	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	325	31	ts	ts	X
ejpam-6598	325	32	(	(	PUNCT
ejpam-6598	325	33	g	g	PROPN
ejpam-6598	325	34	,	,	PUNCT
ejpam-6598	325	35	η	η	NOUN
ejpam-6598	325	36	)	)	PUNCT
ejpam-6598	325	37	.	.	PUNCT
ejpam-6598	326	1	let	let	VERB
ejpam-6598	326	2	ω	ω	NUM
ejpam-6598	326	3	be	be	AUX
ejpam-6598	326	4	pfdb≈f	pfdb≈f	PRON
ejpam-6598	326	5	s	s	PART
ejpam-6598	326	6	in	in	ADP
ejpam-6598	326	7	(	(	PUNCT
ejpam-6598	326	8	g	g	PROPN
ejpam-6598	326	9	,	,	PUNCT
ejpam-6598	326	10	η	η	PROPN
ejpam-6598	326	11	)	)	PUNCT
ejpam-6598	326	12	,	,	PUNCT
ejpam-6598	326	13	that	that	ADV
ejpam-6598	326	14	is	is	ADV
ejpam-6598	326	15	,	,	PUNCT
ejpam-6598	326	16	ω	ω	PROPN
ejpam-6598	326	17	⊆	⊆	NUM
ejpam-6598	326	18	g.	g.	NOUN
ejpam-6598	326	19	then	then	ADV
ejpam-6598	326	20	,	,	PUNCT
ejpam-6598	326	21	σ−1(ω	σ−1(ω	PROPN
ejpam-6598	326	22	)	)	PUNCT
ejpam-6598	326	23	is	be	AUX
ejpam-6598	326	24	pfdb≈f	pfdb≈f	PRON
ejpam-6598	326	25	sin	sin	NOUN
ejpam-6598	326	26	(	(	PUNCT
ejpam-6598	326	27	ξ	ξ	X
ejpam-6598	326	28	,	,	PUNCT
ejpam-6598	326	29	ψ	ψ	NOUN
ejpam-6598	326	30	)	)	PUNCT
ejpam-6598	326	31	,	,	PUNCT
ejpam-6598	326	32	that	that	ADV
ejpam-6598	326	33	is	is	ADV
ejpam-6598	326	34	,	,	PUNCT
ejpam-6598	326	35	σ−1(ω	σ−1(ω	NOUN
ejpam-6598	326	36	)	)	PUNCT
ejpam-6598	326	37	⊆	⊆	NUM
ejpam-6598	326	38	ξ	ξ	NOUN
ejpam-6598	326	39	.	.	PUNCT
ejpam-6598	327	1	because	because	SCONJ
ejpam-6598	327	2	(	(	PUNCT
ejpam-6598	327	3	ξ	ξ	X
ejpam-6598	327	4	,	,	PUNCT
ejpam-6598	327	5	ψ	ψ	NOUN
ejpam-6598	327	6	)	)	PUNCT
ejpam-6598	327	7	is	be	AUX
ejpam-6598	327	8	an	an	DET
ejpam-6598	327	9	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	327	10	−	−	NOUN
ejpam-6598	327	11	ds	ds	ADJ
ejpam-6598	327	12	,	,	PUNCT
ejpam-6598	327	13	σ−1(ω	σ−1(ω	NOUN
ejpam-6598	327	14	)	)	PUNCT
ejpam-6598	327	15	is	be	AUX
ejpam-6598	327	16	a	a	DET
ejpam-6598	327	17	pfdb≈f	pfdb≈f	PRON
ejpam-6598	327	18	os	os	NOUN
ejpam-6598	327	19	or	or	CCONJ
ejpam-6598	327	20	a	a	DET
ejpam-6598	327	21	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	327	22	−	−	NOUN
ejpam-6598	327	23	cs	cs	PROPN
ejpam-6598	327	24	in	in	ADP
ejpam-6598	327	25	(	(	PUNCT
ejpam-6598	327	26	ξ	ξ	PROPN
ejpam-6598	327	27	,	,	PUNCT
ejpam-6598	327	28	ψ	ψ	NOUN
ejpam-6598	327	29	)	)	PUNCT
ejpam-6598	327	30	,	,	PUNCT
ejpam-6598	327	31	because	because	SCONJ
ejpam-6598	327	32	σ	σ	PROPN
ejpam-6598	327	33	(	(	PUNCT
ejpam-6598	327	34	(	(	PUNCT
ejpam-6598	327	35	σ−1(ω	σ−1(ω	NOUN
ejpam-6598	327	36	)	)	PUNCT
ejpam-6598	327	37	)	)	PUNCT
ejpam-6598	328	1	=	=	PUNCT
ejpam-6598	328	2	ω	ω	X
ejpam-6598	328	3	.	.	PUNCT
ejpam-6598	329	1	then	then	ADV
ejpam-6598	329	2	,	,	PUNCT
ejpam-6598	329	3	ω	ω	PROPN
ejpam-6598	329	4	is	be	AUX
ejpam-6598	329	5	either	either	PRON
ejpam-6598	329	6	pfdb≈f	pfdb≈f	PRON
ejpam-6598	329	7	−	−	PROPN
ejpam-6598	330	1	os	os	NOUN
ejpam-6598	331	1	or	or	CCONJ
ejpam-6598	331	2	pfdb≈f	pfdb≈f	PRON
ejpam-6598	331	3	−cs	−cs	PROPN
ejpam-6598	331	4	in	in	ADP
ejpam-6598	331	5	(	(	PUNCT
ejpam-6598	331	6	g	g	PROPN
ejpam-6598	331	7	,	,	PUNCT
ejpam-6598	331	8	η	η	PROPN
ejpam-6598	331	9	)	)	PUNCT
ejpam-6598	331	10	.	.	PUNCT
ejpam-6598	332	1	thus	thus	ADV
ejpam-6598	332	2	,	,	PUNCT
ejpam-6598	332	3	(	(	PUNCT
ejpam-6598	332	4	g	g	PROPN
ejpam-6598	332	5	,	,	PUNCT
ejpam-6598	332	6	η	η	PROPN
ejpam-6598	332	7	)	)	PUNCT
ejpam-6598	332	8	is	be	AUX
ejpam-6598	332	9	the	the	DET
ejpam-6598	332	10	pfdb≈f	pfdb≈f	NUM
ejpam-6598	332	11	−ds	−ds	NOUN
ejpam-6598	332	12	.	.	PUNCT
ejpam-6598	333	1	proposition	proposition	NOUN
ejpam-6598	333	2	11	11	NUM
ejpam-6598	333	3	.	.	PUNCT
ejpam-6598	334	1	a	a	DET
ejpam-6598	334	2	pfdf	pfdf	NOUN
ejpam-6598	334	3	-quasi	-quasi	ADJ
ejpam-6598	334	4	-	-	ADJ
ejpam-6598	334	5	compact	compact	ADJ
ejpam-6598	334	6	image	image	NOUN
ejpam-6598	334	7	of	of	ADP
ejpam-6598	334	8	an	an	DET
ejpam-6598	334	9	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	334	10	−ds	−ds	NOUN
ejpam-6598	334	11	is	be	AUX
ejpam-6598	334	12	an	an	DET
ejpam-6598	334	13	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	334	14	−ds	−ds	NOUN
ejpam-6598	334	15	.	.	PUNCT
ejpam-6598	335	1	proof	proof	NOUN
ejpam-6598	335	2	.	.	PUNCT
ejpam-6598	336	1	let	let	VERB
ejpam-6598	336	2	σ	σ	NOUN
ejpam-6598	336	3	:	:	PUNCT
ejpam-6598	336	4	(	(	PUNCT
ejpam-6598	336	5	ξ	ξ	X
ejpam-6598	336	6	,	,	PUNCT
ejpam-6598	336	7	ψ	ψ	NOUN
ejpam-6598	336	8	)	)	PUNCT
ejpam-6598	336	9	→	→	SYM
ejpam-6598	336	10	(	(	PUNCT
ejpam-6598	336	11	g	g	PROPN
ejpam-6598	336	12	,	,	PUNCT
ejpam-6598	336	13	η	η	NOUN
ejpam-6598	336	14	)	)	PUNCT
ejpam-6598	336	15	be	be	VERB
ejpam-6598	336	16	a	a	DET
ejpam-6598	336	17	pfdb≈f	pfdb≈f	NUM
ejpam-6598	336	18	-quasi	-quasi	NOUN
ejpam-6598	336	19	compact	compact	ADJ
ejpam-6598	336	20	function	function	NOUN
ejpam-6598	336	21	from	from	ADP
ejpam-6598	336	22	a	a	DET
ejpam-6598	336	23	pfdb≈f	pfdb≈f	NUM
ejpam-6598	336	24	−	−	NOUN
ejpam-6598	336	25	ds	ds	ADJ
ejpam-6598	336	26	(	(	PUNCT
ejpam-6598	336	27	ξ	ξ	PROPN
ejpam-6598	336	28	,	,	PUNCT
ejpam-6598	336	29	ψ	ψ	NOUN
ejpam-6598	336	30	)	)	PUNCT
ejpam-6598	336	31	into	into	ADP
ejpam-6598	336	32	another	another	DET
ejpam-6598	336	33	pfd	pfd	NOUN
ejpam-6598	336	34	b≈f	b≈f	PRON
ejpam-6598	336	35	ts	ts	X
ejpam-6598	336	36	(	(	PUNCT
ejpam-6598	336	37	g	g	PROPN
ejpam-6598	336	38	,	,	PUNCT
ejpam-6598	336	39	η	η	NOUN
ejpam-6598	336	40	)	)	PUNCT
ejpam-6598	336	41	.	.	PUNCT
ejpam-6598	337	1	let	let	VERB
ejpam-6598	337	2	ς	ς	PRON
ejpam-6598	337	3	be	be	AUX
ejpam-6598	337	4	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	337	5	s	s	VERB
ejpam-6598	337	6	in	in	ADP
ejpam-6598	337	7	(	(	PUNCT
ejpam-6598	337	8	g	g	PROPN
ejpam-6598	337	9	,	,	PUNCT
ejpam-6598	337	10	η	η	NOUN
ejpam-6598	337	11	)	)	PUNCT
ejpam-6598	337	12	.	.	PUNCT
ejpam-6598	338	1	we	we	PRON
ejpam-6598	338	2	have	have	VERB
ejpam-6598	338	3	to	to	PART
ejpam-6598	338	4	prove	prove	VERB
ejpam-6598	338	5	that	that	SCONJ
ejpam-6598	338	6	ς	ς	PROPN
ejpam-6598	338	7	is	be	AUX
ejpam-6598	338	8	either	either	CCONJ
ejpam-6598	338	9	pfdb≈f	pfdb≈f	PRON
ejpam-6598	338	10	−os	−os	NOUN
ejpam-6598	338	11	or	or	CCONJ
ejpam-6598	338	12	pfdb≈f	pfdb≈f	PRON
ejpam-6598	338	13	−cs	−cs	PROPN
ejpam-6598	338	14	in	in	ADP
ejpam-6598	338	15	(	(	PUNCT
ejpam-6598	338	16	g	g	PROPN
ejpam-6598	338	17	,	,	PUNCT
ejpam-6598	338	18	η	η	NOUN
ejpam-6598	338	19	)	)	PUNCT
ejpam-6598	338	20	.	.	PUNCT
ejpam-6598	339	1	because	because	SCONJ
ejpam-6598	339	2	(	(	PUNCT
ejpam-6598	339	3	ξ	ξ	X
ejpam-6598	339	4	,	,	PUNCT
ejpam-6598	339	5	ψ	ψ	NOUN
ejpam-6598	339	6	)	)	PUNCT
ejpam-6598	339	7	is	be	AUX
ejpam-6598	339	8	an	an	DET
ejpam-6598	339	9	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	339	10	−ds	−ds	NOUN
ejpam-6598	339	11	and	and	CCONJ
ejpam-6598	339	12	σ−1(ξ	σ−1(ξ	NOUN
ejpam-6598	339	13	)	)	PUNCT
ejpam-6598	339	14	=	=	SYM
ejpam-6598	339	15	ω	ω	PROPN
ejpam-6598	339	16	,	,	PUNCT
ejpam-6598	339	17	then	then	ADV
ejpam-6598	339	18	ω	ω	PROPN
ejpam-6598	339	19	is	be	AUX
ejpam-6598	339	20	either	either	CCONJ
ejpam-6598	339	21	pfdb≈f	pfdb≈f	PRON
ejpam-6598	339	22	−os	−os	NOUN
ejpam-6598	339	23	or	or	CCONJ
ejpam-6598	339	24	pfdb≈f	pfdb≈f	PRON
ejpam-6598	339	25	−cs	−cs	NOUN
ejpam-6598	339	26	in	in	ADP
ejpam-6598	339	27	(	(	PUNCT
ejpam-6598	339	28	ξ	ξ	PROPN
ejpam-6598	339	29	,	,	PUNCT
ejpam-6598	339	30	ψ	ψ	NOUN
ejpam-6598	339	31	)	)	PUNCT
ejpam-6598	339	32	.	.	PUNCT
ejpam-6598	340	1	suppose	suppose	VERB
ejpam-6598	340	2	that	that	SCONJ
ejpam-6598	340	3	ω	ω	PROPN
ejpam-6598	340	4	is	be	AUX
ejpam-6598	340	5	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	340	6	−os	−os	NOUN
ejpam-6598	340	7	,	,	PUNCT
ejpam-6598	340	8	and	and	CCONJ
ejpam-6598	340	9	clearly	clearly	ADV
ejpam-6598	340	10	σ(ω	σ(ω	PROPN
ejpam-6598	340	11	)	)	PUNCT
ejpam-6598	340	12	⊆	⊆	NUM
ejpam-6598	340	13	ς	ς	PROPN
ejpam-6598	340	14	.	.	PUNCT
ejpam-6598	340	15	thus	thus	ADV
ejpam-6598	340	16	,	,	PUNCT
ejpam-6598	340	17	σ−1(σ(ω	σ−1(σ(ω	ADJ
ejpam-6598	340	18	)	)	PUNCT
ejpam-6598	340	19	)	)	PUNCT
ejpam-6598	341	1	⊆	⊆	NUM
ejpam-6598	341	2	σ−1(ς	σ−1(ς	PROPN
ejpam-6598	341	3	)	)	PUNCT
ejpam-6598	341	4	=	=	PUNCT
ejpam-6598	341	5	ω	ω	PROPN
ejpam-6598	341	6	⊆	⊆	NUM
ejpam-6598	341	7	σ−1(σ(ω	σ−1(σ(ω	NOUN
ejpam-6598	341	8	)	)	PUNCT
ejpam-6598	341	9	)	)	PUNCT
ejpam-6598	341	10	or	or	CCONJ
ejpam-6598	341	11	equivalently	equivalently	ADV
ejpam-6598	341	12	,	,	PUNCT
ejpam-6598	341	13	ω	ω	NOUN
ejpam-6598	341	14	=	=	SYM
ejpam-6598	341	15	σ−1(σ(ω	σ−1(σ(ω	NOUN
ejpam-6598	341	16	)	)	PUNCT
ejpam-6598	341	17	)	)	PUNCT
ejpam-6598	341	18	.	.	PUNCT
ejpam-6598	342	1	by	by	ADP
ejpam-6598	342	2	assumption	assumption	NOUN
ejpam-6598	342	3	,	,	PUNCT
ejpam-6598	342	4	σ(ω	σ(ω	PROPN
ejpam-6598	342	5	)	)	PUNCT
ejpam-6598	342	6	=	=	SYM
ejpam-6598	342	7	σ	σ	PROPN
ejpam-6598	342	8	(	(	PUNCT
ejpam-6598	342	9	(	(	PUNCT
ejpam-6598	342	10	σ−1(ς	σ−1(ς	PROPN
ejpam-6598	342	11	)	)	PUNCT
ejpam-6598	342	12	)	)	PUNCT
ejpam-6598	343	1	=	=	SYM
ejpam-6598	343	2	ς	ς	PROPN
ejpam-6598	343	3	∩	∩	X
ejpam-6598	343	4	σ(1∼	σ(1∼	X
ejpam-6598	343	5	)	)	PUNCT
ejpam-6598	343	6	=	=	SYM
ejpam-6598	343	7	ς	ς	PROPN
ejpam-6598	343	8	∩	∩	NOUN
ejpam-6598	343	9	1∼	1∼	NUM
ejpam-6598	343	10	=	=	SYM
ejpam-6598	343	11	ς	ς	PROPN
ejpam-6598	343	12	is	be	AUX
ejpam-6598	343	13	pfd	pfd	NOUN
ejpam-6598	344	1	b≈f	b≈f	VERB
ejpam-6598	344	2	−	−	PROPN
ejpam-6598	344	3	os	os	NOUN
ejpam-6598	344	4	in	in	ADP
ejpam-6598	344	5	(	(	PUNCT
ejpam-6598	344	6	g	g	PROPN
ejpam-6598	344	7	,	,	PUNCT
ejpam-6598	344	8	η	η	PROPN
ejpam-6598	344	9	)	)	PUNCT
ejpam-6598	344	10	.	.	PUNCT
ejpam-6598	345	1	we	we	PRON
ejpam-6598	345	2	now	now	ADV
ejpam-6598	345	3	assume	assume	VERB
ejpam-6598	345	4	that	that	SCONJ
ejpam-6598	345	5	ω	ω	PROPN
ejpam-6598	345	6	is	be	AUX
ejpam-6598	345	7	pfdb≈f	pfdb≈f	NUM
ejpam-6598	345	8	−	−	NOUN
ejpam-6598	345	9	cs	cs	PROPN
ejpam-6598	345	10	in	in	ADP
ejpam-6598	345	11	(	(	PUNCT
ejpam-6598	345	12	ξ	ξ	PROPN
ejpam-6598	345	13	,	,	PUNCT
ejpam-6598	345	14	ψ	ψ	NOUN
ejpam-6598	345	15	)	)	PUNCT
ejpam-6598	345	16	.	.	PUNCT
ejpam-6598	346	1	then	then	ADV
ejpam-6598	346	2	,	,	PUNCT
ejpam-6598	346	3	1∼\σ−1(ζ	1∼\σ−1(ζ	NUM
ejpam-6598	346	4	)	)	PUNCT
ejpam-6598	347	1	=	=	SYM
ejpam-6598	347	2	σ−1(1∼\ζ	σ−1(1∼\ζ	NOUN
ejpam-6598	347	3	)	)	PUNCT
ejpam-6598	347	4	is	be	AUX
ejpam-6598	347	5	pfdb≈f	pfdb≈f	NUM
ejpam-6598	347	6	−	−	NOUN
ejpam-6598	347	7	os	os	NOUN
ejpam-6598	347	8	in	in	ADP
ejpam-6598	347	9	(	(	PUNCT
ejpam-6598	347	10	ξ	ξ	PROPN
ejpam-6598	347	11	,	,	PUNCT
ejpam-6598	347	12	ψ	ψ	NOUN
ejpam-6598	347	13	)	)	PUNCT
ejpam-6598	347	14	.	.	PUNCT
ejpam-6598	348	1	hence	hence	ADV
ejpam-6598	348	2	,	,	PUNCT
ejpam-6598	348	3	(	(	PUNCT
ejpam-6598	348	4	1∼\ζ	1∼\ζ	NUM
ejpam-6598	348	5	)	)	PUNCT
ejpam-6598	348	6	∩	∩	NOUN
ejpam-6598	348	7	σ(1∼	σ(1∼	X
ejpam-6598	348	8	)	)	PUNCT
ejpam-6598	348	9	=	=	PUNCT
ejpam-6598	349	1	1∼\ζ	1∼\ζ	PROPN
ejpam-6598	349	2	is	be	AUX
ejpam-6598	349	3	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	349	4	-os	-os	X
ejpam-6598	349	5	in	in	ADP
ejpam-6598	349	6	(	(	PUNCT
ejpam-6598	349	7	g	g	PROPN
ejpam-6598	349	8	,	,	PUNCT
ejpam-6598	349	9	η	η	PROPN
ejpam-6598	349	10	)	)	PUNCT
ejpam-6598	349	11	;	;	PUNCT
ejpam-6598	349	12	thus	thus	ADV
ejpam-6598	349	13	,	,	PUNCT
ejpam-6598	349	14	1∼\(1∼\ζ	1∼\(1∼\ζ	X
ejpam-6598	349	15	)	)	PUNCT
ejpam-6598	349	16	=	=	SYM
ejpam-6598	350	1	ζ	ζ	NOUN
ejpam-6598	350	2	is	be	AUX
ejpam-6598	350	3	pfdb≈f	pfdb≈f	INTJ
ejpam-6598	350	4	-cs	-cs	PRON
ejpam-6598	350	5	(	(	PUNCT
ejpam-6598	350	6	g	g	PROPN
ejpam-6598	350	7	,	,	PUNCT
ejpam-6598	350	8	η	η	NOUN
ejpam-6598	350	9	)	)	PUNCT
ejpam-6598	350	10	.	.	PUNCT
ejpam-6598	351	1	therefore	therefore	ADV
ejpam-6598	351	2	,	,	PUNCT
ejpam-6598	351	3	(	(	PUNCT
ejpam-6598	351	4	g	g	PROPN
ejpam-6598	351	5	,	,	PUNCT
ejpam-6598	351	6	η	η	NOUN
ejpam-6598	351	7	)	)	PUNCT
ejpam-6598	351	8	is	be	AUX
ejpam-6598	351	9	the	the	DET
ejpam-6598	351	10	pfdb≈f	pfdb≈f	NUM
ejpam-6598	351	11	−ds	−ds	NOUN
ejpam-6598	351	12	.	.	PUNCT
ejpam-6598	352	1	corollary	corollary	ADJ
ejpam-6598	352	2	1	1	NUM
ejpam-6598	352	3	.	.	PUNCT
ejpam-6598	353	1	pfdb≈f	pfdb≈f	PRON
ejpam-6598	353	2	-open	-open	NOUN
ejpam-6598	353	3	images	image	NOUN
ejpam-6598	353	4	as	as	ADV
ejpam-6598	353	5	well	well	ADV
ejpam-6598	353	6	as	as	ADP
ejpam-6598	353	7	pfdb≈f	pfdb≈f	NUM
ejpam-6598	353	8	-closed	-closed	ADJ
ejpam-6598	353	9	images	image	NOUN
ejpam-6598	353	10	of	of	ADP
ejpam-6598	353	11	a	a	DET
ejpam-6598	353	12	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	353	13	−ds	−ds	NOUN
ejpam-6598	353	14	are	be	AUX
ejpam-6598	353	15	pfdb≈f	pfdb≈f	ADJ
ejpam-6598	353	16	−ds	−ds	NOUN
ejpam-6598	353	17	.	.	PUNCT
ejpam-6598	354	1	proof	proof	NOUN
ejpam-6598	354	2	.	.	PUNCT
ejpam-6598	355	1	since	since	SCONJ
ejpam-6598	355	2	every	every	DET
ejpam-6598	355	3	pfdb≈f	pfdb≈f	NUM
ejpam-6598	355	4	-os	-os	X
ejpam-6598	355	5	(	(	PUNCT
ejpam-6598	355	6	resp	resp	NOUN
ejpam-6598	355	7	,	,	PUNCT
ejpam-6598	355	8	pfdb≈f	pfdb≈f	PROPN
ejpam-6598	355	9	-cs	-cs	NOUN
ejpam-6598	355	10	)	)	PUNCT
ejpam-6598	355	11	surjective	surjective	ADJ
ejpam-6598	355	12	function	function	NOUN
ejpam-6598	355	13	is	be	AUX
ejpam-6598	355	14	pfdb≈f	pfdb≈f	NUM
ejpam-6598	355	15	quasicompact	quasicompact	NOUN
ejpam-6598	355	16	,	,	PUNCT
ejpam-6598	355	17	it	it	PRON
ejpam-6598	355	18	is	be	AUX
ejpam-6598	355	19	an	an	DET
ejpam-6598	355	20	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	355	21	−ds	−ds	NOUN
ejpam-6598	355	22	.	.	PUNCT
ejpam-6598	356	1	5	5	NUM
ejpam-6598	356	2	.	.	X
ejpam-6598	356	3	selection	selection	NOUN
ejpam-6598	356	4	of	of	ADP
ejpam-6598	356	5	best	good	ADJ
ejpam-6598	356	6	menstrual	menstrual	ADJ
ejpam-6598	356	7	hygiene	hygiene	NOUN
ejpam-6598	356	8	product	product	NOUN
ejpam-6598	356	9	for	for	ADP
ejpam-6598	356	10	rural	rural	ADJ
ejpam-6598	356	11	women	woman	NOUN
ejpam-6598	356	12	selecting	select	VERB
ejpam-6598	356	13	the	the	DET
ejpam-6598	356	14	best	well	ADV
ejpam-6598	356	15	menstrual	menstrual	ADJ
ejpam-6598	356	16	hygiene	hygiene	NOUN
ejpam-6598	356	17	product	product	NOUN
ejpam-6598	356	18	for	for	ADP
ejpam-6598	356	19	rural	rural	ADJ
ejpam-6598	356	20	women	woman	NOUN
ejpam-6598	356	21	serves	serve	VERB
ejpam-6598	356	22	multiple	multiple	ADJ
ejpam-6598	356	23	vital	vital	ADJ
ejpam-6598	356	24	purposes	purpose	NOUN
ejpam-6598	356	25	that	that	PRON
ejpam-6598	356	26	go	go	VERB
ejpam-6598	356	27	beyond	beyond	ADP
ejpam-6598	356	28	basic	basic	ADJ
ejpam-6598	356	29	hygiene	hygiene	NOUN
ejpam-6598	356	30	.	.	PUNCT
ejpam-6598	357	1	first	first	ADV
ejpam-6598	357	2	of	of	ADP
ejpam-6598	357	3	all	all	PRON
ejpam-6598	357	4	,	,	PUNCT
ejpam-6598	357	5	it	it	PRON
ejpam-6598	357	6	improves	improve	VERB
ejpam-6598	357	7	health	health	NOUN
ejpam-6598	357	8	by	by	ADP
ejpam-6598	357	9	lowering	lower	VERB
ejpam-6598	357	10	the	the	DET
ejpam-6598	357	11	risk	risk	NOUN
ejpam-6598	357	12	of	of	ADP
ejpam-6598	357	13	diseases	disease	NOUN
ejpam-6598	357	14	including	include	VERB
ejpam-6598	357	15	recurrent	recurrent	ADJ
ejpam-6598	357	16	and	and	CCONJ
ejpam-6598	357	17	urinary	urinary	ADJ
ejpam-6598	357	18	tract	tract	NOUN
ejpam-6598	357	19	infections	infection	NOUN
ejpam-6598	357	20	,	,	PUNCT
ejpam-6598	357	21	which	which	PRON
ejpam-6598	357	22	are	be	AUX
ejpam-6598	357	23	frequently	frequently	ADV
ejpam-6598	357	24	brought	bring	VERB
ejpam-6598	357	25	on	on	ADP
ejpam-6598	357	26	by	by	ADP
ejpam-6598	357	27	the	the	DET
ejpam-6598	357	28	use	use	NOUN
ejpam-6598	357	29	of	of	ADP
ejpam-6598	357	30	unsanitary	unsanitary	ADJ
ejpam-6598	357	31	substitutes	substitute	NOUN
ejpam-6598	357	32	like	like	ADP
ejpam-6598	357	33	ash	ash	NOUN
ejpam-6598	357	34	,	,	PUNCT
ejpam-6598	357	35	sand	sand	NOUN
ejpam-6598	357	36	,	,	PUNCT
ejpam-6598	357	37	or	or	CCONJ
ejpam-6598	357	38	old	old	ADJ
ejpam-6598	357	39	fabric	fabric	NOUN
ejpam-6598	357	40	.	.	PUNCT
ejpam-6598	358	1	a	a	DET
ejpam-6598	358	2	suitable	suitable	ADJ
ejpam-6598	358	3	product	product	NOUN
ejpam-6598	358	4	also	also	ADV
ejpam-6598	358	5	enhances	enhance	VERB
ejpam-6598	358	6	a	a	DET
ejpam-6598	358	7	woman	woman	NOUN
ejpam-6598	358	8	’s	’s	PART
ejpam-6598	358	9	comfort	comfort	NOUN
ejpam-6598	358	10	and	and	CCONJ
ejpam-6598	358	11	confidence	confidence	NOUN
ejpam-6598	358	12	,	,	PUNCT
ejpam-6598	358	13	helping	help	VERB
ejpam-6598	358	14	her	she	PRON
ejpam-6598	358	15	manage	manage	VERB
ejpam-6598	358	16	menstruation	menstruation	NOUN
ejpam-6598	358	17	with	with	ADP
ejpam-6598	358	18	dignity	dignity	NOUN
ejpam-6598	358	19	,	,	PUNCT
ejpam-6598	358	20	free	free	ADJ
ejpam-6598	358	21	from	from	ADP
ejpam-6598	358	22	embarrassment	embarrassment	NOUN
ejpam-6598	358	23	or	or	CCONJ
ejpam-6598	358	24	fear	fear	NOUN
ejpam-6598	358	25	of	of	ADP
ejpam-6598	358	26	leaks	leak	NOUN
ejpam-6598	358	27	and	and	CCONJ
ejpam-6598	358	28	odor	odor	NOUN
ejpam-6598	358	29	.	.	PUNCT
ejpam-6598	359	1	importantly	importantly	ADV
ejpam-6598	359	2	,	,	PUNCT
ejpam-6598	359	3	access	access	NOUN
ejpam-6598	359	4	to	to	ADP
ejpam-6598	359	5	proper	proper	ADJ
ejpam-6598	359	6	menstrual	menstrual	ADJ
ejpam-6598	359	7	hygiene	hygiene	NOUN
ejpam-6598	359	8	products	product	NOUN
ejpam-6598	359	9	enables	enable	VERB
ejpam-6598	359	10	girls	girl	NOUN
ejpam-6598	359	11	to	to	PART
ejpam-6598	359	12	continue	continue	VERB
ejpam-6598	359	13	attending	attend	VERB
ejpam-6598	359	14	school	school	NOUN
ejpam-6598	359	15	and	and	CCONJ
ejpam-6598	359	16	women	woman	NOUN
ejpam-6598	359	17	to	to	PART
ejpam-6598	359	18	participate	participate	VERB
ejpam-6598	359	19	fully	fully	ADV
ejpam-6598	359	20	in	in	ADP
ejpam-6598	359	21	work	work	NOUN
ejpam-6598	359	22	and	and	CCONJ
ejpam-6598	359	23	community	community	NOUN
ejpam-6598	359	24	life	life	NOUN
ejpam-6598	359	25	,	,	PUNCT
ejpam-6598	359	26	thereby	thereby	ADV
ejpam-6598	359	27	supporting	support	VERB
ejpam-6598	359	28	their	their	PRON
ejpam-6598	359	29	educational	educational	ADJ
ejpam-6598	359	30	and	and	CCONJ
ejpam-6598	359	31	economic	economic	ADJ
ejpam-6598	359	32	growth	growth	NOUN
ejpam-6598	359	33	.	.	PUNCT
ejpam-6598	360	1	moreover	moreover	ADV
ejpam-6598	360	2	,	,	PUNCT
ejpam-6598	360	3	choosing	choose	VERB
ejpam-6598	360	4	the	the	DET
ejpam-6598	360	5	right	right	ADJ
ejpam-6598	360	6	product	product	NOUN
ejpam-6598	360	7	contributes	contribute	VERB
ejpam-6598	360	8	significantly	significantly	ADV
ejpam-6598	360	9	to	to	ADP
ejpam-6598	360	10	women	woman	NOUN
ejpam-6598	360	11	’s	’s	PART
ejpam-6598	360	12	empowerment	empowerment	NOUN
ejpam-6598	360	13	and	and	CCONJ
ejpam-6598	360	14	gender	gender	NOUN
ejpam-6598	360	15	equality	equality	NOUN
ejpam-6598	360	16	by	by	ADP
ejpam-6598	360	17	encouraging	encourage	VERB
ejpam-6598	360	18	open	open	ADJ
ejpam-6598	360	19	conversations	conversation	NOUN
ejpam-6598	360	20	about	about	ADP
ejpam-6598	360	21	menstruation	menstruation	NOUN
ejpam-6598	360	22	and	and	CCONJ
ejpam-6598	360	23	helping	help	VERB
ejpam-6598	360	24	women	woman	NOUN
ejpam-6598	360	25	take	take	VERB
ejpam-6598	360	26	control	control	NOUN
ejpam-6598	360	27	of	of	ADP
ejpam-6598	360	28	their	their	PRON
ejpam-6598	360	29	health	health	NOUN
ejpam-6598	360	30	.	.	PUNCT
ejpam-6598	361	1	environmentally	environmentally	ADV
ejpam-6598	361	2	,	,	PUNCT
ejpam-6598	361	3	sustainable	sustainable	ADJ
ejpam-6598	361	4	options	option	NOUN
ejpam-6598	361	5	such	such	ADJ
ejpam-6598	361	6	as	as	ADP
ejpam-6598	361	7	reusable	reusable	ADJ
ejpam-6598	361	8	or	or	CCONJ
ejpam-6598	361	9	biodegradable	biodegradable	ADJ
ejpam-6598	361	10	products	product	NOUN
ejpam-6598	361	11	help	help	NOUN
ejpam-6598	361	12	reduce	reduce	VERB
ejpam-6598	361	13	plastic	plastic	ADJ
ejpam-6598	361	14	waste	waste	NOUN
ejpam-6598	361	15	,	,	PUNCT
ejpam-6598	361	16	which	which	PRON
ejpam-6598	361	17	is	be	AUX
ejpam-6598	361	18	especially	especially	ADV
ejpam-6598	361	19	crucial	crucial	ADJ
ejpam-6598	361	20	in	in	ADP
ejpam-6598	361	21	rural	rural	ADJ
ejpam-6598	361	22	areas	area	NOUN
ejpam-6598	361	23	lacking	lack	VERB
ejpam-6598	361	24	proper	proper	ADJ
ejpam-6598	361	25	waste	waste	NOUN
ejpam-6598	361	26	disposal	disposal	NOUN
ejpam-6598	361	27	systems	system	NOUN
ejpam-6598	361	28	.	.	PUNCT
ejpam-6598	362	1	economically	economically	ADV
ejpam-6598	362	2	,	,	PUNCT
ejpam-6598	362	3	reusable	reusable	ADJ
ejpam-6598	362	4	products	product	NOUN
ejpam-6598	362	5	offer	offer	VERB
ejpam-6598	362	6	long	long	ADJ
ejpam-6598	362	7	-	-	PUNCT
ejpam-6598	362	8	term	term	NOUN
ejpam-6598	362	9	cost	cost	NOUN
ejpam-6598	362	10	savings	saving	NOUN
ejpam-6598	362	11	,	,	PUNCT
ejpam-6598	362	12	reducing	reduce	VERB
ejpam-6598	362	13	reliance	reliance	NOUN
ejpam-6598	362	14	on	on	ADP
ejpam-6598	362	15	continuous	continuous	ADJ
ejpam-6598	362	16	external	external	ADJ
ejpam-6598	362	17	aid	aid	NOUN
ejpam-6598	362	18	.	.	PUNCT
ejpam-6598	363	1	additionally	additionally	ADV
ejpam-6598	363	2	,	,	PUNCT
ejpam-6598	363	3	promoting	promote	VERB
ejpam-6598	363	4	locally	locally	ADV
ejpam-6598	363	5	made	make	VERB
ejpam-6598	363	6	menstrual	menstrual	ADJ
ejpam-6598	363	7	products	product	NOUN
ejpam-6598	363	8	creates	create	VERB
ejpam-6598	363	9	livelihood	livelihood	ADJ
ejpam-6598	363	10	opportunities	opportunity	NOUN
ejpam-6598	363	11	for	for	ADP
ejpam-6598	363	12	women	woman	NOUN
ejpam-6598	363	13	through	through	ADP
ejpam-6598	363	14	community	community	NOUN
ejpam-6598	363	15	-	-	PUNCT
ejpam-6598	363	16	based	base	VERB
ejpam-6598	363	17	production	production	NOUN
ejpam-6598	363	18	,	,	PUNCT
ejpam-6598	363	19	further	far	ADV
ejpam-6598	363	20	boosting	boost	VERB
ejpam-6598	363	21	rural	rural	ADJ
ejpam-6598	363	22	economies	economy	NOUN
ejpam-6598	363	23	.	.	PUNCT
ejpam-6598	364	1	lastly	lastly	ADV
ejpam-6598	364	2	,	,	PUNCT
ejpam-6598	364	3	involving	involve	VERB
ejpam-6598	364	4	n.	n.	PROPN
ejpam-6598	364	5	preethi	preethi	ADV
ejpam-6598	364	6	,	,	PUNCT
ejpam-6598	364	7	g.	g.	PROPN
ejpam-6598	364	8	k.	k.	PROPN
ejpam-6598	364	9	revathi	revathi	PROPN
ejpam-6598	364	10	/	/	SYM
ejpam-6598	364	11	eur	eur	PROPN
ejpam-6598	364	12	.	.	PUNCT
ejpam-6598	365	1	j.	j.	PROPN
ejpam-6598	365	2	pure	pure	PROPN
ejpam-6598	365	3	appl	appl	PROPN
ejpam-6598	365	4	.	.	PROPN
ejpam-6598	365	5	math	math	PROPN
ejpam-6598	365	6	,	,	PUNCT
ejpam-6598	365	7	18	18	NUM
ejpam-6598	365	8	(	(	PUNCT
ejpam-6598	365	9	3	3	NUM
ejpam-6598	365	10	)	)	PUNCT
ejpam-6598	365	11	(	(	PUNCT
ejpam-6598	365	12	2025	2025	NUM
ejpam-6598	365	13	)	)	PUNCT
ejpam-6598	365	14	,	,	PUNCT
ejpam-6598	365	15	6598	6598	NUM
ejpam-6598	365	16	12	12	NUM
ejpam-6598	365	17	of	of	ADP
ejpam-6598	365	18	17	17	NUM
ejpam-6598	365	19	communities	community	NOUN
ejpam-6598	365	20	in	in	ADP
ejpam-6598	365	21	menstrual	menstrual	ADJ
ejpam-6598	365	22	health	health	NOUN
ejpam-6598	365	23	initiatives	initiative	NOUN
ejpam-6598	365	24	raises	raise	VERB
ejpam-6598	365	25	awareness	awareness	NOUN
ejpam-6598	365	26	,	,	PUNCT
ejpam-6598	365	27	dispels	dispel	VERB
ejpam-6598	365	28	myths	myth	NOUN
ejpam-6598	365	29	,	,	PUNCT
ejpam-6598	365	30	and	and	CCONJ
ejpam-6598	365	31	fosters	foster	VERB
ejpam-6598	365	32	a	a	DET
ejpam-6598	365	33	more	more	ADV
ejpam-6598	365	34	supportive	supportive	ADJ
ejpam-6598	365	35	environment	environment	NOUN
ejpam-6598	365	36	for	for	ADP
ejpam-6598	365	37	women	woman	NOUN
ejpam-6598	365	38	’s	’s	PART
ejpam-6598	365	39	health	health	NOUN
ejpam-6598	365	40	and	and	CCONJ
ejpam-6598	365	41	well	well	ADV
ejpam-6598	365	42	-	-	PUNCT
ejpam-6598	365	43	being	being	NOUN
ejpam-6598	365	44	.	.	PUNCT
ejpam-6598	366	1	in	in	ADP
ejpam-6598	366	2	this	this	DET
ejpam-6598	366	3	regard	regard	NOUN
ejpam-6598	366	4	,	,	PUNCT
ejpam-6598	366	5	the	the	DET
ejpam-6598	366	6	current	current	ADJ
ejpam-6598	366	7	study	study	NOUN
ejpam-6598	366	8	explores	explore	VERB
ejpam-6598	366	9	the	the	DET
ejpam-6598	366	10	possibilities	possibility	NOUN
ejpam-6598	366	11	and	and	CCONJ
ejpam-6598	366	12	attempts	attempt	NOUN
ejpam-6598	366	13	to	to	PART
ejpam-6598	366	14	obtain	obtain	VERB
ejpam-6598	366	15	a	a	DET
ejpam-6598	366	16	meaningful	meaningful	ADJ
ejpam-6598	366	17	solution	solution	NOUN
ejpam-6598	366	18	using	use	VERB
ejpam-6598	366	19	pfdf	pfdf	ADJ
ejpam-6598	366	20	collection	collection	NOUN
ejpam-6598	366	21	sets	set	NOUN
ejpam-6598	366	22	and	and	CCONJ
ejpam-6598	366	23	the	the	DET
ejpam-6598	366	24	pfdfts	pfdft	NOUN
ejpam-6598	366	25	.	.	PUNCT
ejpam-6598	367	1	the	the	DET
ejpam-6598	367	2	structural	structural	ADJ
ejpam-6598	367	3	and	and	CCONJ
ejpam-6598	367	4	topological	topological	ADJ
ejpam-6598	367	5	features	feature	NOUN
ejpam-6598	367	6	of	of	ADP
ejpam-6598	367	7	this	this	DET
ejpam-6598	367	8	proposed	propose	VERB
ejpam-6598	367	9	space	space	NOUN
ejpam-6598	367	10	are	be	AUX
ejpam-6598	367	11	leveraged	leverage	VERB
ejpam-6598	367	12	to	to	PART
ejpam-6598	367	13	establish	establish	VERB
ejpam-6598	367	14	a	a	DET
ejpam-6598	367	15	clear	clear	ADJ
ejpam-6598	367	16	and	and	CCONJ
ejpam-6598	367	17	coherent	coherent	ADJ
ejpam-6598	367	18	framework	framework	NOUN
ejpam-6598	367	19	that	that	PRON
ejpam-6598	367	20	aligns	align	VERB
ejpam-6598	367	21	with	with	ADP
ejpam-6598	367	22	theoretical	theoretical	ADJ
ejpam-6598	367	23	rigor	rigor	NOUN
ejpam-6598	367	24	.	.	PUNCT
ejpam-6598	368	1	this	this	DET
ejpam-6598	368	2	application	application	NOUN
ejpam-6598	368	3	illustrates	illustrate	VERB
ejpam-6598	368	4	how	how	SCONJ
ejpam-6598	368	5	the	the	DET
ejpam-6598	368	6	construction	construction	NOUN
ejpam-6598	368	7	and	and	CCONJ
ejpam-6598	368	8	conditions	condition	NOUN
ejpam-6598	368	9	of	of	ADP
ejpam-6598	368	10	the	the	DET
ejpam-6598	368	11	pfdfts	pfdft	NOUN
ejpam-6598	368	12	can	can	AUX
ejpam-6598	368	13	facilitate	facilitate	VERB
ejpam-6598	368	14	the	the	DET
ejpam-6598	368	15	systematic	systematic	ADJ
ejpam-6598	368	16	organization	organization	NOUN
ejpam-6598	368	17	and	and	CCONJ
ejpam-6598	368	18	refinement	refinement	NOUN
ejpam-6598	368	19	of	of	ADP
ejpam-6598	368	20	the	the	DET
ejpam-6598	368	21	selection	selection	NOUN
ejpam-6598	368	22	process	process	NOUN
ejpam-6598	368	23	.	.	PUNCT
ejpam-6598	369	1	by	by	ADP
ejpam-6598	369	2	anchoring	anchor	VERB
ejpam-6598	369	3	the	the	DET
ejpam-6598	369	4	approach	approach	NOUN
ejpam-6598	369	5	in	in	ADP
ejpam-6598	369	6	a	a	DET
ejpam-6598	369	7	robust	robust	ADJ
ejpam-6598	369	8	mathematical	mathematical	ADJ
ejpam-6598	369	9	foundation	foundation	NOUN
ejpam-6598	369	10	,	,	PUNCT
ejpam-6598	369	11	the	the	DET
ejpam-6598	369	12	study	study	NOUN
ejpam-6598	369	13	highlights	highlight	VERB
ejpam-6598	369	14	the	the	DET
ejpam-6598	369	15	practical	practical	ADJ
ejpam-6598	369	16	relevance	relevance	NOUN
ejpam-6598	369	17	and	and	CCONJ
ejpam-6598	369	18	real	real	ADJ
ejpam-6598	369	19	-	-	PUNCT
ejpam-6598	369	20	world	world	NOUN
ejpam-6598	369	21	applicability	applicability	NOUN
ejpam-6598	369	22	of	of	ADP
ejpam-6598	369	23	the	the	DET
ejpam-6598	369	24	theoretical	theoretical	ADJ
ejpam-6598	369	25	model	model	NOUN
ejpam-6598	369	26	,	,	PUNCT
ejpam-6598	369	27	particularly	particularly	ADV
ejpam-6598	369	28	in	in	ADP
ejpam-6598	369	29	addressing	address	VERB
ejpam-6598	369	30	the	the	DET
ejpam-6598	369	31	needs	need	NOUN
ejpam-6598	369	32	of	of	ADP
ejpam-6598	369	33	rural	rural	ADJ
ejpam-6598	369	34	women	woman	NOUN
ejpam-6598	369	35	.	.	PUNCT
ejpam-6598	370	1	beyond	beyond	ADP
ejpam-6598	370	2	the	the	DET
ejpam-6598	370	3	theoretical	theoretical	ADJ
ejpam-6598	370	4	framework	framework	NOUN
ejpam-6598	370	5	,	,	PUNCT
ejpam-6598	370	6	the	the	DET
ejpam-6598	370	7	study	study	NOUN
ejpam-6598	370	8	explores	explore	VERB
ejpam-6598	370	9	the	the	DET
ejpam-6598	370	10	practical	practical	ADJ
ejpam-6598	370	11	implementation	implementation	NOUN
ejpam-6598	370	12	of	of	ADP
ejpam-6598	370	13	the	the	DET
ejpam-6598	370	14	pfdfts	pfdft	NOUN
ejpam-6598	370	15	and	and	CCONJ
ejpam-6598	370	16	its	its	PRON
ejpam-6598	370	17	associated	associated	ADJ
ejpam-6598	370	18	fine	fine	ADJ
ejpam-6598	370	19	collection	collection	NOUN
ejpam-6598	370	20	sets	set	NOUN
ejpam-6598	370	21	.	.	PUNCT
ejpam-6598	371	1	it	it	PRON
ejpam-6598	371	2	demonstrates	demonstrate	VERB
ejpam-6598	371	3	the	the	DET
ejpam-6598	371	4	critical	critical	ADJ
ejpam-6598	371	5	role	role	NOUN
ejpam-6598	371	6	this	this	DET
ejpam-6598	371	7	space	space	NOUN
ejpam-6598	371	8	plays	play	VERB
ejpam-6598	371	9	in	in	ADP
ejpam-6598	371	10	identifying	identify	VERB
ejpam-6598	371	11	the	the	DET
ejpam-6598	371	12	most	most	ADV
ejpam-6598	371	13	suitable	suitable	ADJ
ejpam-6598	371	14	menstrual	menstrual	ADJ
ejpam-6598	371	15	hygiene	hygiene	NOUN
ejpam-6598	371	16	product	product	NOUN
ejpam-6598	371	17	for	for	ADP
ejpam-6598	371	18	rural	rural	ADJ
ejpam-6598	371	19	women	woman	NOUN
ejpam-6598	371	20	.	.	PUNCT
ejpam-6598	372	1	by	by	ADP
ejpam-6598	372	2	utilizing	utilize	VERB
ejpam-6598	372	3	defined	define	VERB
ejpam-6598	372	4	parameters	parameter	NOUN
ejpam-6598	372	5	,	,	PUNCT
ejpam-6598	372	6	theoretical	theoretical	ADJ
ejpam-6598	372	7	structures	structure	NOUN
ejpam-6598	372	8	,	,	PUNCT
ejpam-6598	372	9	and	and	CCONJ
ejpam-6598	372	10	specific	specific	ADJ
ejpam-6598	372	11	conditions	condition	NOUN
ejpam-6598	372	12	,	,	PUNCT
ejpam-6598	372	13	this	this	DET
ejpam-6598	372	14	approach	approach	NOUN
ejpam-6598	372	15	enhances	enhance	VERB
ejpam-6598	372	16	the	the	DET
ejpam-6598	372	17	effectiveness	effectiveness	NOUN
ejpam-6598	372	18	and	and	CCONJ
ejpam-6598	372	19	precision	precision	NOUN
ejpam-6598	372	20	of	of	ADP
ejpam-6598	372	21	the	the	DET
ejpam-6598	372	22	selection	selection	NOUN
ejpam-6598	372	23	process	process	NOUN
ejpam-6598	372	24	,	,	PUNCT
ejpam-6598	372	25	as	as	SCONJ
ejpam-6598	372	26	detailed	detailed	ADJ
ejpam-6598	372	27	in	in	ADP
ejpam-6598	372	28	the	the	DET
ejpam-6598	372	29	following	follow	VERB
ejpam-6598	372	30	subsections	subsection	NOUN
ejpam-6598	372	31	.	.	PUNCT
ejpam-6598	373	1	5.1	5.1	NUM
ejpam-6598	373	2	.	.	PUNCT
ejpam-6598	373	3	algorithm	algorithm	NOUN
ejpam-6598	373	4	of	of	ADP
ejpam-6598	373	5	selecting	select	VERB
ejpam-6598	373	6	the	the	DET
ejpam-6598	373	7	best	well	ADV
ejpam-6598	373	8	menstrual	menstrual	ADJ
ejpam-6598	373	9	hygiene	hygiene	NOUN
ejpam-6598	373	10	product	product	NOUN
ejpam-6598	373	11	using	use	VERB
ejpam-6598	373	12	pythagorean	pythagorean	PROPN
ejpam-6598	373	13	fuzzy	fuzzy	ADJ
ejpam-6598	373	14	digital	digital	PROPN
ejpam-6598	373	15	fine	fine	ADJ
ejpam-6598	373	16	topological	topological	ADJ
ejpam-6598	373	17	space	space	NOUN
ejpam-6598	373	18	step-1	step-1	PROPN
ejpam-6598	373	19	:	:	PUNCT
ejpam-6598	373	20	let	let	VERB
ejpam-6598	373	21	ξ	ξ	X
ejpam-6598	373	22	=	=	PUNCT
ejpam-6598	373	23	{	{	PUNCT
ejpam-6598	373	24	a	a	PRON
ejpam-6598	373	25	}	}	PUNCT
ejpam-6598	373	26	be	be	AUX
ejpam-6598	373	27	a	a	DET
ejpam-6598	373	28	non	non	X
ejpam-6598	373	29	empty	empty	ADJ
ejpam-6598	373	30	set	set	NOUN
ejpam-6598	373	31	and	and	CCONJ
ejpam-6598	373	32	τ	τ	PROPN
ejpam-6598	373	33	=	=	PUNCT
ejpam-6598	373	34	{	{	PUNCT
ejpam-6598	373	35	0∼	0∼	NUM
ejpam-6598	373	36	,	,	PUNCT
ejpam-6598	373	37	1∼	1∼	NUM
ejpam-6598	373	38	,	,	PUNCT
ejpam-6598	373	39	ω	ω	NUM
ejpam-6598	373	40	}	}	PUNCT
ejpam-6598	373	41	is	be	AUX
ejpam-6598	373	42	a	a	DET
ejpam-6598	373	43	pfd	pfd	PROPN
ejpam-6598	373	44	topology	topology	NOUN
ejpam-6598	373	45	on	on	ADP
ejpam-6598	373	46	ξ	ξ	PROPN
ejpam-6598	373	47	.	.	PUNCT
ejpam-6598	374	1	step-2	step-2	PROPN
ejpam-6598	374	2	:	:	PUNCT
ejpam-6598	374	3	define	define	VERB
ejpam-6598	374	4	τ̂f	τ̂f	PUNCT
ejpam-6598	374	5	=	=	SYM
ejpam-6598	374	6	{	{	PUNCT
ejpam-6598	374	7	0∼	0∼	ADP
ejpam-6598	374	8	,	,	PUNCT
ejpam-6598	374	9	1∼	1∼	NUM
ejpam-6598	374	10	,	,	PUNCT
ejpam-6598	374	11	⋃	⋃	PUNCT
ejpam-6598	374	12	α∈j	α∈j	NOUN
ejpam-6598	374	13	gα	gα	ADP
ejpam-6598	374	14	}	}	PUNCT
ejpam-6598	374	15	.	.	PUNCT
ejpam-6598	375	1	here	here	ADV
ejpam-6598	375	2	the	the	DET
ejpam-6598	375	3	operator	operator	NOUN
ejpam-6598	375	4	“	"	PUNCT
ejpam-6598	375	5	⋃	⋃	PROPN
ejpam-6598	375	6	”	"	PUNCT
ejpam-6598	375	7	denotes	denote	VERB
ejpam-6598	375	8	the	the	DET
ejpam-6598	375	9	union	union	NOUN
ejpam-6598	375	10	of	of	ADP
ejpam-6598	375	11	the	the	DET
ejpam-6598	375	12	set	set	NOUN
ejpam-6598	375	13	of	of	ADP
ejpam-6598	375	14	all	all	DET
ejpam-6598	375	15	fine	fine	ADJ
ejpam-6598	375	16	collections	collection	NOUN
ejpam-6598	375	17	of	of	ADP
ejpam-6598	375	18	gα	gα	NOUN
ejpam-6598	375	19	.	.	PUNCT
ejpam-6598	376	1	then	then	ADV
ejpam-6598	376	2	τ̂f	τ̂f	NUM
ejpam-6598	376	3	is	be	AUX
ejpam-6598	376	4	said	say	VERB
ejpam-6598	376	5	to	to	PART
ejpam-6598	376	6	be	be	AUX
ejpam-6598	376	7	the	the	DET
ejpam-6598	376	8	pfdfs	pfdfs	NOUN
ejpam-6598	376	9	of	of	ADP
ejpam-6598	376	10	ξ	ξ	PROPN
ejpam-6598	376	11	.	.	PUNCT
ejpam-6598	377	1	step-3	step-3	NOUN
ejpam-6598	377	2	:	:	PUNCT
ejpam-6598	377	3	construct	construct	VERB
ejpam-6598	377	4	the	the	DET
ejpam-6598	377	5	pfdfts	pfdft	NOUN
ejpam-6598	377	6	(	(	PUNCT
ejpam-6598	377	7	ξ	ξ	PROPN
ejpam-6598	377	8	,	,	PUNCT
ejpam-6598	377	9	τ	τ	PROPN
ejpam-6598	377	10	,	,	PUNCT
ejpam-6598	377	11	τ̂f	τ̂f	NUM
ejpam-6598	377	12	)	)	PUNCT
ejpam-6598	377	13	generated	generate	VERB
ejpam-6598	377	14	by	by	ADP
ejpam-6598	377	15	the	the	DET
ejpam-6598	377	16	topology	topology	NOUN
ejpam-6598	377	17	τ	τ	PROPN
ejpam-6598	377	18	on	on	ADP
ejpam-6598	377	19	ξ	ξ	PROPN
ejpam-6598	377	20	.	.	PUNCT
ejpam-6598	378	1	step-4	step-4	NUM
ejpam-6598	378	2	:	:	PUNCT
ejpam-6598	378	3	assume	assume	VERB
ejpam-6598	378	4	the	the	DET
ejpam-6598	378	5	weight	weight	NOUN
ejpam-6598	378	6	vector	vector	NOUN
ejpam-6598	378	7	w	w	NOUN
ejpam-6598	378	8	=	=	PUNCT
ejpam-6598	378	9	(	(	PUNCT
ejpam-6598	378	10	w1,w2,w3	w1,w2,w3	NOUN
ejpam-6598	378	11	,	,	PUNCT
ejpam-6598	378	12	.	.	PUNCT
ejpam-6598	378	13	.	.	PUNCT
ejpam-6598	378	14	.	.	PUNCT
ejpam-6598	378	15	.	.	PUNCT
ejpam-6598	378	16	.	.	PUNCT
ejpam-6598	379	1	.	.	PUNCT
ejpam-6598	380	1	,	,	PUNCT
ejpam-6598	380	2	wn	wn	PROPN
ejpam-6598	380	3	)	)	PUNCT
ejpam-6598	380	4	t	t	PROPN
ejpam-6598	380	5	the	the	DET
ejpam-6598	380	6	pfdfns	pfdfns	NOUN
ejpam-6598	380	7	such	such	ADJ
ejpam-6598	380	8	that	that	PRON
ejpam-6598	380	9	wi(i	wi(i	NUM
ejpam-6598	381	1	=	=	SYM
ejpam-6598	381	2	1	1	NUM
ejpam-6598	381	3	,	,	PUNCT
ejpam-6598	381	4	2	2	NUM
ejpam-6598	381	5	,	,	PUNCT
ejpam-6598	381	6	3	3	NUM
ejpam-6598	381	7	,	,	PUNCT
ejpam-6598	381	8	.	.	PUNCT
ejpam-6598	381	9	.	.	PUNCT
ejpam-6598	382	1	.n	.n	PROPN
ejpam-6598	382	2	)	)	PUNCT
ejpam-6598	382	3	∈	∈	PROPN
ejpam-6598	383	1	[	[	X
ejpam-6598	383	2	0	0	NUM
ejpam-6598	383	3	,	,	PUNCT
ejpam-6598	383	4	1	1	NUM
ejpam-6598	383	5	]	]	PUNCT
ejpam-6598	383	6	and	and	CCONJ
ejpam-6598	383	7	∑n	∑n	PROPN
ejpam-6598	383	8	i=1wi	i=1wi	X
ejpam-6598	384	1	=	=	SYM
ejpam-6598	384	2	1	1	NUM
ejpam-6598	384	3	corresponding	correspond	VERB
ejpam-6598	384	4	to	to	ADP
ejpam-6598	384	5	the	the	DET
ejpam-6598	384	6	six	six	NUM
ejpam-6598	384	7	criteria	criterion	NOUN
ejpam-6598	384	8	affordability	affordability	NOUN
ejpam-6598	384	9	and	and	CCONJ
ejpam-6598	384	10	accessibility	accessibility	NOUN
ejpam-6598	384	11	,	,	PUNCT
ejpam-6598	384	12	cultural	cultural	ADJ
ejpam-6598	384	13	acceptance	acceptance	NOUN
ejpam-6598	384	14	and	and	CCONJ
ejpam-6598	384	15	awareness	awareness	NOUN
ejpam-6598	384	16	,	,	PUNCT
ejpam-6598	384	17	hygiene	hygiene	NOUN
ejpam-6598	384	18	and	and	CCONJ
ejpam-6598	384	19	health	health	NOUN
ejpam-6598	384	20	impact	impact	NOUN
ejpam-6598	384	21	,	,	PUNCT
ejpam-6598	384	22	product	product	NOUN
ejpam-6598	384	23	availability	availability	NOUN
ejpam-6598	384	24	and	and	CCONJ
ejpam-6598	384	25	supply	supply	NOUN
ejpam-6598	384	26	consistency	consistency	NOUN
ejpam-6598	384	27	,	,	PUNCT
ejpam-6598	384	28	comfort	comfort	NOUN
ejpam-6598	384	29	and	and	CCONJ
ejpam-6598	384	30	ease	ease	NOUN
ejpam-6598	384	31	of	of	ADP
ejpam-6598	384	32	use	use	NOUN
ejpam-6598	384	33	,	,	PUNCT
ejpam-6598	384	34	and	and	CCONJ
ejpam-6598	384	35	disposal	disposal	NOUN
ejpam-6598	384	36	and	and	CCONJ
ejpam-6598	384	37	waste	waste	NOUN
ejpam-6598	384	38	management	management	NOUN
ejpam-6598	384	39	.	.	PUNCT
ejpam-6598	385	1	step-5	step-5	NUM
ejpam-6598	385	2	:	:	PUNCT
ejpam-6598	385	3	calculate	calculate	VERB
ejpam-6598	385	4	the	the	DET
ejpam-6598	385	5	score	score	NOUN
ejpam-6598	385	6	function	function	NOUN
ejpam-6598	385	7	using	use	VERB
ejpam-6598	385	8	pfwa	pfwa	ADJ
ejpam-6598	385	9	operator	operator	NOUN
ejpam-6598	385	10	formula	formula	NOUN
ejpam-6598	385	11	pfwa	pfwa	NOUN
ejpam-6598	385	12	(	(	PUNCT
ejpam-6598	385	13	i1	i1	PROPN
ejpam-6598	385	14	,	,	PUNCT
ejpam-6598	385	15	i2	i2	PROPN
ejpam-6598	385	16	,	,	PUNCT
ejpam-6598	385	17	i3	i3	NOUN
ejpam-6598	385	18	,	,	PUNCT
ejpam-6598	385	19	.	.	PUNCT
ejpam-6598	385	20	.	.	PUNCT
ejpam-6598	385	21	.	.	PUNCT
ejpam-6598	386	1	jn	jn	PROPN
ejpam-6598	386	2	)	)	PUNCT
ejpam-6598	387	1	=	=	PUNCT
ejpam-6598	387	2	〈	〈	PROPN
ejpam-6598	387	3	√	√	PROPN
ejpam-6598	387	4	1−	1−	NUM
ejpam-6598	387	5	∏n	∏n	ADJ
ejpam-6598	387	6	i=1	i=1	PROPN
ejpam-6598	387	7	(	(	PUNCT
ejpam-6598	387	8	1−	1−	NUM
ejpam-6598	387	9	µ2i	µ2i	NOUN
ejpam-6598	387	10	)	)	PUNCT
ejpam-6598	387	11	wi	wi	PROPN
ejpam-6598	387	12	,	,	PUNCT
ejpam-6598	387	13	∏n	∏n	PROPN
ejpam-6598	387	14	i=1	i=1	PROPN
ejpam-6598	387	15	ϑ	ϑ	PROPN
ejpam-6598	387	16	wi	wi	PROPN
ejpam-6598	387	17	i	i	PROPN
ejpam-6598	387	18	〉	〉	NOUN
ejpam-6598	387	19	,	,	PUNCT
ejpam-6598	387	20	pfwg	pfwg	NOUN
ejpam-6598	387	21	operator	operator	NOUN
ejpam-6598	387	22	formula	formula	NOUN
ejpam-6598	387	23	pfwg	pfwg	NOUN
ejpam-6598	387	24	(	(	PUNCT
ejpam-6598	387	25	i1	i1	PROPN
ejpam-6598	387	26	,	,	PUNCT
ejpam-6598	387	27	j2	j2	PROPN
ejpam-6598	387	28	,	,	PUNCT
ejpam-6598	387	29	j3	j3	PROPN
ejpam-6598	387	30	,	,	PUNCT
ejpam-6598	387	31	.	.	PUNCT
ejpam-6598	387	32	.	.	PUNCT
ejpam-6598	388	1	.	.	PUNCT
ejpam-6598	389	1	,	,	PUNCT
ejpam-6598	389	2	in	in	ADP
ejpam-6598	389	3	)	)	PUNCT
ejpam-6598	389	4	=	=	PUNCT
ejpam-6598	390	1	〈	〈	PROPN
ejpam-6598	390	2	∏n	∏n	PROPN
ejpam-6598	390	3	i=1	i=1	PROPN
ejpam-6598	390	4	µ	µ	PROPN
ejpam-6598	390	5	wi	wi	PROPN
ejpam-6598	390	6	i	i	PRON
ejpam-6598	390	7	,	,	PUNCT
ejpam-6598	390	8	√	√	PROPN
ejpam-6598	390	9	1−	1−	NUM
ejpam-6598	390	10	∏n	∏n	ADJ
ejpam-6598	390	11	i=1	i=1	PROPN
ejpam-6598	390	12	(	(	PUNCT
ejpam-6598	390	13	1−	1−	NUM
ejpam-6598	390	14	ϑ2i	ϑ2i	ADJ
ejpam-6598	390	15	)	)	PUNCT
ejpam-6598	390	16	wi	wi	PROPN
ejpam-6598	390	17	〉	〉	NOUN
ejpam-6598	390	18	and	and	CCONJ
ejpam-6598	390	19	select	select	VERB
ejpam-6598	390	20	the	the	DET
ejpam-6598	390	21	best	well	ADV
ejpam-6598	390	22	menstrual	menstrual	ADJ
ejpam-6598	390	23	hygiene	hygiene	NOUN
ejpam-6598	390	24	product	product	NOUN
ejpam-6598	390	25	.	.	PUNCT
ejpam-6598	391	1	5.2	5.2	NUM
ejpam-6598	391	2	.	.	PUNCT
ejpam-6598	391	3	proposed	propose	VERB
ejpam-6598	391	4	study	study	NOUN
ejpam-6598	391	5	to	to	PART
ejpam-6598	391	6	identify	identify	VERB
ejpam-6598	391	7	the	the	DET
ejpam-6598	391	8	best	well	ADV
ejpam-6598	391	9	menstrual	menstrual	ADJ
ejpam-6598	391	10	hygiene	hygiene	NOUN
ejpam-6598	391	11	product	product	NOUN
ejpam-6598	391	12	for	for	ADP
ejpam-6598	391	13	rural	rural	ADJ
ejpam-6598	391	14	women	woman	NOUN
ejpam-6598	391	15	using	use	VERB
ejpam-6598	391	16	pythagorean	pythagorean	PROPN
ejpam-6598	391	17	fuzzy	fuzzy	ADJ
ejpam-6598	391	18	digital	digital	PROPN
ejpam-6598	391	19	fine	fine	ADJ
ejpam-6598	391	20	topological	topological	ADJ
ejpam-6598	391	21	space	space	NOUN
ejpam-6598	391	22	in	in	ADP
ejpam-6598	391	23	order	order	NOUN
ejpam-6598	391	24	to	to	PART
ejpam-6598	391	25	make	make	VERB
ejpam-6598	391	26	this	this	DET
ejpam-6598	391	27	process	process	NOUN
ejpam-6598	391	28	,	,	PUNCT
ejpam-6598	391	29	consider	consider	VERB
ejpam-6598	391	30	three	three	NUM
ejpam-6598	391	31	different	different	ADJ
ejpam-6598	391	32	menstrual	menstrual	ADJ
ejpam-6598	391	33	hygiene	hygiene	NOUN
ejpam-6598	391	34	products	product	NOUN
ejpam-6598	391	35	as	as	ADP
ejpam-6598	391	36	cloth	cloth	NOUN
ejpam-6598	391	37	pads	pad	NOUN
ejpam-6598	391	38	,	,	PUNCT
ejpam-6598	391	39	menstrual	menstrual	ADJ
ejpam-6598	391	40	cups	cup	NOUN
ejpam-6598	391	41	and	and	CCONJ
ejpam-6598	391	42	sanitary	sanitary	NOUN
ejpam-6598	391	43	pads	pad	NOUN
ejpam-6598	391	44	say	say	VERB
ejpam-6598	391	45	h	h	NOUN
ejpam-6598	391	46	=	=	PRON
ejpam-6598	391	47	{	{	PUNCT
ejpam-6598	391	48	h1,h2,h3	h1,h2,h3	PROPN
ejpam-6598	391	49	}	}	PUNCT
ejpam-6598	391	50	and	and	CCONJ
ejpam-6598	391	51	the	the	DET
ejpam-6598	391	52	six	six	NUM
ejpam-6598	391	53	factors	factor	NOUN
ejpam-6598	391	54	c	c	NOUN
ejpam-6598	391	55	=	=	SYM
ejpam-6598	391	56	{	{	PUNCT
ejpam-6598	391	57	c1,c2,c3,c4,c5,c6	c1,c2,c3,c4,c5,c6	X
ejpam-6598	391	58	}	}	PUNCT
ejpam-6598	391	59	.	.	PUNCT
ejpam-6598	392	1	the	the	DET
ejpam-6598	392	2	selected	select	VERB
ejpam-6598	392	3	evaluation	evaluation	NOUN
ejpam-6598	392	4	criteria	criterion	NOUN
ejpam-6598	392	5	affordability	affordability	NOUN
ejpam-6598	392	6	and	and	CCONJ
ejpam-6598	392	7	accessibility	accessibility	NOUN
ejpam-6598	392	8	,	,	PUNCT
ejpam-6598	392	9	n.	n.	PROPN
ejpam-6598	392	10	preethi	preethi	ADV
ejpam-6598	392	11	,	,	PUNCT
ejpam-6598	392	12	g.	g.	PROPN
ejpam-6598	392	13	k.	k.	PROPN
ejpam-6598	392	14	revathi	revathi	PROPN
ejpam-6598	392	15	/	/	SYM
ejpam-6598	392	16	eur	eur	PROPN
ejpam-6598	392	17	.	.	PUNCT
ejpam-6598	393	1	j.	j.	PROPN
ejpam-6598	393	2	pure	pure	PROPN
ejpam-6598	393	3	appl	appl	PROPN
ejpam-6598	393	4	.	.	PROPN
ejpam-6598	393	5	math	math	PROPN
ejpam-6598	393	6	,	,	PUNCT
ejpam-6598	393	7	18	18	NUM
ejpam-6598	393	8	(	(	PUNCT
ejpam-6598	393	9	3	3	NUM
ejpam-6598	393	10	)	)	PUNCT
ejpam-6598	393	11	(	(	PUNCT
ejpam-6598	393	12	2025	2025	NUM
ejpam-6598	393	13	)	)	PUNCT
ejpam-6598	393	14	,	,	PUNCT
ejpam-6598	393	15	6598	6598	NUM
ejpam-6598	393	16	13	13	NUM
ejpam-6598	393	17	of	of	ADP
ejpam-6598	393	18	17	17	NUM
ejpam-6598	393	19	cultural	cultural	ADJ
ejpam-6598	393	20	acceptance	acceptance	NOUN
ejpam-6598	393	21	and	and	CCONJ
ejpam-6598	393	22	awareness	awareness	NOUN
ejpam-6598	393	23	,	,	PUNCT
ejpam-6598	393	24	hygiene	hygiene	NOUN
ejpam-6598	393	25	and	and	CCONJ
ejpam-6598	393	26	health	health	NOUN
ejpam-6598	393	27	impact	impact	NOUN
ejpam-6598	393	28	,	,	PUNCT
ejpam-6598	393	29	product	product	NOUN
ejpam-6598	393	30	availability	availability	NOUN
ejpam-6598	393	31	and	and	CCONJ
ejpam-6598	393	32	supply	supply	NOUN
ejpam-6598	393	33	consistency	consistency	NOUN
ejpam-6598	393	34	,	,	PUNCT
ejpam-6598	393	35	comfort	comfort	NOUN
ejpam-6598	393	36	and	and	CCONJ
ejpam-6598	393	37	ease	ease	NOUN
ejpam-6598	393	38	of	of	ADP
ejpam-6598	393	39	use	use	NOUN
ejpam-6598	393	40	,	,	PUNCT
ejpam-6598	393	41	and	and	CCONJ
ejpam-6598	393	42	disposal	disposal	NOUN
ejpam-6598	393	43	and	and	CCONJ
ejpam-6598	393	44	waste	waste	NOUN
ejpam-6598	393	45	management	management	NOUN
ejpam-6598	393	46	serve	serve	VERB
ejpam-6598	393	47	as	as	ADP
ejpam-6598	393	48	comprehensive	comprehensive	ADJ
ejpam-6598	393	49	and	and	CCONJ
ejpam-6598	393	50	practical	practical	ADJ
ejpam-6598	393	51	dimensions	dimension	NOUN
ejpam-6598	393	52	for	for	ADP
ejpam-6598	393	53	assessing	assess	VERB
ejpam-6598	393	54	menstrual	menstrual	ADJ
ejpam-6598	393	55	hygiene	hygiene	NOUN
ejpam-6598	393	56	products	product	NOUN
ejpam-6598	393	57	,	,	PUNCT
ejpam-6598	393	58	particularly	particularly	ADV
ejpam-6598	393	59	in	in	ADP
ejpam-6598	393	60	rural	rural	ADJ
ejpam-6598	393	61	and	and	CCONJ
ejpam-6598	393	62	under	under	ADV
ejpam-6598	393	63	-	-	PUNCT
ejpam-6598	393	64	resourced	resource	VERB
ejpam-6598	393	65	settings	setting	NOUN
ejpam-6598	393	66	.	.	PUNCT
ejpam-6598	394	1	these	these	DET
ejpam-6598	394	2	parameters	parameter	NOUN
ejpam-6598	394	3	collectively	collectively	ADV
ejpam-6598	394	4	address	address	VERB
ejpam-6598	394	5	essential	essential	ADJ
ejpam-6598	394	6	aspects	aspect	NOUN
ejpam-6598	394	7	such	such	ADJ
ejpam-6598	394	8	as	as	ADP
ejpam-6598	394	9	economic	economic	ADJ
ejpam-6598	394	10	feasibility	feasibility	NOUN
ejpam-6598	394	11	,	,	PUNCT
ejpam-6598	394	12	sociocultural	sociocultural	ADJ
ejpam-6598	394	13	acceptability	acceptability	NOUN
ejpam-6598	394	14	,	,	PUNCT
ejpam-6598	394	15	health	health	NOUN
ejpam-6598	394	16	considerations	consideration	NOUN
ejpam-6598	394	17	,	,	PUNCT
ejpam-6598	394	18	supply	supply	NOUN
ejpam-6598	394	19	reliability	reliability	NOUN
ejpam-6598	394	20	,	,	PUNCT
ejpam-6598	394	21	user	user	NOUN
ejpam-6598	394	22	experience	experience	NOUN
ejpam-6598	394	23	,	,	PUNCT
ejpam-6598	394	24	and	and	CCONJ
ejpam-6598	394	25	environmental	environmental	ADJ
ejpam-6598	394	26	impact	impact	NOUN
ejpam-6598	394	27	.	.	PUNCT
ejpam-6598	395	1	affordability	affordability	NOUN
ejpam-6598	395	2	and	and	CCONJ
ejpam-6598	395	3	accessibility	accessibility	NOUN
ejpam-6598	395	4	reflect	reflect	VERB
ejpam-6598	395	5	the	the	DET
ejpam-6598	395	6	importance	importance	NOUN
ejpam-6598	395	7	of	of	ADP
ejpam-6598	395	8	cost	cost	NOUN
ejpam-6598	395	9	and	and	CCONJ
ejpam-6598	395	10	product	product	NOUN
ejpam-6598	395	11	reach	reach	NOUN
ejpam-6598	395	12	.	.	PUNCT
ejpam-6598	396	1	cultural	cultural	ADJ
ejpam-6598	396	2	acceptance	acceptance	NOUN
ejpam-6598	396	3	and	and	CCONJ
ejpam-6598	396	4	awareness	awareness	NOUN
ejpam-6598	396	5	consider	consider	VERB
ejpam-6598	396	6	societal	societal	ADJ
ejpam-6598	396	7	norms	norm	NOUN
ejpam-6598	396	8	and	and	CCONJ
ejpam-6598	396	9	awareness	awareness	NOUN
ejpam-6598	396	10	levels	level	NOUN
ejpam-6598	396	11	that	that	PRON
ejpam-6598	396	12	influence	influence	VERB
ejpam-6598	396	13	product	product	NOUN
ejpam-6598	396	14	adoption	adoption	NOUN
ejpam-6598	396	15	.	.	PUNCT
ejpam-6598	397	1	hygiene	hygiene	NOUN
ejpam-6598	397	2	and	and	CCONJ
ejpam-6598	397	3	health	health	NOUN
ejpam-6598	397	4	impact	impact	NOUN
ejpam-6598	397	5	captures	capture	VERB
ejpam-6598	397	6	the	the	DET
ejpam-6598	397	7	sanitary	sanitary	NOUN
ejpam-6598	397	8	and	and	CCONJ
ejpam-6598	397	9	safety	safety	NOUN
ejpam-6598	397	10	implications	implication	NOUN
ejpam-6598	397	11	of	of	ADP
ejpam-6598	397	12	use	use	NOUN
ejpam-6598	397	13	.	.	PUNCT
ejpam-6598	398	1	product	product	NOUN
ejpam-6598	398	2	availability	availability	NOUN
ejpam-6598	398	3	and	and	CCONJ
ejpam-6598	398	4	supply	supply	NOUN
ejpam-6598	398	5	consistency	consistency	NOUN
ejpam-6598	398	6	ensures	ensure	VERB
ejpam-6598	398	7	the	the	DET
ejpam-6598	398	8	reliability	reliability	NOUN
ejpam-6598	398	9	of	of	ADP
ejpam-6598	398	10	access	access	NOUN
ejpam-6598	398	11	over	over	ADP
ejpam-6598	398	12	time	time	NOUN
ejpam-6598	398	13	.	.	PUNCT
ejpam-6598	399	1	comfort	comfort	NOUN
ejpam-6598	399	2	and	and	CCONJ
ejpam-6598	399	3	ease	ease	NOUN
ejpam-6598	399	4	of	of	ADP
ejpam-6598	399	5	use	use	NOUN
ejpam-6598	399	6	examines	examine	NOUN
ejpam-6598	399	7	user	user	NOUN
ejpam-6598	399	8	-	-	PUNCT
ejpam-6598	399	9	friendliness	friendliness	ADJ
ejpam-6598	399	10	and	and	CCONJ
ejpam-6598	399	11	physical	physical	ADJ
ejpam-6598	399	12	comfort	comfort	NOUN
ejpam-6598	399	13	.	.	PUNCT
ejpam-6598	400	1	disposal	disposal	NOUN
ejpam-6598	400	2	and	and	CCONJ
ejpam-6598	400	3	waste	waste	NOUN
ejpam-6598	400	4	management	management	NOUN
ejpam-6598	400	5	accounts	account	NOUN
ejpam-6598	400	6	for	for	ADP
ejpam-6598	400	7	environmental	environmental	ADJ
ejpam-6598	400	8	concerns	concern	NOUN
ejpam-6598	400	9	and	and	CCONJ
ejpam-6598	400	10	the	the	DET
ejpam-6598	400	11	practical	practical	ADJ
ejpam-6598	400	12	aspects	aspect	NOUN
ejpam-6598	400	13	of	of	ADP
ejpam-6598	400	14	waste	waste	NOUN
ejpam-6598	400	15	handling	handling	NOUN
ejpam-6598	400	16	.	.	PUNCT
ejpam-6598	401	1	together	together	ADV
ejpam-6598	401	2	,	,	PUNCT
ejpam-6598	401	3	these	these	DET
ejpam-6598	401	4	parameters	parameter	NOUN
ejpam-6598	401	5	offer	offer	VERB
ejpam-6598	401	6	a	a	DET
ejpam-6598	401	7	balanced	balanced	ADJ
ejpam-6598	401	8	and	and	CCONJ
ejpam-6598	401	9	realistic	realistic	ADJ
ejpam-6598	401	10	framework	framework	NOUN
ejpam-6598	401	11	for	for	ADP
ejpam-6598	401	12	decision	decision	NOUN
ejpam-6598	401	13	-	-	PUNCT
ejpam-6598	401	14	making	making	NOUN
ejpam-6598	401	15	.	.	PUNCT
ejpam-6598	402	1	in	in	ADP
ejpam-6598	402	2	this	this	DET
ejpam-6598	402	3	study	study	NOUN
ejpam-6598	402	4	,	,	PUNCT
ejpam-6598	402	5	both	both	CCONJ
ejpam-6598	402	6	membership	membership	NOUN
ejpam-6598	402	7	and	and	CCONJ
ejpam-6598	402	8	non	non	ADJ
ejpam-6598	402	9	-	-	ADJ
ejpam-6598	402	10	membership	membership	ADJ
ejpam-6598	402	11	values	value	NOUN
ejpam-6598	402	12	are	be	AUX
ejpam-6598	402	13	assigned	assign	VERB
ejpam-6598	402	14	to	to	ADP
ejpam-6598	402	15	each	each	DET
ejpam-6598	402	16	product	product	NOUN
ejpam-6598	402	17	based	base	VERB
ejpam-6598	402	18	on	on	ADP
ejpam-6598	402	19	these	these	DET
ejpam-6598	402	20	six	six	NUM
ejpam-6598	402	21	criteria	criterion	NOUN
ejpam-6598	402	22	.	.	PUNCT
ejpam-6598	403	1	these	these	DET
ejpam-6598	403	2	values	value	NOUN
ejpam-6598	403	3	are	be	AUX
ejpam-6598	403	4	subjectively	subjectively	ADV
ejpam-6598	403	5	assigned	assign	VERB
ejpam-6598	403	6	by	by	ADP
ejpam-6598	403	7	the	the	DET
ejpam-6598	403	8	authors	author	NOUN
ejpam-6598	403	9	based	base	VERB
ejpam-6598	403	10	on	on	ADP
ejpam-6598	403	11	an	an	DET
ejpam-6598	403	12	analysis	analysis	NOUN
ejpam-6598	403	13	of	of	ADP
ejpam-6598	403	14	common	common	ADJ
ejpam-6598	403	15	product	product	NOUN
ejpam-6598	403	16	attributes	attribute	VERB
ejpam-6598	403	17	,	,	PUNCT
ejpam-6598	403	18	user	user	NOUN
ejpam-6598	403	19	preferences	preference	NOUN
ejpam-6598	403	20	,	,	PUNCT
ejpam-6598	403	21	and	and	CCONJ
ejpam-6598	403	22	practical	practical	ADJ
ejpam-6598	403	23	challenges	challenge	NOUN
ejpam-6598	403	24	encountered	encounter	VERB
ejpam-6598	403	25	in	in	ADP
ejpam-6598	403	26	everyday	everyday	ADJ
ejpam-6598	403	27	life	life	NOUN
ejpam-6598	403	28	.	.	PUNCT
ejpam-6598	404	1	for	for	ADP
ejpam-6598	404	2	instance	instance	NOUN
ejpam-6598	404	3	,	,	PUNCT
ejpam-6598	404	4	cloth	cloth	NOUN
ejpam-6598	404	5	pads	pad	NOUN
ejpam-6598	404	6	are	be	AUX
ejpam-6598	404	7	considered	consider	VERB
ejpam-6598	404	8	economically	economically	ADV
ejpam-6598	404	9	affordable	affordable	ADJ
ejpam-6598	404	10	and	and	CCONJ
ejpam-6598	404	11	culturally	culturally	ADV
ejpam-6598	404	12	acceptable	acceptable	ADJ
ejpam-6598	404	13	,	,	PUNCT
ejpam-6598	404	14	which	which	PRON
ejpam-6598	404	15	leads	lead	VERB
ejpam-6598	404	16	to	to	ADP
ejpam-6598	404	17	higher	high	ADJ
ejpam-6598	404	18	membership	membership	NOUN
ejpam-6598	404	19	and	and	CCONJ
ejpam-6598	404	20	lower	low	ADJ
ejpam-6598	404	21	non	non	ADJ
ejpam-6598	404	22	-	-	ADJ
ejpam-6598	404	23	membership	membership	ADJ
ejpam-6598	404	24	values	value	NOUN
ejpam-6598	404	25	in	in	ADP
ejpam-6598	404	26	those	those	DET
ejpam-6598	404	27	categories	category	NOUN
ejpam-6598	404	28	.	.	PUNCT
ejpam-6598	405	1	however	however	ADV
ejpam-6598	405	2	,	,	PUNCT
ejpam-6598	405	3	they	they	PRON
ejpam-6598	405	4	score	score	VERB
ejpam-6598	405	5	lower	lower	ADV
ejpam-6598	405	6	in	in	ADP
ejpam-6598	405	7	terms	term	NOUN
ejpam-6598	405	8	of	of	ADP
ejpam-6598	405	9	hygiene	hygiene	NOUN
ejpam-6598	405	10	and	and	CCONJ
ejpam-6598	405	11	availability	availability	NOUN
ejpam-6598	405	12	.	.	PUNCT
ejpam-6598	406	1	menstrual	menstrual	ADJ
ejpam-6598	406	2	cups	cup	NOUN
ejpam-6598	406	3	exhibit	exhibit	VERB
ejpam-6598	406	4	high	high	ADJ
ejpam-6598	406	5	membership	membership	NOUN
ejpam-6598	406	6	values	value	NOUN
ejpam-6598	406	7	in	in	ADP
ejpam-6598	406	8	hygiene	hygiene	NOUN
ejpam-6598	406	9	and	and	CCONJ
ejpam-6598	406	10	long	long	ADJ
ejpam-6598	406	11	-	-	PUNCT
ejpam-6598	406	12	term	term	NOUN
ejpam-6598	406	13	affordability	affordability	NOUN
ejpam-6598	406	14	but	but	CCONJ
ejpam-6598	406	15	face	face	VERB
ejpam-6598	406	16	lower	low	ADJ
ejpam-6598	406	17	cultural	cultural	ADJ
ejpam-6598	406	18	acceptance	acceptance	NOUN
ejpam-6598	406	19	and	and	CCONJ
ejpam-6598	406	20	usability	usability	NOUN
ejpam-6598	406	21	,	,	PUNCT
ejpam-6598	406	22	resulting	result	VERB
ejpam-6598	406	23	in	in	ADP
ejpam-6598	406	24	higher	high	ADJ
ejpam-6598	406	25	non	non	ADJ
ejpam-6598	406	26	-	-	NOUN
ejpam-6598	406	27	membership	membership	NOUN
ejpam-6598	406	28	in	in	ADP
ejpam-6598	406	29	those	those	DET
ejpam-6598	406	30	areas	area	NOUN
ejpam-6598	406	31	.	.	PUNCT
ejpam-6598	407	1	sanitary	sanitary	NOUN
ejpam-6598	407	2	pads	pad	NOUN
ejpam-6598	407	3	generally	generally	ADV
ejpam-6598	407	4	show	show	VERB
ejpam-6598	407	5	moderate	moderate	ADJ
ejpam-6598	407	6	performance	performance	NOUN
ejpam-6598	407	7	across	across	ADP
ejpam-6598	407	8	most	most	ADJ
ejpam-6598	407	9	criteria	criterion	NOUN
ejpam-6598	407	10	but	but	CCONJ
ejpam-6598	407	11	receive	receive	VERB
ejpam-6598	407	12	low	low	ADJ
ejpam-6598	407	13	scores	score	NOUN
ejpam-6598	407	14	in	in	ADP
ejpam-6598	407	15	waste	waste	NOUN
ejpam-6598	407	16	management	management	NOUN
ejpam-6598	407	17	due	due	ADP
ejpam-6598	407	18	to	to	ADP
ejpam-6598	407	19	their	their	PRON
ejpam-6598	407	20	environmental	environmental	ADJ
ejpam-6598	407	21	impact	impact	NOUN
ejpam-6598	407	22	.	.	PUNCT
ejpam-6598	408	1	these	these	DET
ejpam-6598	408	2	values	value	NOUN
ejpam-6598	408	3	conform	conform	VERB
ejpam-6598	408	4	to	to	ADP
ejpam-6598	408	5	the	the	DET
ejpam-6598	408	6	pfs	pfs	ADJ
ejpam-6598	408	7	conditions	condition	NOUN
ejpam-6598	408	8	and	and	CCONJ
ejpam-6598	408	9	serve	serve	VERB
ejpam-6598	408	10	as	as	ADP
ejpam-6598	408	11	input	input	NOUN
ejpam-6598	408	12	for	for	ADP
ejpam-6598	408	13	evaluating	evaluate	VERB
ejpam-6598	408	14	the	the	DET
ejpam-6598	408	15	suitability	suitability	NOUN
ejpam-6598	408	16	of	of	ADP
ejpam-6598	408	17	each	each	DET
ejpam-6598	408	18	product	product	NOUN
ejpam-6598	408	19	using	use	VERB
ejpam-6598	408	20	pfwa	pfwa	NOUN
ejpam-6598	408	21	and	and	CCONJ
ejpam-6598	408	22	pfwg	pfwg	NOUN
ejpam-6598	408	23	operators	operator	NOUN
ejpam-6598	408	24	in	in	ADP
ejpam-6598	408	25	the	the	DET
ejpam-6598	408	26	proposed	propose	VERB
ejpam-6598	408	27	model	model	NOUN
ejpam-6598	408	28	.	.	PUNCT
ejpam-6598	409	1	the	the	DET
ejpam-6598	409	2	following	follow	VERB
ejpam-6598	409	3	are	be	AUX
ejpam-6598	409	4	the	the	DET
ejpam-6598	409	5	analyses	analysis	NOUN
ejpam-6598	409	6	performed	perform	VERB
ejpam-6598	409	7	to	to	PART
ejpam-6598	409	8	discover	discover	VERB
ejpam-6598	409	9	the	the	DET
ejpam-6598	409	10	best	good	ADJ
ejpam-6598	409	11	alternative	alternative	NOUN
ejpam-6598	409	12	among	among	ADP
ejpam-6598	409	13	the	the	DET
ejpam-6598	409	14	possible	possible	ADJ
ejpam-6598	409	15	ones	one	NOUN
ejpam-6598	409	16	utilising	utilise	VERB
ejpam-6598	409	17	the	the	DET
ejpam-6598	409	18	pfwa	pfwa	ADJ
ejpam-6598	409	19	and	and	CCONJ
ejpam-6598	409	20	pfwg	pfwg	NOUN
ejpam-6598	409	21	operators	operator	NOUN
ejpam-6598	409	22	stated	state	VERB
ejpam-6598	409	23	in	in	ADP
ejpam-6598	409	24	definition	definition	NOUN
ejpam-6598	409	25	20	20	NUM
ejpam-6598	409	26	.	.	PUNCT
ejpam-6598	410	1	step	step	NOUN
ejpam-6598	410	2	1	1	NUM
ejpam-6598	410	3	:	:	PUNCT
ejpam-6598	410	4	let	let	VERB
ejpam-6598	410	5	ξ	ξ	X
ejpam-6598	410	6	=	=	PUNCT
ejpam-6598	410	7	{	{	PUNCT
ejpam-6598	410	8	a	a	PRON
ejpam-6598	410	9	}	}	PUNCT
ejpam-6598	410	10	be	be	AUX
ejpam-6598	410	11	a	a	DET
ejpam-6598	410	12	non	non	X
ejpam-6598	410	13	empty	empty	ADJ
ejpam-6598	410	14	set	set	NOUN
ejpam-6598	410	15	and	and	CCONJ
ejpam-6598	410	16	τ	τ	PROPN
ejpam-6598	410	17	=	=	PUNCT
ejpam-6598	410	18	{	{	PUNCT
ejpam-6598	410	19	0∼	0∼	NUM
ejpam-6598	410	20	,	,	PUNCT
ejpam-6598	410	21	1∼	1∼	NUM
ejpam-6598	410	22	,	,	PUNCT
ejpam-6598	410	23	ω	ω	NUM
ejpam-6598	410	24	}	}	PUNCT
ejpam-6598	410	25	is	be	AUX
ejpam-6598	410	26	a	a	DET
ejpam-6598	410	27	pfd	pfd	NOUN
ejpam-6598	410	28	topology	topology	NOUN
ejpam-6598	410	29	on	on	ADP
ejpam-6598	410	30	ξ	ξ	PROPN
ejpam-6598	410	31	where	where	SCONJ
ejpam-6598	410	32	0∼	0∼	X
ejpam-6598	410	33	=	=	PRON
ejpam-6598	410	34	{	{	PUNCT
ejpam-6598	410	35	(	(	PUNCT
ejpam-6598	410	36	0	0	NUM
ejpam-6598	410	37	,	,	PUNCT
ejpam-6598	410	38	1	1	NUM
ejpam-6598	410	39	)	)	PUNCT
ejpam-6598	410	40	}	}	PUNCT
ejpam-6598	410	41	,	,	PUNCT
ejpam-6598	410	42	1∼	1∼	X
ejpam-6598	410	43	=	=	SYM
ejpam-6598	410	44	{	{	PUNCT
ejpam-6598	410	45	(	(	PUNCT
ejpam-6598	410	46	1	1	NUM
ejpam-6598	410	47	,	,	PUNCT
ejpam-6598	410	48	0	0	NUM
ejpam-6598	410	49	)	)	PUNCT
ejpam-6598	410	50	}	}	PUNCT
ejpam-6598	410	51	and	and	CCONJ
ejpam-6598	410	52	ω	ω	X
ejpam-6598	410	53	=	=	SYM
ejpam-6598	410	54	{	{	PUNCT
ejpam-6598	410	55	(	(	PUNCT
ejpam-6598	410	56	0.21	0.21	NUM
ejpam-6598	410	57	,	,	PUNCT
ejpam-6598	410	58	0.97	0.97	NUM
ejpam-6598	410	59	)	)	PUNCT
ejpam-6598	410	60	}	}	PUNCT
ejpam-6598	410	61	where	where	SCONJ
ejpam-6598	410	62	ω	ω	PROPN
ejpam-6598	410	63	is	be	AUX
ejpam-6598	410	64	a	a	DET
ejpam-6598	410	65	pfd	pfd	PROPN
ejpam-6598	410	66	open	open	NOUN
ejpam-6598	410	67	set	set	VERB
ejpam-6598	410	68	on	on	ADP
ejpam-6598	410	69	ξ	ξ	PROPN
ejpam-6598	410	70	.	.	PUNCT
ejpam-6598	411	1	step	step	NOUN
ejpam-6598	411	2	2	2	NUM
ejpam-6598	411	3	:	:	PUNCT
ejpam-6598	411	4	define	define	VERB
ejpam-6598	411	5	τ(ω	τ(ω	PUNCT
ejpam-6598	411	6	)	)	PUNCT
ejpam-6598	411	7	=	=	SYM
ejpam-6598	411	8	τ̂α	τ̂α	PUNCT
ejpam-6598	412	1	=	=	NOUN
ejpam-6598	412	2	{	{	PUNCT
ejpam-6598	412	3	gα	gα	X
ejpam-6598	412	4	(	(	PUNCT
ejpam-6598	412	5	̸=	̸=	PROPN
ejpam-6598	412	6	1∼	1∼	NUM
ejpam-6598	412	7	)	)	PUNCT
ejpam-6598	412	8	;	;	PUNCT
ejpam-6598	412	9	gα	gα	ADP
ejpam-6598	412	10	∩	∩	PROPN
ejpam-6598	412	11	ω	ω	PROPN
ejpam-6598	412	12	̸=	̸=	PROPN
ejpam-6598	412	13	0∼	0∼	NUM
ejpam-6598	412	14	,	,	PUNCT
ejpam-6598	412	15	for	for	ADP
ejpam-6598	412	16	ω	ω	PROPN
ejpam-6598	412	17	∈	∈	PROPN
ejpam-6598	412	18	τ	τ	PROPN
ejpam-6598	412	19	ω	ω	NUM
ejpam-6598	412	20	̸=	̸=	PROPN
ejpam-6598	412	21	0∼	0∼	NUM
ejpam-6598	412	22	for	for	ADP
ejpam-6598	412	23	some	some	DET
ejpam-6598	412	24	α	α	NOUN
ejpam-6598	412	25	∈	∈	PROPN
ejpam-6598	412	26	j	j	PROPN
ejpam-6598	412	27	,	,	PUNCT
ejpam-6598	412	28	j	j	PROPN
ejpam-6598	412	29	is	be	AUX
ejpam-6598	412	30	an	an	DET
ejpam-6598	412	31	index	index	NOUN
ejpam-6598	412	32	set	set	NOUN
ejpam-6598	412	33	.	.	PUNCT
ejpam-6598	413	1	•	•	NUM
ejpam-6598	413	2	considerg1	considerg1	NOUN
ejpam-6598	414	1	=	=	PRON
ejpam-6598	414	2	{	{	PUNCT
ejpam-6598	414	3	(	(	PUNCT
ejpam-6598	414	4	0.34	0.34	NUM
ejpam-6598	414	5	,	,	PUNCT
ejpam-6598	414	6	0.84)},g2	0.84)},g2	NOUN
ejpam-6598	414	7	=	=	SYM
ejpam-6598	414	8	{	{	PUNCT
ejpam-6598	414	9	(	(	PUNCT
ejpam-6598	414	10	0.38	0.38	NUM
ejpam-6598	414	11	,	,	PUNCT
ejpam-6598	414	12	0.72)},g3	0.72)},g3	NOUN
ejpam-6598	414	13	=	=	SYM
ejpam-6598	414	14	{	{	PUNCT
ejpam-6598	414	15	(	(	PUNCT
ejpam-6598	414	16	0.46	0.46	NUM
ejpam-6598	414	17	,	,	PUNCT
ejpam-6598	414	18	0.77	0.77	NUM
ejpam-6598	414	19	)	)	PUNCT
ejpam-6598	414	20	}	}	PUNCT
ejpam-6598	414	21	,	,	PUNCT
ejpam-6598	414	22	g4	g4	NOUN
ejpam-6598	414	23	=	=	SYM
ejpam-6598	414	24	{	{	PUNCT
ejpam-6598	414	25	(	(	PUNCT
ejpam-6598	414	26	0.71	0.71	NUM
ejpam-6598	414	27	,	,	PUNCT
ejpam-6598	414	28	0.42	0.42	NUM
ejpam-6598	414	29	)	)	PUNCT
ejpam-6598	414	30	}	}	PUNCT
ejpam-6598	414	31	,	,	PUNCT
ejpam-6598	414	32	g5	g5	NOUN
ejpam-6598	414	33	=	=	PRON
ejpam-6598	414	34	{	{	PUNCT
ejpam-6598	414	35	(	(	PUNCT
ejpam-6598	414	36	0.91	0.91	NUM
ejpam-6598	414	37	,	,	PUNCT
ejpam-6598	414	38	0.26)},g6	0.26)},g6	PROPN
ejpam-6598	414	39	=	=	X
ejpam-6598	414	40	{	{	PUNCT
ejpam-6598	414	41	(	(	PUNCT
ejpam-6598	414	42	0.28	0.28	NUM
ejpam-6598	414	43	,	,	PUNCT
ejpam-6598	414	44	0.83)},g7	0.83)},g7	NUM
ejpam-6598	414	45	=	=	SYM
ejpam-6598	414	46	{	{	PUNCT
ejpam-6598	414	47	(	(	PUNCT
ejpam-6598	414	48	0.44	0.44	NUM
ejpam-6598	414	49	,	,	PUNCT
ejpam-6598	414	50	0.85)},g8	0.85)},g8	PROPN
ejpam-6598	414	51	=	=	SYM
ejpam-6598	414	52	{	{	PUNCT
ejpam-6598	414	53	(	(	PUNCT
ejpam-6598	414	54	0.61	0.61	NUM
ejpam-6598	414	55	,	,	PUNCT
ejpam-6598	414	56	0.66	0.66	NUM
ejpam-6598	414	57	)	)	PUNCT
ejpam-6598	414	58	}	}	PUNCT
ejpam-6598	414	59	,	,	PUNCT
ejpam-6598	414	60	g9	g9	NOUN
ejpam-6598	414	61	=	=	SYM
ejpam-6598	414	62	{	{	PUNCT
ejpam-6598	414	63	(	(	PUNCT
ejpam-6598	414	64	0.75	0.75	NUM
ejpam-6598	414	65	,	,	PUNCT
ejpam-6598	414	66	0.72)},g10	0.72)},g10	X
ejpam-6598	414	67	=	=	SYM
ejpam-6598	414	68	{	{	PUNCT
ejpam-6598	414	69	(	(	PUNCT
ejpam-6598	414	70	0.54	0.54	NUM
ejpam-6598	414	71	,	,	PUNCT
ejpam-6598	414	72	0.77)},g11	0.77)},g11	NUM
ejpam-6598	414	73	=	=	SYM
ejpam-6598	414	74	{	{	PUNCT
ejpam-6598	414	75	(	(	PUNCT
ejpam-6598	414	76	0.49	0.49	NUM
ejpam-6598	414	77	,	,	PUNCT
ejpam-6598	414	78	0.63)},g12	0.63)},g12	NUM
ejpam-6598	414	79	=	=	SYM
ejpam-6598	414	80	{	{	PUNCT
ejpam-6598	414	81	(	(	PUNCT
ejpam-6598	414	82	0.58	0.58	NUM
ejpam-6598	414	83	,	,	PUNCT
ejpam-6598	414	84	0.61	0.61	NUM
ejpam-6598	414	85	)	)	PUNCT
ejpam-6598	414	86	}	}	PUNCT
ejpam-6598	414	87	,	,	PUNCT
ejpam-6598	414	88	g13	g13	NOUN
ejpam-6598	414	89	=	=	SYM
ejpam-6598	414	90	{	{	PUNCT
ejpam-6598	414	91	(	(	PUNCT
ejpam-6598	414	92	0.67	0.67	NUM
ejpam-6598	414	93	,	,	PUNCT
ejpam-6598	414	94	0.51)},g14	0.51)},g14	NUM
ejpam-6598	414	95	=	=	SYM
ejpam-6598	414	96	{	{	PUNCT
ejpam-6598	414	97	(	(	PUNCT
ejpam-6598	414	98	0.62	0.62	NUM
ejpam-6598	414	99	,	,	PUNCT
ejpam-6598	414	100	0.75)},g15	0.75)},g15	NUM
ejpam-6598	414	101	=	=	SYM
ejpam-6598	414	102	{	{	PUNCT
ejpam-6598	414	103	(	(	PUNCT
ejpam-6598	414	104	0.73	0.73	NUM
ejpam-6598	414	105	,	,	PUNCT
ejpam-6598	414	106	0.56	0.56	NUM
ejpam-6598	414	107	)	)	PUNCT
ejpam-6598	414	108	}	}	PUNCT
ejpam-6598	414	109	be	be	AUX
ejpam-6598	414	110	the	the	DET
ejpam-6598	414	111	pfds	pfds	NOUN
ejpam-6598	414	112	’s	’s	NOUN
ejpam-6598	414	113	.	.	PUNCT
ejpam-6598	415	1	•	•	NUM
ejpam-6598	416	1	so	so	ADV
ejpam-6598	416	2	the	the	DET
ejpam-6598	416	3	pfdf	pfdf	ADJ
ejpam-6598	416	4	collections	collection	NOUN
ejpam-6598	416	5	are	be	AUX
ejpam-6598	416	6	gα	gα	ADP
ejpam-6598	416	7	=	=	PUNCT
ejpam-6598	416	8	{	{	PUNCT
ejpam-6598	416	9	(	(	PUNCT
ejpam-6598	416	10	0.34	0.34	NUM
ejpam-6598	416	11	,	,	PUNCT
ejpam-6598	416	12	0.84	0.84	NUM
ejpam-6598	416	13	)	)	PUNCT
ejpam-6598	416	14	,	,	PUNCT
ejpam-6598	416	15	(	(	PUNCT
ejpam-6598	416	16	0.38,0.72	0.38,0.72	NOUN
ejpam-6598	416	17	)	)	PUNCT
ejpam-6598	416	18	,	,	PUNCT
ejpam-6598	416	19	(	(	PUNCT
ejpam-6598	416	20	0.46,0.77	0.46,0.77	X
ejpam-6598	416	21	)	)	PUNCT
ejpam-6598	416	22	,	,	PUNCT
ejpam-6598	416	23	(	(	PUNCT
ejpam-6598	416	24	0.71,0.42	0.71,0.42	ADP
ejpam-6598	416	25	)	)	PUNCT
ejpam-6598	416	26	,	,	PUNCT
ejpam-6598	416	27	(	(	PUNCT
ejpam-6598	416	28	0.91,0.26	0.91,0.26	NOUN
ejpam-6598	416	29	)	)	PUNCT
ejpam-6598	416	30	,	,	PUNCT
ejpam-6598	416	31	(	(	PUNCT
ejpam-6598	416	32	0.28,0.83	0.28,0.83	X
ejpam-6598	416	33	)	)	PUNCT
ejpam-6598	416	34	,	,	PUNCT
ejpam-6598	416	35	(	(	PUNCT
ejpam-6598	416	36	0.44,0.85	0.44,0.85	INTJ
ejpam-6598	416	37	)	)	PUNCT
ejpam-6598	416	38	,	,	PUNCT
ejpam-6598	416	39	(	(	PUNCT
ejpam-6598	416	40	0.61,0.66	0.61,0.66	NUM
ejpam-6598	416	41	)	)	PUNCT
ejpam-6598	416	42	,	,	PUNCT
ejpam-6598	416	43	(	(	PUNCT
ejpam-6598	416	44	0.75,0.72	0.75,0.72	NOUN
ejpam-6598	416	45	)	)	PUNCT
ejpam-6598	416	46	,	,	PUNCT
ejpam-6598	416	47	(	(	PUNCT
ejpam-6598	416	48	0.54,0.77	0.54,0.77	NUM
ejpam-6598	416	49	)	)	PUNCT
ejpam-6598	416	50	,	,	PUNCT
ejpam-6598	416	51	(	(	PUNCT
ejpam-6598	416	52	0.49,0.63	0.49,0.63	ADJ
ejpam-6598	416	53	)	)	PUNCT
ejpam-6598	416	54	,	,	PUNCT
ejpam-6598	416	55	(	(	PUNCT
ejpam-6598	416	56	0.58	0.58	NUM
ejpam-6598	416	57	,	,	PUNCT
ejpam-6598	416	58	0.61	0.61	NUM
ejpam-6598	416	59	)	)	PUNCT
ejpam-6598	416	60	,	,	PUNCT
ejpam-6598	416	61	(	(	PUNCT
ejpam-6598	416	62	0.67	0.67	NUM
ejpam-6598	416	63	,	,	PUNCT
ejpam-6598	416	64	0.51	0.51	NUM
ejpam-6598	416	65	)	)	PUNCT
ejpam-6598	416	66	,	,	PUNCT
ejpam-6598	416	67	(	(	PUNCT
ejpam-6598	416	68	0.62	0.62	NUM
ejpam-6598	416	69	,	,	PUNCT
ejpam-6598	416	70	0.75	0.75	NUM
ejpam-6598	416	71	)	)	PUNCT
ejpam-6598	416	72	,	,	PUNCT
ejpam-6598	416	73	(	(	PUNCT
ejpam-6598	416	74	0.73	0.73	NUM
ejpam-6598	416	75	,	,	PUNCT
ejpam-6598	416	76	0.56	0.56	NUM
ejpam-6598	416	77	)	)	PUNCT
ejpam-6598	416	78	}	}	PUNCT
ejpam-6598	416	79	which	which	PRON
ejpam-6598	416	80	satisfies	satisfy	VERB
ejpam-6598	416	81	the	the	DET
ejpam-6598	416	82	condition	condition	NOUN
ejpam-6598	416	83	gα	gα	ADP
ejpam-6598	416	84	∩	∩	ADJ
ejpam-6598	416	85	ω	ω	PROPN
ejpam-6598	416	86	̸=	̸=	PROPN
ejpam-6598	416	87	0∼.	0∼.	PROPN
ejpam-6598	416	88	n.	n.	PROPN
ejpam-6598	416	89	preethi	preethi	ADV
ejpam-6598	416	90	,	,	PUNCT
ejpam-6598	416	91	g.	g.	PROPN
ejpam-6598	416	92	k.	k.	PROPN
ejpam-6598	416	93	revathi	revathi	PROPN
ejpam-6598	416	94	/	/	SYM
ejpam-6598	416	95	eur	eur	PROPN
ejpam-6598	416	96	.	.	PUNCT
ejpam-6598	417	1	j.	j.	PROPN
ejpam-6598	417	2	pure	pure	PROPN
ejpam-6598	417	3	appl	appl	PROPN
ejpam-6598	417	4	.	.	PROPN
ejpam-6598	417	5	math	math	PROPN
ejpam-6598	417	6	,	,	PUNCT
ejpam-6598	417	7	18	18	NUM
ejpam-6598	417	8	(	(	PUNCT
ejpam-6598	417	9	3	3	NUM
ejpam-6598	417	10	)	)	PUNCT
ejpam-6598	417	11	(	(	PUNCT
ejpam-6598	417	12	2025	2025	NUM
ejpam-6598	417	13	)	)	PUNCT
ejpam-6598	417	14	,	,	PUNCT
ejpam-6598	417	15	6598	6598	NUM
ejpam-6598	417	16	14	14	NUM
ejpam-6598	417	17	of	of	ADP
ejpam-6598	417	18	17	17	NUM
ejpam-6598	417	19	•	•	NOUN
ejpam-6598	417	20	hence	hence	ADV
ejpam-6598	417	21	τ̂f	τ̂f	PUNCT
ejpam-6598	417	22	=	=	SYM
ejpam-6598	417	23	{	{	PUNCT
ejpam-6598	417	24	0∼	0∼	NOUN
ejpam-6598	417	25	,	,	PUNCT
ejpam-6598	417	26	1∼,gα	1∼,gα	NUM
ejpam-6598	417	27	}	}	PUNCT
ejpam-6598	417	28	is	be	AUX
ejpam-6598	417	29	called	call	VERB
ejpam-6598	417	30	the	the	DET
ejpam-6598	417	31	pfdf	pfdf	ADJ
ejpam-6598	417	32	collections	collection	NOUN
ejpam-6598	417	33	of	of	ADP
ejpam-6598	417	34	subsets	subset	NOUN
ejpam-6598	417	35	of	of	ADP
ejpam-6598	417	36	ξ	ξ	PROPN
ejpam-6598	417	37	and	and	CCONJ
ejpam-6598	417	38	(	(	PUNCT
ejpam-6598	417	39	ξ	ξ	PROPN
ejpam-6598	417	40	,	,	PUNCT
ejpam-6598	417	41	τ	τ	PROPN
ejpam-6598	417	42	,	,	PUNCT
ejpam-6598	417	43	τ̂f	τ̂f	NUM
ejpam-6598	417	44	)	)	PUNCT
ejpam-6598	417	45	is	be	AUX
ejpam-6598	417	46	said	say	VERB
ejpam-6598	417	47	to	to	PART
ejpam-6598	417	48	be	be	AUX
ejpam-6598	417	49	the	the	DET
ejpam-6598	417	50	pfdfts	pfdft	NOUN
ejpam-6598	417	51	generated	generate	VERB
ejpam-6598	417	52	by	by	ADP
ejpam-6598	417	53	the	the	DET
ejpam-6598	417	54	topology	topology	NOUN
ejpam-6598	417	55	τ	τ	PROPN
ejpam-6598	417	56	on	on	ADP
ejpam-6598	417	57	ξ	ξ	PROPN
ejpam-6598	417	58	.	.	PUNCT
ejpam-6598	418	1	step	step	NOUN
ejpam-6598	418	2	3	3	NUM
ejpam-6598	418	3	:	:	PUNCT
ejpam-6598	418	4	all	all	DET
ejpam-6598	418	5	the	the	DET
ejpam-6598	418	6	pfdf	pfdf	ADJ
ejpam-6598	418	7	subsets	subset	NOUN
ejpam-6598	418	8	in	in	ADP
ejpam-6598	418	9	the	the	DET
ejpam-6598	418	10	pfdft	pfdft	NOUN
ejpam-6598	418	11	on	on	ADP
ejpam-6598	418	12	ξ	ξ	PROPN
ejpam-6598	418	13	can	can	AUX
ejpam-6598	418	14	be	be	AUX
ejpam-6598	418	15	represented	represent	VERB
ejpam-6598	418	16	using	use	VERB
ejpam-6598	418	17	the	the	DET
ejpam-6598	418	18	ms	ms	PROPN
ejpam-6598	418	19	and	and	CCONJ
ejpam-6598	418	20	nms	nms	PROPN
ejpam-6598	418	21	values	value	NOUN
ejpam-6598	418	22	corresponding	correspond	VERB
ejpam-6598	418	23	to	to	ADP
ejpam-6598	418	24	the	the	DET
ejpam-6598	418	25	parameters	parameter	NOUN
ejpam-6598	418	26	c1,c2,c3,c4,c5	c1,c2,c3,c4,c5	NOUN
ejpam-6598	418	27	,	,	PUNCT
ejpam-6598	418	28	and	and	CCONJ
ejpam-6598	418	29	c6	c6	PROPN
ejpam-6598	418	30	.	.	PUNCT
ejpam-6598	419	1	these	these	DET
ejpam-6598	419	2	parameters	parameter	NOUN
ejpam-6598	419	3	denote	denote	VERB
ejpam-6598	419	4	affordability	affordability	NOUN
ejpam-6598	419	5	and	and	CCONJ
ejpam-6598	419	6	accessibility	accessibility	NOUN
ejpam-6598	419	7	,	,	PUNCT
ejpam-6598	419	8	cultural	cultural	ADJ
ejpam-6598	419	9	acceptance	acceptance	NOUN
ejpam-6598	419	10	and	and	CCONJ
ejpam-6598	419	11	awareness	awareness	NOUN
ejpam-6598	419	12	,	,	PUNCT
ejpam-6598	419	13	hygiene	hygiene	NOUN
ejpam-6598	419	14	and	and	CCONJ
ejpam-6598	419	15	health	health	NOUN
ejpam-6598	419	16	impact	impact	NOUN
ejpam-6598	419	17	,	,	PUNCT
ejpam-6598	419	18	product	product	NOUN
ejpam-6598	419	19	availability	availability	NOUN
ejpam-6598	419	20	and	and	CCONJ
ejpam-6598	419	21	supply	supply	NOUN
ejpam-6598	419	22	consistency	consistency	NOUN
ejpam-6598	419	23	,	,	PUNCT
ejpam-6598	419	24	comfort	comfort	NOUN
ejpam-6598	419	25	and	and	CCONJ
ejpam-6598	419	26	ease	ease	NOUN
ejpam-6598	419	27	of	of	ADP
ejpam-6598	419	28	use	use	NOUN
ejpam-6598	419	29	,	,	PUNCT
ejpam-6598	419	30	and	and	CCONJ
ejpam-6598	419	31	disposal	disposal	NOUN
ejpam-6598	419	32	and	and	CCONJ
ejpam-6598	419	33	waste	waste	NOUN
ejpam-6598	419	34	management	management	NOUN
ejpam-6598	419	35	respectively	respectively	ADV
ejpam-6598	419	36	.	.	PUNCT
ejpam-6598	420	1	the	the	DET
ejpam-6598	420	2	values	value	NOUN
ejpam-6598	420	3	for	for	ADP
ejpam-6598	420	4	c1	c1	PROPN
ejpam-6598	420	5	to	to	ADP
ejpam-6598	420	6	c6	c6	PROPN
ejpam-6598	420	7	for	for	ADP
ejpam-6598	420	8	the	the	DET
ejpam-6598	420	9	products	product	NOUN
ejpam-6598	420	10	are	be	AUX
ejpam-6598	420	11	assigned	assign	VERB
ejpam-6598	420	12	randomly	randomly	ADV
ejpam-6598	420	13	,	,	PUNCT
ejpam-6598	420	14	based	base	VERB
ejpam-6598	420	15	on	on	ADP
ejpam-6598	420	16	the	the	DET
ejpam-6598	420	17	characteristics	characteristic	NOUN
ejpam-6598	420	18	described	describe	VERB
ejpam-6598	420	19	by	by	ADP
ejpam-6598	420	20	these	these	DET
ejpam-6598	420	21	parameters	parameter	NOUN
ejpam-6598	420	22	.	.	PUNCT
ejpam-6598	421	1	for	for	ADP
ejpam-6598	421	2	instance	instance	NOUN
ejpam-6598	421	3	,	,	PUNCT
ejpam-6598	421	4	in	in	ADP
ejpam-6598	421	5	terms	term	NOUN
ejpam-6598	421	6	of	of	ADP
ejpam-6598	421	7	affordability	affordability	NOUN
ejpam-6598	421	8	,	,	PUNCT
ejpam-6598	421	9	menstrual	menstrual	ADJ
ejpam-6598	421	10	cups	cup	NOUN
ejpam-6598	421	11	are	be	AUX
ejpam-6598	421	12	generally	generally	ADV
ejpam-6598	421	13	less	less	ADV
ejpam-6598	421	14	affordable	affordable	ADJ
ejpam-6598	421	15	than	than	ADP
ejpam-6598	421	16	cloth	cloth	NOUN
ejpam-6598	421	17	pads	pad	NOUN
ejpam-6598	421	18	for	for	ADP
ejpam-6598	421	19	women	woman	NOUN
ejpam-6598	421	20	in	in	ADP
ejpam-6598	421	21	rural	rural	ADJ
ejpam-6598	421	22	areas	area	NOUN
ejpam-6598	421	23	.	.	PUNCT
ejpam-6598	422	1	therefore	therefore	ADV
ejpam-6598	422	2	,	,	PUNCT
ejpam-6598	422	3	the	the	DET
ejpam-6598	422	4	ms	ms	PROPN
ejpam-6598	422	5	value	value	NOUN
ejpam-6598	422	6	for	for	ADP
ejpam-6598	422	7	the	the	DET
ejpam-6598	422	8	affordability	affordability	NOUN
ejpam-6598	422	9	of	of	ADP
ejpam-6598	422	10	menstrual	menstrual	ADJ
ejpam-6598	422	11	cups	cup	NOUN
ejpam-6598	422	12	is	be	AUX
ejpam-6598	422	13	taken	take	VERB
ejpam-6598	422	14	as	as	ADP
ejpam-6598	422	15	0.44	0.44	NUM
ejpam-6598	422	16	,	,	PUNCT
ejpam-6598	422	17	which	which	PRON
ejpam-6598	422	18	is	be	AUX
ejpam-6598	422	19	lower	low	ADJ
ejpam-6598	422	20	than	than	ADP
ejpam-6598	422	21	that	that	PRON
ejpam-6598	422	22	of	of	ADP
ejpam-6598	422	23	cloth	cloth	NOUN
ejpam-6598	422	24	pads	pad	NOUN
ejpam-6598	422	25	.	.	PUNCT
ejpam-6598	423	1	similarly	similarly	ADV
ejpam-6598	423	2	,	,	PUNCT
ejpam-6598	423	3	for	for	ADP
ejpam-6598	423	4	cultural	cultural	ADJ
ejpam-6598	423	5	awareness	awareness	NOUN
ejpam-6598	423	6	,	,	PUNCT
ejpam-6598	423	7	the	the	DET
ejpam-6598	423	8	ms	ms	PROPN
ejpam-6598	423	9	value	value	NOUN
ejpam-6598	423	10	of	of	ADP
ejpam-6598	423	11	cloth	cloth	NOUN
ejpam-6598	423	12	pads	pad	NOUN
ejpam-6598	423	13	is	be	AUX
ejpam-6598	423	14	higher	high	ADJ
ejpam-6598	423	15	than	than	ADP
ejpam-6598	423	16	that	that	PRON
ejpam-6598	423	17	of	of	ADP
ejpam-6598	423	18	sanitary	sanitary	NOUN
ejpam-6598	423	19	pads	pad	NOUN
ejpam-6598	423	20	,	,	PUNCT
ejpam-6598	423	21	which	which	PRON
ejpam-6598	423	22	in	in	ADP
ejpam-6598	423	23	turn	turn	NOUN
ejpam-6598	423	24	is	be	AUX
ejpam-6598	423	25	higher	high	ADJ
ejpam-6598	423	26	than	than	ADP
ejpam-6598	423	27	that	that	PRON
ejpam-6598	423	28	of	of	ADP
ejpam-6598	423	29	menstrual	menstrual	ADJ
ejpam-6598	423	30	cups	cup	NOUN
ejpam-6598	423	31	.	.	PUNCT
ejpam-6598	424	1	following	follow	VERB
ejpam-6598	424	2	this	this	DET
ejpam-6598	424	3	rationale	rationale	NOUN
ejpam-6598	424	4	,	,	PUNCT
ejpam-6598	424	5	the	the	DET
ejpam-6598	424	6	pfdf	pfdf	ADJ
ejpam-6598	424	7	subsets	subset	NOUN
ejpam-6598	424	8	are	be	AUX
ejpam-6598	424	9	assigned	assign	VERB
ejpam-6598	424	10	values	value	NOUN
ejpam-6598	424	11	as	as	SCONJ
ejpam-6598	424	12	illustrated	illustrate	VERB
ejpam-6598	424	13	in	in	ADP
ejpam-6598	424	14	the	the	DET
ejpam-6598	424	15	table	table	NOUN
ejpam-6598	424	16	2	2	NUM
ejpam-6598	424	17	.	.	PUNCT
ejpam-6598	424	18	table	table	NOUN
ejpam-6598	424	19	2	2	NUM
ejpam-6598	424	20	:	:	PUNCT
ejpam-6598	424	21	criteria	criterion	NOUN
ejpam-6598	424	22	wise	wise	ADJ
ejpam-6598	424	23	membership	membership	NOUN
ejpam-6598	424	24	and	and	CCONJ
ejpam-6598	424	25	non	non	ADJ
ejpam-6598	424	26	-	-	ADJ
ejpam-6598	424	27	membership	membership	ADJ
ejpam-6598	424	28	values	value	NOUN
ejpam-6598	424	29	for	for	ADP
ejpam-6598	424	30	menstrual	menstrual	ADJ
ejpam-6598	424	31	hygiene	hygiene	NOUN
ejpam-6598	424	32	products	product	NOUN
ejpam-6598	424	33	c1	c1	PROPN
ejpam-6598	424	34	c2	c2	PROPN
ejpam-6598	424	35	c3	c3	PROPN
ejpam-6598	424	36	c4	c4	PROPN
ejpam-6598	424	37	c5	c5	PROPN
ejpam-6598	424	38	c6	c6	PROPN
ejpam-6598	424	39	h1	h1	PROPN
ejpam-6598	424	40	(	(	PUNCT
ejpam-6598	424	41	cloth	cloth	NOUN
ejpam-6598	424	42	pads	pad	NOUN
ejpam-6598	424	43	)	)	PUNCT
ejpam-6598	424	44	(	(	PUNCT
ejpam-6598	424	45	0.91,0.26	0.91,0.26	NOUN
ejpam-6598	424	46	)	)	PUNCT
ejpam-6598	424	47	(	(	PUNCT
ejpam-6598	424	48	0.71,0.42	0.71,0.42	NUM
ejpam-6598	424	49	)	)	PUNCT
ejpam-6598	424	50	(	(	PUNCT
ejpam-6598	424	51	0.38,0.72	0.38,0.72	NUM
ejpam-6598	424	52	)	)	PUNCT
ejpam-6598	424	53	(	(	PUNCT
ejpam-6598	424	54	0.21,0.97	0.21,0.97	NOUN
ejpam-6598	424	55	)	)	PUNCT
ejpam-6598	424	56	(	(	PUNCT
ejpam-6598	424	57	0.46,0.77	0.46,0.77	NUM
ejpam-6598	424	58	)	)	PUNCT
ejpam-6598	424	59	(	(	PUNCT
ejpam-6598	424	60	0.34,0.84	0.34,0.84	NOUN
ejpam-6598	424	61	)	)	PUNCT
ejpam-6598	424	62	h2	h2	NOUN
ejpam-6598	424	63	(	(	PUNCT
ejpam-6598	424	64	menstrual	menstrual	ADJ
ejpam-6598	424	65	cups	cup	NOUN
ejpam-6598	424	66	)	)	PUNCT
ejpam-6598	424	67	(	(	PUNCT
ejpam-6598	424	68	0.44,0.85	0.44,0.85	INTJ
ejpam-6598	424	69	)	)	PUNCT
ejpam-6598	424	70	(	(	PUNCT
ejpam-6598	424	71	0.28,0.83	0.28,0.83	X
ejpam-6598	424	72	)	)	PUNCT
ejpam-6598	424	73	(	(	PUNCT
ejpam-6598	424	74	1	1	NUM
ejpam-6598	424	75	,	,	PUNCT
ejpam-6598	424	76	0	0	NUM
ejpam-6598	424	77	)	)	PUNCT
ejpam-6598	424	78	(	(	PUNCT
ejpam-6598	424	79	0.61,0.66	0.61,0.66	NUM
ejpam-6598	424	80	)	)	PUNCT
ejpam-6598	424	81	(	(	PUNCT
ejpam-6598	424	82	0.75,0.72	0.75,0.72	NOUN
ejpam-6598	424	83	)	)	PUNCT
ejpam-6598	424	84	(	(	PUNCT
ejpam-6598	424	85	0.54,0.77	0.54,0.77	X
ejpam-6598	424	86	)	)	PUNCT
ejpam-6598	424	87	h3	h3	NOUN
ejpam-6598	424	88	(	(	PUNCT
ejpam-6598	424	89	sanitary	sanitary	NOUN
ejpam-6598	424	90	pads	pad	NOUN
ejpam-6598	424	91	)	)	PUNCT
ejpam-6598	424	92	(	(	PUNCT
ejpam-6598	424	93	0.49,0.63	0.49,0.63	NUM
ejpam-6598	424	94	)	)	PUNCT
ejpam-6598	424	95	(	(	PUNCT
ejpam-6598	424	96	0.58,0.61	0.58,0.61	NOUN
ejpam-6598	424	97	)	)	PUNCT
ejpam-6598	424	98	(	(	PUNCT
ejpam-6598	424	99	0.67,0.51	0.67,0.51	NUM
ejpam-6598	424	100	)	)	PUNCT
ejpam-6598	424	101	(	(	PUNCT
ejpam-6598	424	102	0.73,0.56	0.73,0.56	NUM
ejpam-6598	424	103	)	)	PUNCT
ejpam-6598	424	104	(	(	PUNCT
ejpam-6598	424	105	0.62,0.75	0.62,0.75	X
ejpam-6598	424	106	)	)	PUNCT
ejpam-6598	424	107	(	(	PUNCT
ejpam-6598	424	108	0	0	NUM
ejpam-6598	424	109	,	,	PUNCT
ejpam-6598	424	110	1	1	X
ejpam-6598	424	111	)	)	PUNCT
ejpam-6598	424	112	step	step	NOUN
ejpam-6598	424	113	4	4	NUM
ejpam-6598	424	114	:	:	PUNCT
ejpam-6598	424	115	the	the	DET
ejpam-6598	424	116	weight	weight	NOUN
ejpam-6598	424	117	vector	vector	NOUN
ejpam-6598	424	118	corresponding	correspond	VERB
ejpam-6598	424	119	to	to	ADP
ejpam-6598	424	120	these	these	DET
ejpam-6598	424	121	six	six	NUM
ejpam-6598	424	122	criteria	criterion	NOUN
ejpam-6598	424	123	c	c	NOUN
ejpam-6598	425	1	=	=	PRON
ejpam-6598	425	2	{	{	PUNCT
ejpam-6598	425	3	c1,c2,c3,c4,c5,c6	c1,c2,c3,c4,c5,c6	X
ejpam-6598	425	4	}	}	PUNCT
ejpam-6598	425	5	is	be	AUX
ejpam-6598	425	6	w	w	NOUN
ejpam-6598	425	7	=	=	PUNCT
ejpam-6598	425	8	{	{	PUNCT
ejpam-6598	425	9	0.17	0.17	NUM
ejpam-6598	425	10	,	,	PUNCT
ejpam-6598	425	11	0.24	0.24	NUM
ejpam-6598	425	12	,	,	PUNCT
ejpam-6598	425	13	0.3	0.3	NUM
ejpam-6598	425	14	,	,	PUNCT
ejpam-6598	425	15	0.04	0.04	NUM
ejpam-6598	425	16	,	,	PUNCT
ejpam-6598	425	17	0.15	0.15	NUM
ejpam-6598	425	18	,	,	PUNCT
ejpam-6598	425	19	0.1}t	0.1}t	NUM
ejpam-6598	425	20	where	where	SCONJ
ejpam-6598	425	21	wi	wi	PROPN
ejpam-6598	425	22	∈	∈	PROPN
ejpam-6598	426	1	[	[	X
ejpam-6598	426	2	0	0	NUM
ejpam-6598	426	3	,	,	PUNCT
ejpam-6598	426	4	1	1	NUM
ejpam-6598	426	5	]	]	PUNCT
ejpam-6598	426	6	and	and	CCONJ
ejpam-6598	426	7	∑n	∑n	PROPN
ejpam-6598	426	8	i=1wi	i=1wi	X
ejpam-6598	427	1	=	=	SYM
ejpam-6598	427	2	1	1	X
ejpam-6598	427	3	.	.	X
ejpam-6598	427	4	step	step	NOUN
ejpam-6598	427	5	5	5	NUM
ejpam-6598	427	6	:	:	PUNCT
ejpam-6598	427	7	to	to	PART
ejpam-6598	427	8	determine	determine	VERB
ejpam-6598	427	9	the	the	DET
ejpam-6598	427	10	most	most	ADV
ejpam-6598	427	11	suitable	suitable	ADJ
ejpam-6598	427	12	product	product	NOUN
ejpam-6598	427	13	among	among	ADP
ejpam-6598	427	14	cloth	cloth	NOUN
ejpam-6598	427	15	pads	pad	NOUN
ejpam-6598	427	16	,	,	PUNCT
ejpam-6598	427	17	menstrual	menstrual	ADJ
ejpam-6598	427	18	cups	cup	NOUN
ejpam-6598	427	19	,	,	PUNCT
ejpam-6598	427	20	and	and	CCONJ
ejpam-6598	427	21	sanitary	sanitary	NOUN
ejpam-6598	427	22	pads	pad	NOUN
ejpam-6598	427	23	,	,	PUNCT
ejpam-6598	427	24	the	the	DET
ejpam-6598	427	25	scoring	scoring	NOUN
ejpam-6598	427	26	function	function	NOUN
ejpam-6598	427	27	values	value	NOUN
ejpam-6598	427	28	must	must	AUX
ejpam-6598	427	29	be	be	AUX
ejpam-6598	427	30	calculated	calculate	VERB
ejpam-6598	427	31	using	use	VERB
ejpam-6598	427	32	the	the	DET
ejpam-6598	427	33	formula	formula	NOUN
ejpam-6598	427	34	provided	provide	VERB
ejpam-6598	427	35	in	in	ADP
ejpam-6598	427	36	equation	equation	NOUN
ejpam-6598	427	37	2.20	2.20	NUM
ejpam-6598	427	38	.	.	PUNCT
ejpam-6598	428	1	pfwa	pfwa	ADJ
ejpam-6598	428	2	calculation	calculation	NOUN
ejpam-6598	428	3	:	:	PUNCT
ejpam-6598	428	4	pfwa(j1	pfwa(j1	PROPN
ejpam-6598	428	5	,	,	PUNCT
ejpam-6598	428	6	j2	j2	PROPN
ejpam-6598	428	7	,	,	PUNCT
ejpam-6598	428	8	j3	j3	PROPN
ejpam-6598	428	9	,	,	PUNCT
ejpam-6598	428	10	...	...	PUNCT
ejpam-6598	428	11	,	,	PUNCT
ejpam-6598	428	12	jn	jn	PROPN
ejpam-6598	428	13	)	)	PUNCT
ejpam-6598	428	14	=	=	PUNCT
ejpam-6598	429	1	〈	〈	PROPN
ejpam-6598	429	2	√	√	PROPN
ejpam-6598	429	3	1−	1−	NUM
ejpam-6598	429	4	∏n	∏n	ADJ
ejpam-6598	429	5	i=1	i=1	PROPN
ejpam-6598	429	6	(	(	PUNCT
ejpam-6598	429	7	1−	1−	NUM
ejpam-6598	429	8	µ2i	µ2i	NOUN
ejpam-6598	429	9	)	)	PUNCT
ejpam-6598	429	10	wi	wi	PROPN
ejpam-6598	429	11	,	,	PUNCT
ejpam-6598	429	12	∏n	∏n	PROPN
ejpam-6598	429	13	i=1	i=1	PROPN
ejpam-6598	429	14	ϑi	ϑi	PROPN
ejpam-6598	429	15	wi	wi	PROPN
ejpam-6598	429	16	〉	〉	NOUN
ejpam-6598	429	17	the	the	DET
ejpam-6598	429	18	score	score	NOUN
ejpam-6598	429	19	values	value	NOUN
ejpam-6598	429	20	corresponding	correspond	VERB
ejpam-6598	429	21	to	to	ADP
ejpam-6598	429	22	them	they	PRON
ejpam-6598	429	23	are	be	AUX
ejpam-6598	429	24	sc	sc	PROPN
ejpam-6598	429	25	(	(	PUNCT
ejpam-6598	429	26	h1	h1	PROPN
ejpam-6598	429	27	)	)	PUNCT
ejpam-6598	429	28	=	=	SYM
ejpam-6598	430	1	−0.136	−0.136	ADJ
ejpam-6598	430	2	,	,	PUNCT
ejpam-6598	430	3	sc	sc	PROPN
ejpam-6598	430	4	(	(	PUNCT
ejpam-6598	430	5	h2	h2	PROPN
ejpam-6598	430	6	)	)	PUNCT
ejpam-6598	430	7	=	=	SYM
ejpam-6598	431	1	1.000	1.000	NUM
ejpam-6598	431	2	and	and	CCONJ
ejpam-6598	431	3	sc	sc	PROPN
ejpam-6598	431	4	(	(	PUNCT
ejpam-6598	431	5	h3	h3	NOUN
ejpam-6598	431	6	)	)	PUNCT
ejpam-6598	431	7	=	=	NOUN
ejpam-6598	431	8	0.009	0.009	NUM
ejpam-6598	431	9	.	.	PUNCT
ejpam-6598	432	1	since	since	SCONJ
ejpam-6598	432	2	sc	sc	PROPN
ejpam-6598	432	3	(	(	PUNCT
ejpam-6598	432	4	h2	h2	PROPN
ejpam-6598	432	5	)	)	PUNCT
ejpam-6598	432	6	>	>	X
ejpam-6598	432	7	sc	sc	PROPN
ejpam-6598	432	8	(	(	PUNCT
ejpam-6598	432	9	h3	h3	PROPN
ejpam-6598	432	10	)	)	PUNCT
ejpam-6598	432	11	>	>	X
ejpam-6598	432	12	sc	sc	PROPN
ejpam-6598	432	13	(	(	PUNCT
ejpam-6598	432	14	h1	h1	PROPN
ejpam-6598	432	15	)	)	PUNCT
ejpam-6598	432	16	,	,	PUNCT
ejpam-6598	432	17	we	we	PRON
ejpam-6598	432	18	have	have	VERB
ejpam-6598	432	19	h2	h2	NOUN
ejpam-6598	432	20	>	>	X
ejpam-6598	432	21	h3	h3	PROPN
ejpam-6598	432	22	>	>	X
ejpam-6598	432	23	h1	h1	PROPN
ejpam-6598	432	24	.	.	PUNCT
ejpam-6598	433	1	hence	hence	ADV
ejpam-6598	433	2	h2	h2	PROPN
ejpam-6598	433	3	(	(	PUNCT
ejpam-6598	433	4	menstrual	menstrual	ADJ
ejpam-6598	433	5	cups	cup	NOUN
ejpam-6598	433	6	)	)	PUNCT
ejpam-6598	433	7	is	be	AUX
ejpam-6598	433	8	the	the	DET
ejpam-6598	433	9	greatest	great	ADJ
ejpam-6598	433	10	product	product	NOUN
ejpam-6598	433	11	for	for	ADP
ejpam-6598	433	12	rural	rural	ADJ
ejpam-6598	433	13	women	woman	NOUN
ejpam-6598	433	14	’s	’s	PART
ejpam-6598	433	15	menstruation	menstruation	NOUN
ejpam-6598	433	16	hygiene	hygiene	NOUN
ejpam-6598	433	17	.	.	PUNCT
ejpam-6598	434	1	pfwg	pfwg	NOUN
ejpam-6598	434	2	calculation	calculation	NOUN
ejpam-6598	434	3	:	:	PUNCT
ejpam-6598	434	4	pfwg(i1	pfwg(i1	PROPN
ejpam-6598	434	5	,	,	PUNCT
ejpam-6598	434	6	i2	i2	PROPN
ejpam-6598	434	7	,	,	PUNCT
ejpam-6598	434	8	i3	i3	NOUN
ejpam-6598	434	9	,	,	PUNCT
ejpam-6598	434	10	.	.	PUNCT
ejpam-6598	434	11	.	.	PUNCT
ejpam-6598	434	12	.	.	PUNCT
ejpam-6598	434	13	.	.	PUNCT
ejpam-6598	434	14	.	.	PUNCT
ejpam-6598	434	15	.	.	PUNCT
ejpam-6598	435	1	..	..	PUNCT
ejpam-6598	435	2	,	,	PUNCT
ejpam-6598	435	3	in	in	ADP
ejpam-6598	435	4	)	)	PUNCT
ejpam-6598	435	5	=	=	PUNCT
ejpam-6598	436	1	〈	〈	PROPN
ejpam-6598	436	2	∏n	∏n	PROPN
ejpam-6598	436	3	i=1	i=1	PROPN
ejpam-6598	436	4	µ	µ	PROPN
ejpam-6598	436	5	wi	wi	PROPN
ejpam-6598	436	6	i	i	PRON
ejpam-6598	436	7	,	,	PUNCT
ejpam-6598	436	8	√	√	PROPN
ejpam-6598	436	9	1−	1−	NUM
ejpam-6598	436	10	∏n	∏n	ADJ
ejpam-6598	436	11	i=1	i=1	PROPN
ejpam-6598	436	12	(	(	PUNCT
ejpam-6598	436	13	1−	1−	NUM
ejpam-6598	436	14	ϑ2i	ϑ2i	ADJ
ejpam-6598	436	15	)	)	PUNCT
ejpam-6598	436	16	wi	wi	PROPN
ejpam-6598	436	17	〉	〉	NOUN
ejpam-6598	436	18	the	the	DET
ejpam-6598	436	19	score	score	NOUN
ejpam-6598	436	20	values	value	NOUN
ejpam-6598	436	21	corresponding	correspond	VERB
ejpam-6598	436	22	to	to	ADP
ejpam-6598	436	23	them	they	PRON
ejpam-6598	436	24	are	be	AUX
ejpam-6598	436	25	sc	sc	PROPN
ejpam-6598	436	26	(	(	PUNCT
ejpam-6598	436	27	h1	h1	PROPN
ejpam-6598	436	28	)	)	PUNCT
ejpam-6598	436	29	=	=	SYM
ejpam-6598	437	1	−0.627	−0.627	PROPN
ejpam-6598	437	2	,	,	PUNCT
ejpam-6598	437	3	sc	sc	PROPN
ejpam-6598	437	4	(	(	PUNCT
ejpam-6598	437	5	h2	h2	PROPN
ejpam-6598	437	6	)	)	PUNCT
ejpam-6598	437	7	=	=	SYM
ejpam-6598	437	8	−0.399	−0.399	NOUN
ejpam-6598	437	9	and	and	CCONJ
ejpam-6598	437	10	sc	sc	PROPN
ejpam-6598	437	11	(	(	PUNCT
ejpam-6598	437	12	h3	h3	NOUN
ejpam-6598	437	13	)	)	PUNCT
ejpam-6598	437	14	=	=	PUNCT
ejpam-6598	438	1	-1.000	-1.000	PROPN
ejpam-6598	438	2	.	.	PUNCT
ejpam-6598	439	1	since	since	SCONJ
ejpam-6598	439	2	sc	sc	PROPN
ejpam-6598	439	3	(	(	PUNCT
ejpam-6598	439	4	h2	h2	PROPN
ejpam-6598	439	5	)	)	PUNCT
ejpam-6598	439	6	>	>	X
ejpam-6598	439	7	sc	sc	PROPN
ejpam-6598	439	8	(	(	PUNCT
ejpam-6598	439	9	h1	h1	PROPN
ejpam-6598	439	10	)	)	PUNCT
ejpam-6598	439	11	>	>	X
ejpam-6598	439	12	sc	sc	PROPN
ejpam-6598	439	13	(	(	PUNCT
ejpam-6598	439	14	h3	h3	NOUN
ejpam-6598	439	15	)	)	PUNCT
ejpam-6598	439	16	,	,	PUNCT
ejpam-6598	439	17	we	we	PRON
ejpam-6598	439	18	have	have	VERB
ejpam-6598	439	19	h2	h2	PROPN
ejpam-6598	439	20	>	>	X
ejpam-6598	439	21	h1	h1	PROPN
ejpam-6598	439	22	>	>	X
ejpam-6598	439	23	h3	h3	NOUN
ejpam-6598	439	24	.	.	PUNCT
ejpam-6598	440	1	hence	hence	ADV
ejpam-6598	440	2	h2	h2	PROPN
ejpam-6598	440	3	(	(	PUNCT
ejpam-6598	440	4	menstrual	menstrual	ADJ
ejpam-6598	440	5	cups	cup	NOUN
ejpam-6598	440	6	)	)	PUNCT
ejpam-6598	440	7	is	be	AUX
ejpam-6598	440	8	the	the	PRON
ejpam-6598	440	9	is	be	AUX
ejpam-6598	440	10	the	the	DET
ejpam-6598	440	11	greatest	great	ADJ
ejpam-6598	440	12	product	product	NOUN
ejpam-6598	440	13	for	for	ADP
ejpam-6598	440	14	rural	rural	ADJ
ejpam-6598	440	15	women	woman	NOUN
ejpam-6598	440	16	’s	’s	PART
ejpam-6598	440	17	menstruation	menstruation	NOUN
ejpam-6598	440	18	hygiene	hygiene	NOUN
ejpam-6598	440	19	.	.	PUNCT
ejpam-6598	441	1	the	the	DET
ejpam-6598	441	2	fuzzy	fuzzy	ADJ
ejpam-6598	441	3	topological	topological	ADJ
ejpam-6598	441	4	framework	framework	NOUN
ejpam-6598	441	5	adopted	adopt	VERB
ejpam-6598	441	6	in	in	ADP
ejpam-6598	441	7	this	this	DET
ejpam-6598	441	8	study	study	NOUN
ejpam-6598	441	9	offers	offer	VERB
ejpam-6598	441	10	a	a	DET
ejpam-6598	441	11	structured	structured	ADJ
ejpam-6598	441	12	and	and	CCONJ
ejpam-6598	441	13	actionable	actionable	ADJ
ejpam-6598	441	14	basis	basis	NOUN
ejpam-6598	441	15	for	for	ADP
ejpam-6598	441	16	real	real	ADJ
ejpam-6598	441	17	world	world	NOUN
ejpam-6598	441	18	decision	decision	NOUN
ejpam-6598	441	19	making	making	NOUN
ejpam-6598	441	20	in	in	ADP
ejpam-6598	441	21	the	the	DET
ejpam-6598	441	22	domain	domain	NOUN
ejpam-6598	441	23	of	of	ADP
ejpam-6598	441	24	menstrual	menstrual	ADJ
ejpam-6598	441	25	hygiene	hygiene	NOUN
ejpam-6598	441	26	management	management	NOUN
ejpam-6598	441	27	.	.	PUNCT
ejpam-6598	442	1	n.	n.	PROPN
ejpam-6598	442	2	preethi	preethi	PROPN
ejpam-6598	442	3	,	,	PUNCT
ejpam-6598	442	4	g.	g.	PROPN
ejpam-6598	442	5	k.	k.	PROPN
ejpam-6598	442	6	revathi	revathi	PROPN
ejpam-6598	442	7	/	/	SYM
ejpam-6598	442	8	eur	eur	PROPN
ejpam-6598	442	9	.	.	PUNCT
ejpam-6598	443	1	j.	j.	PROPN
ejpam-6598	443	2	pure	pure	PROPN
ejpam-6598	443	3	appl	appl	PROPN
ejpam-6598	443	4	.	.	PROPN
ejpam-6598	443	5	math	math	PROPN
ejpam-6598	443	6	,	,	PUNCT
ejpam-6598	443	7	18	18	NUM
ejpam-6598	443	8	(	(	PUNCT
ejpam-6598	443	9	3	3	NUM
ejpam-6598	443	10	)	)	PUNCT
ejpam-6598	443	11	(	(	PUNCT
ejpam-6598	443	12	2025	2025	NUM
ejpam-6598	443	13	)	)	PUNCT
ejpam-6598	443	14	,	,	PUNCT
ejpam-6598	443	15	6598	6598	NUM
ejpam-6598	443	16	15	15	NUM
ejpam-6598	443	17	of	of	ADP
ejpam-6598	443	18	17	17	NUM
ejpam-6598	443	19	by	by	ADP
ejpam-6598	443	20	utilizing	utilize	VERB
ejpam-6598	443	21	the	the	DET
ejpam-6598	443	22	score	score	NOUN
ejpam-6598	443	23	outputs	output	NOUN
ejpam-6598	443	24	derived	derive	VERB
ejpam-6598	443	25	from	from	ADP
ejpam-6598	443	26	pfwa	pfwa	ADJ
ejpam-6598	443	27	and	and	CCONJ
ejpam-6598	443	28	pfwg	pfwg	NOUN
ejpam-6598	443	29	operators	operator	NOUN
ejpam-6598	444	1	,	,	PUNCT
ejpam-6598	444	2	policymakers	policymaker	NOUN
ejpam-6598	444	3	can	can	AUX
ejpam-6598	444	4	make	make	VERB
ejpam-6598	444	5	informed	informed	ADJ
ejpam-6598	444	6	decisions	decision	NOUN
ejpam-6598	444	7	regarding	regard	VERB
ejpam-6598	444	8	resource	resource	NOUN
ejpam-6598	444	9	allocation	allocation	NOUN
ejpam-6598	444	10	and	and	CCONJ
ejpam-6598	444	11	program	program	NOUN
ejpam-6598	444	12	design	design	NOUN
ejpam-6598	444	13	.	.	PUNCT
ejpam-6598	445	1	for	for	ADP
ejpam-6598	445	2	instance	instance	NOUN
ejpam-6598	445	3	,	,	PUNCT
ejpam-6598	445	4	if	if	SCONJ
ejpam-6598	445	5	the	the	DET
ejpam-6598	445	6	model	model	NOUN
ejpam-6598	445	7	identifies	identify	VERB
ejpam-6598	445	8	menstrual	menstrual	ADJ
ejpam-6598	445	9	cups	cup	NOUN
ejpam-6598	445	10	as	as	ADP
ejpam-6598	445	11	the	the	DET
ejpam-6598	445	12	most	most	ADV
ejpam-6598	445	13	suitable	suitable	ADJ
ejpam-6598	445	14	product	product	NOUN
ejpam-6598	445	15	based	base	VERB
ejpam-6598	445	16	on	on	ADP
ejpam-6598	445	17	the	the	DET
ejpam-6598	445	18	considered	consider	VERB
ejpam-6598	445	19	criteria	criterion	NOUN
ejpam-6598	445	20	,	,	PUNCT
ejpam-6598	445	21	interventions	intervention	NOUN
ejpam-6598	445	22	can	can	AUX
ejpam-6598	445	23	focus	focus	VERB
ejpam-6598	445	24	on	on	ADP
ejpam-6598	445	25	subsidizing	subsidize	VERB
ejpam-6598	445	26	these	these	DET
ejpam-6598	445	27	products	product	NOUN
ejpam-6598	445	28	and	and	CCONJ
ejpam-6598	445	29	organizing	organize	VERB
ejpam-6598	445	30	targeted	target	VERB
ejpam-6598	445	31	distribution	distribution	NOUN
ejpam-6598	445	32	and	and	CCONJ
ejpam-6598	445	33	training	training	NOUN
ejpam-6598	445	34	programs	program	NOUN
ejpam-6598	445	35	to	to	PART
ejpam-6598	445	36	ensure	ensure	VERB
ejpam-6598	445	37	cost	cost	NOUN
ejpam-6598	445	38	effectiveness	effectiveness	NOUN
ejpam-6598	445	39	and	and	CCONJ
ejpam-6598	445	40	community	community	NOUN
ejpam-6598	445	41	acceptance	acceptance	NOUN
ejpam-6598	445	42	.	.	PUNCT
ejpam-6598	446	1	furthermore	furthermore	ADV
ejpam-6598	446	2	,	,	PUNCT
ejpam-6598	446	3	the	the	DET
ejpam-6598	446	4	inclusion	inclusion	NOUN
ejpam-6598	446	5	of	of	ADP
ejpam-6598	446	6	sociocultural	sociocultural	ADJ
ejpam-6598	446	7	factors	factor	NOUN
ejpam-6598	446	8	such	such	ADJ
ejpam-6598	446	9	as	as	ADP
ejpam-6598	446	10	cultural	cultural	ADJ
ejpam-6598	446	11	acceptance	acceptance	NOUN
ejpam-6598	446	12	and	and	CCONJ
ejpam-6598	446	13	awareness	awareness	NOUN
ejpam-6598	446	14	within	within	ADP
ejpam-6598	446	15	the	the	DET
ejpam-6598	446	16	model	model	NOUN
ejpam-6598	446	17	enables	enable	VERB
ejpam-6598	446	18	local	local	ADJ
ejpam-6598	446	19	health	health	NOUN
ejpam-6598	446	20	educators	educator	NOUN
ejpam-6598	446	21	to	to	PART
ejpam-6598	446	22	pinpoint	pinpoint	VERB
ejpam-6598	446	23	barriers	barrier	NOUN
ejpam-6598	446	24	to	to	ADP
ejpam-6598	446	25	adoption	adoption	NOUN
ejpam-6598	446	26	.	.	PUNCT
ejpam-6598	447	1	this	this	PRON
ejpam-6598	447	2	facilitates	facilitate	VERB
ejpam-6598	447	3	the	the	DET
ejpam-6598	447	4	development	development	NOUN
ejpam-6598	447	5	of	of	ADP
ejpam-6598	447	6	tailored	tailor	VERB
ejpam-6598	447	7	educational	educational	ADJ
ejpam-6598	447	8	campaigns	campaign	NOUN
ejpam-6598	447	9	to	to	PART
ejpam-6598	447	10	promote	promote	VERB
ejpam-6598	447	11	lesser	lesser	ADV
ejpam-6598	447	12	known	known	ADJ
ejpam-6598	447	13	but	but	CCONJ
ejpam-6598	447	14	more	more	ADV
ejpam-6598	447	15	beneficial	beneficial	ADJ
ejpam-6598	447	16	products	product	NOUN
ejpam-6598	447	17	.	.	PUNCT
ejpam-6598	448	1	additionally	additionally	ADV
ejpam-6598	448	2	,	,	PUNCT
ejpam-6598	448	3	the	the	DET
ejpam-6598	448	4	model	model	NOUN
ejpam-6598	448	5	’s	’s	PART
ejpam-6598	448	6	adaptability	adaptability	NOUN
ejpam-6598	448	7	allows	allow	VERB
ejpam-6598	448	8	for	for	ADP
ejpam-6598	448	9	regular	regular	ADJ
ejpam-6598	448	10	updates	update	NOUN
ejpam-6598	448	11	using	use	VERB
ejpam-6598	448	12	real	real	ADJ
ejpam-6598	448	13	time	time	NOUN
ejpam-6598	448	14	feedback	feedback	NOUN
ejpam-6598	448	15	from	from	ADP
ejpam-6598	448	16	the	the	DET
ejpam-6598	448	17	field	field	NOUN
ejpam-6598	448	18	,	,	PUNCT
ejpam-6598	448	19	making	make	VERB
ejpam-6598	448	20	it	it	PRON
ejpam-6598	448	21	a	a	DET
ejpam-6598	448	22	dynamic	dynamic	ADJ
ejpam-6598	448	23	tool	tool	NOUN
ejpam-6598	448	24	for	for	ADP
ejpam-6598	448	25	continuous	continuous	ADJ
ejpam-6598	448	26	evaluation	evaluation	NOUN
ejpam-6598	448	27	and	and	CCONJ
ejpam-6598	448	28	policy	policy	NOUN
ejpam-6598	448	29	refinement	refinement	NOUN
ejpam-6598	448	30	.	.	PUNCT
ejpam-6598	449	1	in	in	ADP
ejpam-6598	449	2	this	this	DET
ejpam-6598	449	3	way	way	NOUN
ejpam-6598	449	4	,	,	PUNCT
ejpam-6598	449	5	the	the	DET
ejpam-6598	449	6	proposed	propose	VERB
ejpam-6598	449	7	fuzzy	fuzzy	ADJ
ejpam-6598	449	8	topological	topological	ADJ
ejpam-6598	449	9	framework	framework	NOUN
ejpam-6598	449	10	serves	serve	VERB
ejpam-6598	449	11	not	not	PART
ejpam-6598	449	12	only	only	ADV
ejpam-6598	449	13	as	as	ADP
ejpam-6598	449	14	an	an	DET
ejpam-6598	449	15	evaluative	evaluative	ADJ
ejpam-6598	449	16	mechanism	mechanism	NOUN
ejpam-6598	449	17	but	but	CCONJ
ejpam-6598	449	18	also	also	ADV
ejpam-6598	449	19	as	as	ADP
ejpam-6598	449	20	a	a	DET
ejpam-6598	449	21	practical	practical	ADJ
ejpam-6598	449	22	decision	decision	NOUN
ejpam-6598	449	23	support	support	NOUN
ejpam-6598	449	24	system	system	NOUN
ejpam-6598	449	25	for	for	ADP
ejpam-6598	449	26	stakeholders	stakeholder	NOUN
ejpam-6598	449	27	working	work	VERB
ejpam-6598	449	28	to	to	PART
ejpam-6598	449	29	improve	improve	VERB
ejpam-6598	449	30	menstrual	menstrual	ADJ
ejpam-6598	449	31	health	health	NOUN
ejpam-6598	449	32	outcomes	outcome	NOUN
ejpam-6598	449	33	.	.	PUNCT
ejpam-6598	450	1	6	6	X
ejpam-6598	450	2	.	.	X
ejpam-6598	450	3	validation	validation	NOUN
ejpam-6598	450	4	in	in	ADP
ejpam-6598	450	5	[	[	X
ejpam-6598	450	6	16	16	NUM
ejpam-6598	450	7	]	]	PUNCT
ejpam-6598	450	8	,	,	PUNCT
ejpam-6598	450	9	the	the	DET
ejpam-6598	450	10	authors	author	NOUN
ejpam-6598	450	11	indicate	indicate	VERB
ejpam-6598	450	12	that	that	SCONJ
ejpam-6598	450	13	menstruation	menstruation	NOUN
ejpam-6598	450	14	cups	cup	NOUN
ejpam-6598	450	15	surpass	surpass	VERB
ejpam-6598	450	16	sanitary	sanitary	NOUN
ejpam-6598	450	17	pads	pad	NOUN
ejpam-6598	450	18	in	in	ADP
ejpam-6598	450	19	terms	term	NOUN
ejpam-6598	450	20	of	of	ADP
ejpam-6598	450	21	comfort	comfort	NOUN
ejpam-6598	450	22	,	,	PUNCT
ejpam-6598	450	23	leakage	leakage	NOUN
ejpam-6598	450	24	protection	protection	NOUN
ejpam-6598	450	25	,	,	PUNCT
ejpam-6598	450	26	capacity	capacity	NOUN
ejpam-6598	450	27	,	,	PUNCT
ejpam-6598	450	28	and	and	CCONJ
ejpam-6598	450	29	discretion	discretion	NOUN
ejpam-6598	450	30	.	.	PUNCT
ejpam-6598	451	1	menstrual	menstrual	ADJ
ejpam-6598	451	2	cups	cup	NOUN
ejpam-6598	451	3	and	and	CCONJ
ejpam-6598	451	4	sanitary	sanitary	NOUN
ejpam-6598	451	5	pads	pad	NOUN
ejpam-6598	451	6	are	be	AUX
ejpam-6598	451	7	comparable	comparable	ADJ
ejpam-6598	451	8	in	in	ADP
ejpam-6598	451	9	terms	term	NOUN
ejpam-6598	451	10	of	of	ADP
ejpam-6598	451	11	accessibility	accessibility	NOUN
ejpam-6598	451	12	and	and	CCONJ
ejpam-6598	451	13	usability	usability	NOUN
ejpam-6598	451	14	.	.	PUNCT
ejpam-6598	452	1	higher	high	ADJ
ejpam-6598	452	2	scores	score	NOUN
ejpam-6598	452	3	were	be	AUX
ejpam-6598	452	4	observed	observe	VERB
ejpam-6598	452	5	for	for	ADP
ejpam-6598	452	6	menstrual	menstrual	ADJ
ejpam-6598	452	7	cups	cup	NOUN
ejpam-6598	452	8	regarding	regard	VERB
ejpam-6598	452	9	skin	skin	NOUN
ejpam-6598	452	10	rash	rash	NOUN
ejpam-6598	452	11	prevention	prevention	NOUN
ejpam-6598	452	12	and	and	CCONJ
ejpam-6598	452	13	reduced	reduced	ADJ
ejpam-6598	452	14	frequency	frequency	NOUN
ejpam-6598	452	15	of	of	ADP
ejpam-6598	452	16	change	change	NOUN
ejpam-6598	452	17	compared	compare	VERB
ejpam-6598	452	18	to	to	ADP
ejpam-6598	452	19	sanitary	sanitary	NOUN
ejpam-6598	452	20	pads	pad	NOUN
ejpam-6598	452	21	.	.	PUNCT
ejpam-6598	453	1	overall	overall	ADJ
ejpam-6598	453	2	,	,	PUNCT
ejpam-6598	453	3	menstrual	menstrual	ADJ
ejpam-6598	453	4	cups	cup	NOUN
ejpam-6598	453	5	demonstrate	demonstrate	VERB
ejpam-6598	453	6	significant	significant	ADJ
ejpam-6598	453	7	improvement	improvement	NOUN
ejpam-6598	453	8	with	with	ADP
ejpam-6598	453	9	each	each	DET
ejpam-6598	453	10	menstrual	menstrual	ADJ
ejpam-6598	453	11	cycle	cycle	NOUN
ejpam-6598	453	12	when	when	SCONJ
ejpam-6598	453	13	compared	compare	VERB
ejpam-6598	453	14	to	to	ADP
ejpam-6598	453	15	sanitary	sanitary	ADJ
ejpam-6598	453	16	pads	pad	NOUN
ejpam-6598	453	17	.	.	PUNCT
ejpam-6598	454	1	however	however	ADV
ejpam-6598	454	2	,	,	PUNCT
ejpam-6598	454	3	sanitary	sanitary	NOUN
ejpam-6598	454	4	pads	pad	NOUN
ejpam-6598	454	5	are	be	AUX
ejpam-6598	454	6	still	still	ADV
ejpam-6598	454	7	suggested	suggest	VERB
ejpam-6598	454	8	during	during	ADP
ejpam-6598	454	9	the	the	DET
ejpam-6598	454	10	first	first	ADJ
ejpam-6598	454	11	few	few	ADJ
ejpam-6598	454	12	cycles	cycle	NOUN
ejpam-6598	454	13	of	of	ADP
ejpam-6598	454	14	menstrual	menstrual	ADJ
ejpam-6598	454	15	cup	cup	NOUN
ejpam-6598	454	16	use	use	NOUN
ejpam-6598	454	17	.	.	PUNCT
ejpam-6598	455	1	notably	notably	ADV
ejpam-6598	455	2	,	,	PUNCT
ejpam-6598	455	3	all	all	DET
ejpam-6598	455	4	performance	performance	NOUN
ejpam-6598	455	5	scores	score	NOUN
ejpam-6598	455	6	show	show	VERB
ejpam-6598	455	7	improvement	improvement	NOUN
ejpam-6598	455	8	as	as	SCONJ
ejpam-6598	455	9	users	user	NOUN
ejpam-6598	455	10	become	become	VERB
ejpam-6598	455	11	more	more	ADV
ejpam-6598	455	12	accustomed	accustomed	ADJ
ejpam-6598	455	13	to	to	ADP
ejpam-6598	455	14	menstrual	menstrual	ADJ
ejpam-6598	455	15	cups	cup	NOUN
ejpam-6598	455	16	.	.	PUNCT
ejpam-6598	456	1	further	further	ADJ
ejpam-6598	456	2	research	research	NOUN
ejpam-6598	456	3	is	be	AUX
ejpam-6598	456	4	warranted	warrant	VERB
ejpam-6598	456	5	to	to	PART
ejpam-6598	456	6	evaluate	evaluate	VERB
ejpam-6598	456	7	cost	cost	NOUN
ejpam-6598	456	8	-	-	PUNCT
ejpam-6598	456	9	effectiveness	effectiveness	NOUN
ejpam-6598	456	10	and	and	CCONJ
ejpam-6598	456	11	effectiveness	effectiveness	NOUN
ejpam-6598	456	12	in	in	ADP
ejpam-6598	456	13	specific	specific	ADJ
ejpam-6598	456	14	subgroups	subgroup	NOUN
ejpam-6598	456	15	,	,	PUNCT
ejpam-6598	456	16	such	such	ADJ
ejpam-6598	456	17	as	as	ADP
ejpam-6598	456	18	individuals	individual	NOUN
ejpam-6598	456	19	with	with	ADP
ejpam-6598	456	20	menorrhagia	menorrhagia	NOUN
ejpam-6598	456	21	.	.	PUNCT
ejpam-6598	457	1	promoting	promote	VERB
ejpam-6598	457	2	awareness	awareness	NOUN
ejpam-6598	457	3	and	and	CCONJ
ejpam-6598	457	4	educating	educate	VERB
ejpam-6598	457	5	the	the	DET
ejpam-6598	457	6	population	population	NOUN
ejpam-6598	457	7	on	on	ADP
ejpam-6598	457	8	the	the	DET
ejpam-6598	457	9	environmental	environmental	ADJ
ejpam-6598	457	10	benefits	benefit	NOUN
ejpam-6598	457	11	and	and	CCONJ
ejpam-6598	457	12	initial	initial	ADJ
ejpam-6598	457	13	learning	learning	NOUN
ejpam-6598	457	14	curve	curve	NOUN
ejpam-6598	457	15	associated	associate	VERB
ejpam-6598	457	16	with	with	ADP
ejpam-6598	457	17	menstrual	menstrual	ADJ
ejpam-6598	457	18	cup	cup	NOUN
ejpam-6598	457	19	use	use	NOUN
ejpam-6598	457	20	is	be	AUX
ejpam-6598	457	21	essential	essential	ADJ
ejpam-6598	457	22	.	.	PUNCT
ejpam-6598	458	1	accordingly	accordingly	ADV
ejpam-6598	458	2	,	,	PUNCT
ejpam-6598	458	3	the	the	DET
ejpam-6598	458	4	current	current	ADJ
ejpam-6598	458	5	study	study	NOUN
ejpam-6598	458	6	conveys	convey	VERB
ejpam-6598	458	7	the	the	DET
ejpam-6598	458	8	concept	concept	NOUN
ejpam-6598	458	9	through	through	ADP
ejpam-6598	458	10	a	a	DET
ejpam-6598	458	11	topological	topological	ADJ
ejpam-6598	458	12	framework	framework	NOUN
ejpam-6598	458	13	in	in	ADP
ejpam-6598	458	14	a	a	DET
ejpam-6598	458	15	clear	clear	ADJ
ejpam-6598	458	16	and	and	CCONJ
ejpam-6598	458	17	simplified	simplified	ADJ
ejpam-6598	458	18	way	way	NOUN
ejpam-6598	458	19	.	.	PUNCT
ejpam-6598	459	1	7	7	X
ejpam-6598	459	2	.	.	X
ejpam-6598	459	3	conclusion	conclusion	NOUN
ejpam-6598	459	4	utilizing	utilize	VERB
ejpam-6598	459	5	the	the	DET
ejpam-6598	459	6	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	459	7	s	s	NOUN
ejpam-6598	459	8	as	as	ADP
ejpam-6598	459	9	a	a	DET
ejpam-6598	459	10	basis	basis	NOUN
ejpam-6598	459	11	,	,	PUNCT
ejpam-6598	459	12	we	we	PRON
ejpam-6598	459	13	proposed	propose	VERB
ejpam-6598	459	14	the	the	DET
ejpam-6598	459	15	notion	notion	NOUN
ejpam-6598	459	16	of	of	ADP
ejpam-6598	459	17	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	459	18	−	−	NOUN
ejpam-6598	459	19	ds	ds	NOUN
ejpam-6598	459	20	in	in	ADP
ejpam-6598	459	21	this	this	DET
ejpam-6598	459	22	study	study	NOUN
ejpam-6598	459	23	and	and	CCONJ
ejpam-6598	459	24	studied	study	VERB
ejpam-6598	459	25	its	its	PRON
ejpam-6598	459	26	features	feature	NOUN
ejpam-6598	459	27	.	.	PUNCT
ejpam-6598	460	1	furthermore	furthermore	ADV
ejpam-6598	460	2	,	,	PUNCT
ejpam-6598	460	3	we	we	PRON
ejpam-6598	460	4	provided	provide	VERB
ejpam-6598	460	5	the	the	DET
ejpam-6598	460	6	ideas	idea	NOUN
ejpam-6598	460	7	of	of	ADP
ejpam-6598	460	8	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	460	9	-baire	-baire	NOUN
ejpam-6598	460	10	space	space	NOUN
ejpam-6598	460	11	and	and	CCONJ
ejpam-6598	460	12	pfdb≈f	pfdb≈f	NUM
ejpam-6598	460	13	-submaximal	-submaximal	ADJ
ejpam-6598	460	14	space	space	NOUN
ejpam-6598	460	15	.	.	PUNCT
ejpam-6598	461	1	the	the	DET
ejpam-6598	461	2	characteristics	characteristic	NOUN
ejpam-6598	461	3	of	of	ADP
ejpam-6598	461	4	the	the	DET
ejpam-6598	461	5	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	461	6	−	−	NOUN
ejpam-6598	461	7	ds	ds	NOUN
ejpam-6598	461	8	have	have	AUX
ejpam-6598	461	9	been	be	AUX
ejpam-6598	461	10	defined	define	VERB
ejpam-6598	461	11	.	.	PUNCT
ejpam-6598	462	1	this	this	PRON
ejpam-6598	462	2	relate	relate	VERB
ejpam-6598	462	3	with	with	SCONJ
ejpam-6598	462	4	various	various	ADJ
ejpam-6598	462	5	pfdb≈f	pfdb≈f	NUM
ejpam-6598	462	6	-spaces	-space	NOUN
ejpam-6598	462	7	was	be	AUX
ejpam-6598	462	8	shown	show	VERB
ejpam-6598	462	9	,	,	PUNCT
ejpam-6598	462	10	and	and	CCONJ
ejpam-6598	462	11	the	the	DET
ejpam-6598	462	12	results	result	NOUN
ejpam-6598	462	13	were	be	AUX
ejpam-6598	462	14	interpreted	interpret	VERB
ejpam-6598	462	15	appropriately	appropriately	ADV
ejpam-6598	462	16	.	.	PUNCT
ejpam-6598	463	1	in	in	ADP
ejpam-6598	463	2	addition	addition	NOUN
ejpam-6598	463	3	,	,	PUNCT
ejpam-6598	463	4	it	it	PRON
ejpam-6598	463	5	is	be	AUX
ejpam-6598	463	6	demonstrated	demonstrate	VERB
ejpam-6598	463	7	that	that	SCONJ
ejpam-6598	463	8	a	a	DET
ejpam-6598	463	9	quasi	quasi	ADJ
ejpam-6598	463	10	compact	compact	ADJ
ejpam-6598	463	11	image	image	NOUN
ejpam-6598	463	12	of	of	ADP
ejpam-6598	463	13	a	a	DET
ejpam-6598	463	14	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	463	15	−ds	−ds	NOUN
ejpam-6598	463	16	is	be	AUX
ejpam-6598	463	17	a	a	DET
ejpam-6598	463	18	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	463	19	−ds	−ds	NOUN
ejpam-6598	463	20	and	and	CCONJ
ejpam-6598	463	21	that	that	SCONJ
ejpam-6598	463	22	a	a	DET
ejpam-6598	463	23	pfdb≈f	pfdb≈f	NOUN
ejpam-6598	463	24	−ds	−ds	NOUN
ejpam-6598	463	25	has	have	VERB
ejpam-6598	463	26	a	a	DET
ejpam-6598	463	27	topological	topological	ADJ
ejpam-6598	463	28	property	property	NOUN
ejpam-6598	463	29	.	.	PUNCT
ejpam-6598	464	1	moreover	moreover	ADV
ejpam-6598	464	2	,	,	PUNCT
ejpam-6598	464	3	the	the	DET
ejpam-6598	464	4	framework	framework	NOUN
ejpam-6598	464	5	and	and	CCONJ
ejpam-6598	464	6	conditions	condition	NOUN
ejpam-6598	464	7	of	of	ADP
ejpam-6598	464	8	the	the	DET
ejpam-6598	464	9	pfdfts	pfdft	NOUN
ejpam-6598	464	10	,	,	PUNCT
ejpam-6598	464	11	together	together	ADV
ejpam-6598	464	12	with	with	ADP
ejpam-6598	464	13	its	its	PRON
ejpam-6598	464	14	associated	associated	ADJ
ejpam-6598	464	15	fine	fine	ADJ
ejpam-6598	464	16	collection	collection	NOUN
ejpam-6598	464	17	sets	set	NOUN
ejpam-6598	464	18	,	,	PUNCT
ejpam-6598	464	19	are	be	AUX
ejpam-6598	464	20	systematically	systematically	ADV
ejpam-6598	464	21	utilized	utilize	VERB
ejpam-6598	464	22	to	to	PART
ejpam-6598	464	23	determine	determine	VERB
ejpam-6598	464	24	the	the	DET
ejpam-6598	464	25	most	most	ADV
ejpam-6598	464	26	appropriate	appropriate	ADJ
ejpam-6598	464	27	menstrual	menstrual	ADJ
ejpam-6598	464	28	hygiene	hygiene	NOUN
ejpam-6598	464	29	product	product	NOUN
ejpam-6598	464	30	for	for	ADP
ejpam-6598	464	31	women	woman	NOUN
ejpam-6598	464	32	in	in	ADP
ejpam-6598	464	33	rural	rural	ADJ
ejpam-6598	464	34	areas	area	NOUN
ejpam-6598	464	35	.	.	PUNCT
ejpam-6598	465	1	in	in	ADP
ejpam-6598	465	2	rural	rural	ADJ
ejpam-6598	465	3	areas	area	NOUN
ejpam-6598	465	4	,	,	PUNCT
ejpam-6598	465	5	cultural	cultural	ADJ
ejpam-6598	465	6	awareness	awareness	NOUN
ejpam-6598	465	7	regarding	regard	VERB
ejpam-6598	465	8	the	the	DET
ejpam-6598	465	9	use	use	NOUN
ejpam-6598	465	10	of	of	ADP
ejpam-6598	465	11	menstrual	menstrual	ADJ
ejpam-6598	465	12	cups	cup	NOUN
ejpam-6598	465	13	remains	remain	VERB
ejpam-6598	465	14	relatively	relatively	ADV
ejpam-6598	465	15	low	low	ADJ
ejpam-6598	465	16	.	.	PUNCT
ejpam-6598	466	1	many	many	ADJ
ejpam-6598	466	2	women	woman	NOUN
ejpam-6598	466	3	are	be	AUX
ejpam-6598	466	4	unfamiliar	unfamiliar	ADJ
ejpam-6598	466	5	with	with	ADP
ejpam-6598	466	6	menstrual	menstrual	ADJ
ejpam-6598	466	7	cups	cup	NOUN
ejpam-6598	466	8	due	due	ADP
ejpam-6598	466	9	to	to	ADP
ejpam-6598	466	10	limited	limited	ADJ
ejpam-6598	466	11	access	access	NOUN
ejpam-6598	466	12	to	to	ADP
ejpam-6598	466	13	menstrual	menstrual	ADJ
ejpam-6598	466	14	n.	n.	PROPN
ejpam-6598	466	15	preethi	preethi	ADV
ejpam-6598	466	16	,	,	PUNCT
ejpam-6598	466	17	g.	g.	PROPN
ejpam-6598	466	18	k.	k.	PROPN
ejpam-6598	466	19	revathi	revathi	PROPN
ejpam-6598	466	20	/	/	SYM
ejpam-6598	466	21	eur	eur	PROPN
ejpam-6598	466	22	.	.	PUNCT
ejpam-6598	467	1	j.	j.	PROPN
ejpam-6598	467	2	pure	pure	PROPN
ejpam-6598	467	3	appl	appl	PROPN
ejpam-6598	467	4	.	.	PROPN
ejpam-6598	467	5	math	math	PROPN
ejpam-6598	467	6	,	,	PUNCT
ejpam-6598	467	7	18	18	NUM
ejpam-6598	467	8	(	(	PUNCT
ejpam-6598	467	9	3	3	NUM
ejpam-6598	467	10	)	)	PUNCT
ejpam-6598	467	11	(	(	PUNCT
ejpam-6598	467	12	2025	2025	NUM
ejpam-6598	467	13	)	)	PUNCT
ejpam-6598	467	14	,	,	PUNCT
ejpam-6598	467	15	6598	6598	NUM
ejpam-6598	467	16	16	16	NUM
ejpam-6598	467	17	of	of	ADP
ejpam-6598	467	18	17	17	NUM
ejpam-6598	467	19	health	health	NOUN
ejpam-6598	467	20	education	education	NOUN
ejpam-6598	467	21	and	and	CCONJ
ejpam-6598	467	22	prevailing	prevail	VERB
ejpam-6598	467	23	cultural	cultural	ADJ
ejpam-6598	467	24	taboos	taboo	NOUN
ejpam-6598	467	25	surrounding	surround	VERB
ejpam-6598	467	26	menstruation	menstruation	NOUN
ejpam-6598	467	27	.	.	PUNCT
ejpam-6598	468	1	traditional	traditional	ADJ
ejpam-6598	468	2	practices	practice	NOUN
ejpam-6598	468	3	,	,	PUNCT
ejpam-6598	468	4	such	such	ADJ
ejpam-6598	468	5	as	as	ADP
ejpam-6598	468	6	the	the	DET
ejpam-6598	468	7	use	use	NOUN
ejpam-6598	468	8	of	of	ADP
ejpam-6598	468	9	cloth	cloth	NOUN
ejpam-6598	468	10	pads	pad	NOUN
ejpam-6598	468	11	,	,	PUNCT
ejpam-6598	468	12	are	be	AUX
ejpam-6598	468	13	deeply	deeply	ADV
ejpam-6598	468	14	rooted	root	VERB
ejpam-6598	468	15	and	and	CCONJ
ejpam-6598	468	16	often	often	ADV
ejpam-6598	468	17	preferred	prefer	VERB
ejpam-6598	468	18	,	,	PUNCT
ejpam-6598	468	19	while	while	SCONJ
ejpam-6598	468	20	myths	myth	NOUN
ejpam-6598	468	21	and	and	CCONJ
ejpam-6598	468	22	misconceptions	misconception	NOUN
ejpam-6598	468	23	-	-	PUNCT
ejpam-6598	468	24	particularly	particularly	ADV
ejpam-6598	468	25	concerning	concern	VERB
ejpam-6598	468	26	virginity	virginity	NOUN
ejpam-6598	468	27	,	,	PUNCT
ejpam-6598	468	28	insertion	insertion	NOUN
ejpam-6598	468	29	,	,	PUNCT
ejpam-6598	468	30	and	and	CCONJ
ejpam-6598	468	31	safety	safety	NOUN
ejpam-6598	468	32	create	create	VERB
ejpam-6598	468	33	additional	additional	ADJ
ejpam-6598	468	34	barriers	barrier	NOUN
ejpam-6598	468	35	to	to	PART
ejpam-6598	468	36	acceptance	acceptance	VERB
ejpam-6598	468	37	.	.	PUNCT
ejpam-6598	469	1	the	the	DET
ejpam-6598	469	2	resistance	resistance	NOUN
ejpam-6598	469	3	to	to	ADP
ejpam-6598	469	4	change	change	NOUN
ejpam-6598	469	5	is	be	AUX
ejpam-6598	469	6	often	often	ADV
ejpam-6598	469	7	reinforced	reinforce	VERB
ejpam-6598	469	8	by	by	ADP
ejpam-6598	469	9	generational	generational	ADJ
ejpam-6598	469	10	norms	norm	NOUN
ejpam-6598	469	11	and	and	CCONJ
ejpam-6598	469	12	a	a	DET
ejpam-6598	469	13	lack	lack	NOUN
ejpam-6598	469	14	of	of	ADP
ejpam-6598	469	15	open	open	ADJ
ejpam-6598	469	16	dialogue	dialogue	NOUN
ejpam-6598	469	17	about	about	ADP
ejpam-6598	469	18	menstrual	menstrual	ADJ
ejpam-6598	469	19	health	health	NOUN
ejpam-6598	469	20	.	.	PUNCT
ejpam-6598	470	1	consequently	consequently	ADV
ejpam-6598	470	2	,	,	PUNCT
ejpam-6598	470	3	menstrual	menstrual	ADJ
ejpam-6598	470	4	cups	cup	NOUN
ejpam-6598	470	5	are	be	AUX
ejpam-6598	470	6	perceived	perceive	VERB
ejpam-6598	470	7	as	as	ADP
ejpam-6598	470	8	unfamiliar	unfamiliar	ADJ
ejpam-6598	470	9	and	and	CCONJ
ejpam-6598	470	10	intimidating	intimidate	VERB
ejpam-6598	470	11	.	.	PUNCT
ejpam-6598	471	1	to	to	PART
ejpam-6598	471	2	improve	improve	VERB
ejpam-6598	471	3	awareness	awareness	NOUN
ejpam-6598	471	4	and	and	CCONJ
ejpam-6598	471	5	acceptance	acceptance	NOUN
ejpam-6598	471	6	,	,	PUNCT
ejpam-6598	471	7	targeted	target	VERB
ejpam-6598	471	8	education	education	NOUN
ejpam-6598	471	9	initiatives	initiative	NOUN
ejpam-6598	471	10	and	and	CCONJ
ejpam-6598	471	11	awareness	awareness	NOUN
ejpam-6598	471	12	programs	program	NOUN
ejpam-6598	471	13	are	be	AUX
ejpam-6598	471	14	essential	essential	ADJ
ejpam-6598	471	15	.	.	PUNCT
ejpam-6598	472	1	these	these	DET
ejpam-6598	472	2	efforts	effort	NOUN
ejpam-6598	472	3	should	should	AUX
ejpam-6598	472	4	include	include	VERB
ejpam-6598	472	5	hands	hand	NOUN
ejpam-6598	472	6	-	-	PUNCT
ejpam-6598	472	7	on	on	ADP
ejpam-6598	472	8	demonstrations	demonstration	NOUN
ejpam-6598	472	9	,	,	PUNCT
ejpam-6598	472	10	involvement	involvement	NOUN
ejpam-6598	472	11	of	of	ADP
ejpam-6598	472	12	local	local	ADJ
ejpam-6598	472	13	health	health	NOUN
ejpam-6598	472	14	workers	worker	NOUN
ejpam-6598	472	15	,	,	PUNCT
ejpam-6598	472	16	and	and	CCONJ
ejpam-6598	472	17	the	the	DET
ejpam-6598	472	18	support	support	NOUN
ejpam-6598	472	19	of	of	ADP
ejpam-6598	472	20	community	community	NOUN
ejpam-6598	472	21	leaders	leader	NOUN
ejpam-6598	472	22	to	to	PART
ejpam-6598	472	23	dispel	dispel	VERB
ejpam-6598	472	24	myths	myth	NOUN
ejpam-6598	472	25	and	and	CCONJ
ejpam-6598	472	26	encourage	encourage	VERB
ejpam-6598	472	27	cultural	cultural	ADJ
ejpam-6598	472	28	acceptance	acceptance	NOUN
ejpam-6598	472	29	of	of	ADP
ejpam-6598	472	30	menstrual	menstrual	ADJ
ejpam-6598	472	31	cups	cup	NOUN
ejpam-6598	472	32	as	as	ADP
ejpam-6598	472	33	a	a	DET
ejpam-6598	472	34	safe	safe	ADJ
ejpam-6598	472	35	,	,	PUNCT
ejpam-6598	472	36	sustainable	sustainable	ADJ
ejpam-6598	472	37	,	,	PUNCT
ejpam-6598	472	38	and	and	CCONJ
ejpam-6598	472	39	effective	effective	ADJ
ejpam-6598	472	40	menstrual	menstrual	ADJ
ejpam-6598	472	41	hygiene	hygiene	NOUN
ejpam-6598	472	42	option	option	NOUN
ejpam-6598	472	43	.	.	PUNCT
ejpam-6598	473	1	the	the	DET
ejpam-6598	473	2	present	present	ADJ
ejpam-6598	473	3	work	work	NOUN
ejpam-6598	473	4	explains	explain	VERB
ejpam-6598	473	5	the	the	DET
ejpam-6598	473	6	selection	selection	NOUN
ejpam-6598	473	7	of	of	ADP
ejpam-6598	473	8	the	the	DET
ejpam-6598	473	9	most	most	ADV
ejpam-6598	473	10	suitable	suitable	ADJ
ejpam-6598	473	11	menstrual	menstrual	ADJ
ejpam-6598	473	12	hygiene	hygiene	NOUN
ejpam-6598	473	13	product	product	NOUN
ejpam-6598	473	14	using	use	VERB
ejpam-6598	473	15	pfdft	pfdft	NOUN
ejpam-6598	473	16	.	.	PUNCT
ejpam-6598	474	1	this	this	DET
ejpam-6598	474	2	topological	topological	ADJ
ejpam-6598	474	3	approach	approach	NOUN
ejpam-6598	474	4	provides	provide	VERB
ejpam-6598	474	5	a	a	DET
ejpam-6598	474	6	structured	structured	ADJ
ejpam-6598	474	7	framework	framework	NOUN
ejpam-6598	474	8	,	,	PUNCT
ejpam-6598	474	9	and	and	CCONJ
ejpam-6598	474	10	in	in	ADP
ejpam-6598	474	11	the	the	DET
ejpam-6598	474	12	future	future	NOUN
ejpam-6598	474	13	,	,	PUNCT
ejpam-6598	474	14	it	it	PRON
ejpam-6598	474	15	can	can	AUX
ejpam-6598	474	16	be	be	AUX
ejpam-6598	474	17	applied	apply	VERB
ejpam-6598	474	18	to	to	ADP
ejpam-6598	474	19	real	real	ADJ
ejpam-6598	474	20	-	-	PUNCT
ejpam-6598	474	21	time	time	NOUN
ejpam-6598	474	22	data	datum	NOUN
ejpam-6598	474	23	collected	collect	VERB
ejpam-6598	474	24	from	from	ADP
ejpam-6598	474	25	specific	specific	ADJ
ejpam-6598	474	26	rural	rural	ADJ
ejpam-6598	474	27	areas	area	NOUN
ejpam-6598	474	28	to	to	PART
ejpam-6598	474	29	identify	identify	VERB
ejpam-6598	474	30	the	the	DET
ejpam-6598	474	31	most	most	ADV
ejpam-6598	474	32	appropriate	appropriate	ADJ
ejpam-6598	474	33	product	product	NOUN
ejpam-6598	474	34	based	base	VERB
ejpam-6598	474	35	on	on	ADP
ejpam-6598	474	36	local	local	ADJ
ejpam-6598	474	37	conditions	condition	NOUN
ejpam-6598	474	38	and	and	CCONJ
ejpam-6598	474	39	preferences	preference	NOUN
ejpam-6598	474	40	.	.	PUNCT
ejpam-6598	475	1	disclosure	disclosure	NOUN
ejpam-6598	475	2	statement	statement	NOUN
ejpam-6598	475	3	the	the	DET
ejpam-6598	475	4	author(s	author(s	NOUN
ejpam-6598	475	5	)	)	PUNCT
ejpam-6598	475	6	disclosed	disclose	VERB
ejpam-6598	475	7	no	no	DET
ejpam-6598	475	8	potential	potential	ADJ
ejpam-6598	475	9	conflicts	conflict	NOUN
ejpam-6598	475	10	of	of	ADP
ejpam-6598	475	11	interest	interest	NOUN
ejpam-6598	475	12	.	.	PUNCT
ejpam-6598	476	1	references	reference	NOUN
ejpam-6598	476	2	[	[	X
ejpam-6598	476	3	1	1	NUM
ejpam-6598	476	4	]	]	PUNCT
ejpam-6598	476	5	l.	l.	PROPN
ejpam-6598	476	6	a.	a.	PROPN
ejpam-6598	476	7	zadeh	zadeh	PROPN
ejpam-6598	476	8	.	.	PUNCT
ejpam-6598	477	1	fuzzy	fuzzy	ADJ
ejpam-6598	477	2	sets	set	NOUN
ejpam-6598	477	3	.	.	PUNCT
ejpam-6598	478	1	information	information	NOUN
ejpam-6598	478	2	and	and	CCONJ
ejpam-6598	478	3	control	control	NOUN
ejpam-6598	478	4	,	,	PUNCT
ejpam-6598	478	5	8(3):338–353	8(3):338–353	NUM
ejpam-6598	478	6	,	,	PUNCT
ejpam-6598	478	7	1965	1965	NUM
ejpam-6598	478	8	.	.	PUNCT
ejpam-6598	479	1	[	[	X
ejpam-6598	479	2	2	2	NUM
ejpam-6598	479	3	]	]	PUNCT
ejpam-6598	479	4	k.	k.	PROPN
ejpam-6598	479	5	m.	m.	PROPN
ejpam-6598	479	6	ordenshiya	ordenshiya	PROPN
ejpam-6598	479	7	and	and	CCONJ
ejpam-6598	479	8	g.	g.	PROPN
ejpam-6598	479	9	k.	k.	PROPN
ejpam-6598	479	10	revathi	revathi	PROPN
ejpam-6598	479	11	.	.	PUNCT
ejpam-6598	480	1	enhanced	enhance	VERB
ejpam-6598	480	2	air	air	PROPN
ejpam-6598	480	3	quality	quality	PROPN
ejpam-6598	480	4	index	index	NOUN
ejpam-6598	480	5	prediction	prediction	NOUN
ejpam-6598	480	6	using	use	VERB
ejpam-6598	480	7	fuzzy	fuzzy	ADJ
ejpam-6598	480	8	center	center	NOUN
ejpam-6598	480	9	merge	merge	VERB
ejpam-6598	480	10	labeling	labeling	NOUN
ejpam-6598	480	11	graph	graph	NOUN
ejpam-6598	480	12	based	base	VERB
ejpam-6598	480	13	fuzzy	fuzzy	ADJ
ejpam-6598	480	14	inference	inference	NOUN
ejpam-6598	480	15	system	system	NOUN
ejpam-6598	480	16	model	model	NOUN
ejpam-6598	480	17	.	.	PUNCT
ejpam-6598	481	1	cybernetics	cybernetic	NOUN
ejpam-6598	481	2	and	and	CCONJ
ejpam-6598	481	3	systems	system	NOUN
ejpam-6598	481	4	,	,	PUNCT
ejpam-6598	481	5	pages	page	NOUN
ejpam-6598	481	6	1–43	1–43	PROPN
ejpam-6598	481	7	,	,	PUNCT
ejpam-6598	481	8	2025	2025	NUM
ejpam-6598	481	9	.	.	PUNCT
ejpam-6598	482	1	[	[	X
ejpam-6598	482	2	3	3	NUM
ejpam-6598	482	3	]	]	X
ejpam-6598	482	4	harish	harish	PROPN
ejpam-6598	482	5	garg	garg	PROPN
ejpam-6598	482	6	.	.	PUNCT
ejpam-6598	483	1	confidence	confidence	NOUN
ejpam-6598	483	2	levels	level	NOUN
ejpam-6598	483	3	based	base	VERB
ejpam-6598	483	4	pythagorean	pythagorean	PROPN
ejpam-6598	483	5	fuzzy	fuzzy	ADJ
ejpam-6598	483	6	aggregation	aggregation	NOUN
ejpam-6598	483	7	operators	operator	NOUN
ejpam-6598	483	8	and	and	CCONJ
ejpam-6598	483	9	its	its	PRON
ejpam-6598	483	10	application	application	NOUN
ejpam-6598	483	11	to	to	ADP
ejpam-6598	483	12	decision	decision	NOUN
ejpam-6598	483	13	-	-	PUNCT
ejpam-6598	483	14	making	make	VERB
ejpam-6598	483	15	process	process	NOUN
ejpam-6598	483	16	.	.	PUNCT
ejpam-6598	484	1	computational	computational	ADJ
ejpam-6598	484	2	and	and	CCONJ
ejpam-6598	484	3	mathematical	mathematical	ADJ
ejpam-6598	484	4	organization	organization	NOUN
ejpam-6598	484	5	theory	theory	NOUN
ejpam-6598	484	6	,	,	PUNCT
ejpam-6598	484	7	23(4):546–571	23(4):546–571	PROPN
ejpam-6598	484	8	,	,	PUNCT
ejpam-6598	484	9	2017	2017	NUM
ejpam-6598	484	10	.	.	PUNCT
ejpam-6598	485	1	[	[	X
ejpam-6598	485	2	4	4	NUM
ejpam-6598	485	3	]	]	X
ejpam-6598	485	4	r.	r.	PROPN
ejpam-6598	485	5	r.	r.	PROPN
ejpam-6598	485	6	yager	yager	PROPN
ejpam-6598	485	7	.	.	PUNCT
ejpam-6598	486	1	pythagorean	pythagorean	PROPN
ejpam-6598	486	2	fuzzy	fuzzy	ADJ
ejpam-6598	486	3	subsets	subset	NOUN
ejpam-6598	486	4	.	.	PUNCT
ejpam-6598	487	1	in	in	ADP
ejpam-6598	487	2	proc	proc	PROPN
ejpam-6598	487	3	joint	joint	PROPN
ejpam-6598	487	4	ifsa	ifsa	PROPN
ejpam-6598	487	5	world	world	PROPN
ejpam-6598	487	6	congress	congress	PROPN
ejpam-6598	487	7	and	and	CCONJ
ejpam-6598	487	8	nafips	nafip	NOUN
ejpam-6598	487	9	annual	annual	ADJ
ejpam-6598	487	10	meeting	meeting	NOUN
ejpam-6598	487	11	,	,	PUNCT
ejpam-6598	487	12	2013	2013	NUM
ejpam-6598	487	13	.	.	PUNCT
ejpam-6598	488	1	[	[	X
ejpam-6598	488	2	5	5	NUM
ejpam-6598	488	3	]	]	PUNCT
ejpam-6598	488	4	a.	a.	NOUN
ejpam-6598	488	5	rosenfeld	rosenfeld	PROPN
ejpam-6598	488	6	.	.	PUNCT
ejpam-6598	489	1	fuzzy	fuzzy	ADJ
ejpam-6598	489	2	digital	digital	ADJ
ejpam-6598	489	3	topology	topology	NOUN
ejpam-6598	489	4	.	.	PUNCT
ejpam-6598	490	1	information	information	NOUN
ejpam-6598	490	2	and	and	CCONJ
ejpam-6598	490	3	control	control	NOUN
ejpam-6598	490	4	,	,	PUNCT
ejpam-6598	490	5	40(1):76–87	40(1):76–87	NUM
ejpam-6598	490	6	,	,	PUNCT
ejpam-6598	490	7	1979	1979	NUM
ejpam-6598	490	8	.	.	PUNCT
ejpam-6598	491	1	[	[	X
ejpam-6598	491	2	6	6	NUM
ejpam-6598	491	3	]	]	PUNCT
ejpam-6598	491	4	ankita	ankita	NOUN
ejpam-6598	491	5	shahasane	shahasane	PROPN
ejpam-6598	491	6	,	,	PUNCT
ejpam-6598	491	7	richa	richa	PROPN
ejpam-6598	491	8	singh	singh	PROPN
ejpam-6598	491	9	,	,	PUNCT
ejpam-6598	491	10	and	and	CCONJ
ejpam-6598	491	11	shruti	shruti	PROPN
ejpam-6598	491	12	ugran	ugran	VERB
ejpam-6598	491	13	.	.	PUNCT
ejpam-6598	492	1	menstrual	menstrual	ADJ
ejpam-6598	492	2	cup	cup	PROPN
ejpam-6598	492	3	versus	versus	ADP
ejpam-6598	492	4	sanitary	sanitary	NOUN
ejpam-6598	492	5	cup	cup	NOUN
ejpam-6598	492	6	in	in	ADP
ejpam-6598	492	7	menstrual	menstrual	ADJ
ejpam-6598	492	8	hygiene	hygiene	NOUN
ejpam-6598	492	9	:	:	PUNCT
ejpam-6598	492	10	a	a	DET
ejpam-6598	492	11	prospective	prospective	ADJ
ejpam-6598	492	12	,	,	PUNCT
ejpam-6598	492	13	randomised	randomise	VERB
ejpam-6598	492	14	,	,	PUNCT
ejpam-6598	492	15	two	two	NUM
ejpam-6598	492	16	-	-	PUNCT
ejpam-6598	492	17	way	way	NOUN
ejpam-6598	492	18	crossover	crossover	NOUN
ejpam-6598	492	19	study	study	NOUN
ejpam-6598	492	20	.	.	PUNCT
ejpam-6598	493	1	international	international	ADJ
ejpam-6598	493	2	journal	journal	PROPN
ejpam-6598	493	3	of	of	ADP
ejpam-6598	493	4	pharmaceutical	pharmaceutical	NOUN
ejpam-6598	493	5	and	and	CCONJ
ejpam-6598	493	6	clinical	clinical	ADJ
ejpam-6598	493	7	research	research	NOUN
ejpam-6598	493	8	,	,	PUNCT
ejpam-6598	493	9	15(12):1536–1542	15(12):1536–1542	NUM
ejpam-6598	493	10	,	,	PUNCT
ejpam-6598	493	11	2023	2023	NUM
ejpam-6598	493	12	.	.	PUNCT
ejpam-6598	494	1	[	[	X
ejpam-6598	494	2	7	7	X
ejpam-6598	494	3	]	]	X
ejpam-6598	494	4	r.	r.	PROPN
ejpam-6598	494	5	usha	usha	PROPN
ejpam-6598	494	6	parameswari	parameswari	PROPN
ejpam-6598	494	7	and	and	CCONJ
ejpam-6598	494	8	p.	p.	NOUN
ejpam-6598	494	9	thangavelu	thangavelu	NOUN
ejpam-6598	494	10	.	.	PUNCT
ejpam-6598	495	1	on	on	ADP
ejpam-6598	495	2	b#-open	b#-open	ADJ
ejpam-6598	495	3	sets	set	NOUN
ejpam-6598	495	4	.	.	PUNCT
ejpam-6598	496	1	international	international	ADJ
ejpam-6598	496	2	journal	journal	NOUN
ejpam-6598	496	3	of	of	ADP
ejpam-6598	496	4	mathematics	mathematics	NOUN
ejpam-6598	496	5	trends	trend	NOUN
ejpam-6598	496	6	and	and	CCONJ
ejpam-6598	496	7	technology	technology	NOUN
ejpam-6598	496	8	,	,	PUNCT
ejpam-6598	496	9	5:202–218	5:202–218	NOUN
ejpam-6598	496	10	,	,	PUNCT
ejpam-6598	496	11	2014	2014	NUM
ejpam-6598	496	12	.	.	PUNCT
ejpam-6598	497	1	[	[	X
ejpam-6598	497	2	8	8	X
ejpam-6598	497	3	]	]	PUNCT
ejpam-6598	497	4	s.	s.	PROPN
ejpam-6598	497	5	anjalmose	anjalmose	PROPN
ejpam-6598	497	6	and	and	CCONJ
ejpam-6598	497	7	g.	g.	PROPN
ejpam-6598	497	8	thangaraj	thangaraj	PROPN
ejpam-6598	497	9	.	.	PUNCT
ejpam-6598	498	1	inter	inter	PROPN
ejpam-6598	498	2	relations	relation	NOUN
ejpam-6598	498	3	between	between	ADP
ejpam-6598	498	4	fuzzy	fuzzy	ADJ
ejpam-6598	498	5	door	door	NOUN
ejpam-6598	498	6	space	space	NOUN
ejpam-6598	498	7	and	and	CCONJ
ejpam-6598	498	8	some	some	DET
ejpam-6598	498	9	fuzzy	fuzzy	ADJ
ejpam-6598	498	10	topological	topological	ADJ
ejpam-6598	498	11	spaces	space	NOUN
ejpam-6598	498	12	.	.	PUNCT
ejpam-6598	499	1	international	international	ADJ
ejpam-6598	499	2	journal	journal	PROPN
ejpam-6598	499	3	of	of	ADP
ejpam-6598	499	4	mathematics	mathematic	NOUN
ejpam-6598	499	5	and	and	CCONJ
ejpam-6598	499	6	its	its	PRON
ejpam-6598	499	7	applications	application	NOUN
ejpam-6598	499	8	,	,	PUNCT
ejpam-6598	499	9	4(4):129–136	4(4):129–136	NUM
ejpam-6598	499	10	,	,	PUNCT
ejpam-6598	499	11	2016	2016	NUM
ejpam-6598	499	12	.	.	PUNCT
ejpam-6598	500	1	[	[	X
ejpam-6598	500	2	9	9	NUM
ejpam-6598	500	3	]	]	SYM
ejpam-6598	500	4	dimitrije	dimitrije	NOUN
ejpam-6598	500	5	andrijević.	andrijević.	PROPN
ejpam-6598	500	6	on	on	ADP
ejpam-6598	500	7	b	b	X
ejpam-6598	500	8	-	-	PUNCT
ejpam-6598	500	9	open	open	ADJ
ejpam-6598	500	10	sets	set	NOUN
ejpam-6598	500	11	.	.	PUNCT
ejpam-6598	501	1	matematički	matematički	PROPN
ejpam-6598	501	2	vesnik	vesnik	PROPN
ejpam-6598	501	3	,	,	PUNCT
ejpam-6598	501	4	(	(	PUNCT
ejpam-6598	501	5	205):59–64	205):59–64	NUM
ejpam-6598	501	6	,	,	PUNCT
ejpam-6598	501	7	1996	1996	NUM
ejpam-6598	501	8	.	.	PUNCT
ejpam-6598	502	1	[	[	X
ejpam-6598	502	2	10	10	NUM
ejpam-6598	502	3	]	]	X
ejpam-6598	502	4	n.	n.	NOUN
ejpam-6598	502	5	preethi	preethi	ADV
ejpam-6598	502	6	and	and	CCONJ
ejpam-6598	503	1	g.	g.	PROPN
ejpam-6598	503	2	k.	k.	PROPN
ejpam-6598	503	3	revathi	revathi	PROPN
ejpam-6598	503	4	.	.	PUNCT
ejpam-6598	504	1	a	a	DET
ejpam-6598	504	2	conceptual	conceptual	ADJ
ejpam-6598	504	3	view	view	NOUN
ejpam-6598	504	4	on	on	ADP
ejpam-6598	504	5	pfd	pfd	PROPN
ejpam-6598	504	6	functions	function	NOUN
ejpam-6598	504	7	and	and	CCONJ
ejpam-6598	504	8	its	its	PRON
ejpam-6598	504	9	properties	property	NOUN
ejpam-6598	504	10	.	.	PUNCT
ejpam-6598	505	1	test	test	NOUN
ejpam-6598	505	2	engineering	engineering	NOUN
ejpam-6598	505	3	and	and	CCONJ
ejpam-6598	505	4	management	management	NOUN
ejpam-6598	505	5	,	,	PUNCT
ejpam-6598	505	6	83:20050–20056	83:20050–20056	NUM
ejpam-6598	505	7	,	,	PUNCT
ejpam-6598	505	8	2020	2020	NUM
ejpam-6598	505	9	.	.	PUNCT
ejpam-6598	506	1	[	[	X
ejpam-6598	506	2	11	11	NUM
ejpam-6598	506	3	]	]	PUNCT
ejpam-6598	506	4	abdul	abdul	PROPN
ejpam-6598	506	5	gawad	gawad	PROPN
ejpam-6598	506	6	a.	a.	PROPN
ejpam-6598	506	7	q.	q.	PROPN
ejpam-6598	506	8	al	al	PROPN
ejpam-6598	506	9	-	-	PUNCT
ejpam-6598	506	10	qubati	qubati	PROPN
ejpam-6598	506	11	and	and	CCONJ
ejpam-6598	506	12	mohamed	mohamed	PROPN
ejpam-6598	506	13	el	el	PROPN
ejpam-6598	506	14	sayed	say	VERB
ejpam-6598	506	15	.	.	PUNCT
ejpam-6598	507	1	door	door	NOUN
ejpam-6598	507	2	spaces	space	NOUN
ejpam-6598	507	3	in	in	ADP
ejpam-6598	507	4	intuitionistic	intuitionistic	ADJ
ejpam-6598	507	5	n.	n.	PROPN
ejpam-6598	507	6	preethi	preethi	PROPN
ejpam-6598	507	7	,	,	PUNCT
ejpam-6598	507	8	g.	g.	PROPN
ejpam-6598	507	9	k.	k.	PROPN
ejpam-6598	507	10	revathi	revathi	PROPN
ejpam-6598	507	11	/	/	SYM
ejpam-6598	507	12	eur	eur	PROPN
ejpam-6598	507	13	.	.	PUNCT
ejpam-6598	508	1	j.	j.	PROPN
ejpam-6598	508	2	pure	pure	PROPN
ejpam-6598	508	3	appl	appl	PROPN
ejpam-6598	508	4	.	.	PROPN
ejpam-6598	508	5	math	math	PROPN
ejpam-6598	508	6	,	,	PUNCT
ejpam-6598	508	7	18	18	NUM
ejpam-6598	508	8	(	(	PUNCT
ejpam-6598	508	9	3	3	NUM
ejpam-6598	508	10	)	)	PUNCT
ejpam-6598	508	11	(	(	PUNCT
ejpam-6598	508	12	2025	2025	NUM
ejpam-6598	508	13	)	)	PUNCT
ejpam-6598	508	14	,	,	PUNCT
ejpam-6598	508	15	6598	6598	NUM
ejpam-6598	508	16	17	17	NUM
ejpam-6598	508	17	of	of	ADP
ejpam-6598	508	18	17	17	NUM
ejpam-6598	508	19	fuzzy	fuzzy	ADJ
ejpam-6598	508	20	topological	topological	ADJ
ejpam-6598	508	21	spaces	space	NOUN
ejpam-6598	508	22	.	.	PUNCT
ejpam-6598	509	1	international	international	ADJ
ejpam-6598	509	2	journal	journal	NOUN
ejpam-6598	509	3	of	of	ADP
ejpam-6598	509	4	fuzzy	fuzzy	ADJ
ejpam-6598	509	5	logic	logic	NOUN
ejpam-6598	509	6	and	and	CCONJ
ejpam-6598	509	7	intelligent	intelligent	ADJ
ejpam-6598	509	8	systems	system	NOUN
ejpam-6598	509	9	,	,	PUNCT
ejpam-6598	509	10	22(3):296–302	22(3):296–302	PROPN
ejpam-6598	509	11	,	,	PUNCT
ejpam-6598	509	12	2022	2022	NUM
ejpam-6598	509	13	.	.	PUNCT
ejpam-6598	510	1	[	[	X
ejpam-6598	510	2	12	12	NUM
ejpam-6598	510	3	]	]	X
ejpam-6598	510	4	murat	murat	PROPN
ejpam-6598	510	5	olgun	olgun	PROPN
ejpam-6598	510	6	,	,	PUNCT
ejpam-6598	510	7	mehmet	mehmet	PROPN
ejpam-6598	510	8	unver	unver	PROPN
ejpam-6598	510	9	,	,	PUNCT
ejpam-6598	510	10	and	and	CCONJ
ejpam-6598	510	11	seyhmus	seyhmus	VERB
ejpam-6598	510	12	yardımcı	yardımcı	PROPN
ejpam-6598	510	13	.	.	PUNCT
ejpam-6598	511	1	pythagorean	pythagorean	PROPN
ejpam-6598	511	2	fuzzy	fuzzy	ADJ
ejpam-6598	511	3	topological	topological	ADJ
ejpam-6598	511	4	spaces	space	NOUN
ejpam-6598	511	5	.	.	PUNCT
ejpam-6598	512	1	complex	complex	ADJ
ejpam-6598	512	2	&	&	CCONJ
ejpam-6598	512	3	intelligent	intelligent	ADJ
ejpam-6598	512	4	systems	system	NOUN
ejpam-6598	512	5	,	,	PUNCT
ejpam-6598	512	6	5(2):177–183	5(2):177–183	NUM
ejpam-6598	512	7	,	,	PUNCT
ejpam-6598	512	8	2019	2019	NUM
ejpam-6598	512	9	.	.	PUNCT
ejpam-6598	513	1	[	[	X
ejpam-6598	513	2	13	13	NUM
ejpam-6598	513	3	]	]	PUNCT
ejpam-6598	513	4	t.	t.	PROPN
ejpam-6598	513	5	yung	yung	PROPN
ejpam-6598	513	6	kong	kong	PROPN
ejpam-6598	513	7	and	and	CCONJ
ejpam-6598	513	8	a.	a.	PROPN
ejpam-6598	513	9	rosenfeld	rosenfeld	PROPN
ejpam-6598	513	10	.	.	PUNCT
ejpam-6598	514	1	digital	digital	PROPN
ejpam-6598	514	2	topology	topology	NOUN
ejpam-6598	514	3	:	:	PUNCT
ejpam-6598	514	4	introduction	introduction	NOUN
ejpam-6598	514	5	and	and	CCONJ
ejpam-6598	514	6	survey	survey	NOUN
ejpam-6598	514	7	.	.	PUNCT
ejpam-6598	515	1	computer	computer	NOUN
ejpam-6598	515	2	vision	vision	PROPN
ejpam-6598	515	3	,	,	PUNCT
ejpam-6598	515	4	graphics	graphic	NOUN
ejpam-6598	515	5	,	,	PUNCT
ejpam-6598	515	6	and	and	CCONJ
ejpam-6598	515	7	image	image	NOUN
ejpam-6598	515	8	processing	processing	NOUN
ejpam-6598	515	9	,	,	PUNCT
ejpam-6598	515	10	48(3):357–393	48(3):357–393	PROPN
ejpam-6598	515	11	,	,	PUNCT
ejpam-6598	515	12	1989	1989	NUM
ejpam-6598	515	13	.	.	PUNCT
ejpam-6598	516	1	[	[	X
ejpam-6598	516	2	14	14	NUM
ejpam-6598	516	3	]	]	PUNCT
ejpam-6598	516	4	a.	a.	PROPN
ejpam-6598	516	5	rosenfeld	rosenfeld	PROPN
ejpam-6598	516	6	.	.	PUNCT
ejpam-6598	517	1	digital	digital	PROPN
ejpam-6598	517	2	topology	topology	PROPN
ejpam-6598	517	3	.	.	PUNCT
ejpam-6598	518	1	the	the	DET
ejpam-6598	518	2	american	american	PROPN
ejpam-6598	518	3	mathematical	mathematical	PROPN
ejpam-6598	518	4	monthly	monthly	PROPN
ejpam-6598	518	5	,	,	PUNCT
ejpam-6598	518	6	86(8):621–630	86(8):621–630	PROPN
ejpam-6598	518	7	,	,	PUNCT
ejpam-6598	518	8	1979	1979	NUM
ejpam-6598	518	9	.	.	PUNCT
ejpam-6598	519	1	[	[	X
ejpam-6598	519	2	15	15	NUM
ejpam-6598	519	3	]	]	X
ejpam-6598	519	4	l.	l.	PROPN
ejpam-6598	519	5	vidyarani	vidyarani	PROPN
ejpam-6598	519	6	and	and	CCONJ
ejpam-6598	519	7	a.	a.	PROPN
ejpam-6598	519	8	g.	g.	PROPN
ejpam-6598	519	9	rose	rise	VERB
ejpam-6598	519	10	venish	venish	NOUN
ejpam-6598	519	11	.	.	PUNCT
ejpam-6598	520	1	decomposition	decomposition	NOUN
ejpam-6598	520	2	of	of	ADP
ejpam-6598	520	3	intuitionistic	intuitionistic	ADJ
ejpam-6598	520	4	fine	fine	ADJ
ejpam-6598	520	5	closed	closed	ADJ
ejpam-6598	520	6	sets	set	NOUN
ejpam-6598	520	7	in	in	ADP
ejpam-6598	520	8	intuitionistic	intuitionistic	ADJ
ejpam-6598	520	9	fine	fine	ADJ
ejpam-6598	520	10	topological	topological	ADJ
ejpam-6598	520	11	spaces	space	NOUN
ejpam-6598	520	12	.	.	PUNCT
ejpam-6598	521	1	advances	advance	NOUN
ejpam-6598	521	2	and	and	CCONJ
ejpam-6598	521	3	applications	application	NOUN
ejpam-6598	521	4	in	in	ADP
ejpam-6598	521	5	mathematical	mathematical	ADJ
ejpam-6598	521	6	sciences	science	NOUN
ejpam-6598	521	7	,	,	PUNCT
ejpam-6598	521	8	22:2243–2254	22:2243–2254	NUM
ejpam-6598	521	9	,	,	PUNCT
ejpam-6598	521	10	2023	2023	NUM
ejpam-6598	521	11	.	.	PUNCT
ejpam-6598	522	1	[	[	X
ejpam-6598	522	2	16	16	NUM
ejpam-6598	522	3	]	]	PUNCT
ejpam-6598	522	4	k.	k.	PROPN
ejpam-6598	522	5	t.	t.	PROPN
ejpam-6598	522	6	atanassov	atanassov	PROPN
ejpam-6598	522	7	.	.	PUNCT
ejpam-6598	523	1	intuitionistic	intuitionistic	ADJ
ejpam-6598	523	2	fuzzy	fuzzy	ADJ
ejpam-6598	523	3	sets	set	NOUN
ejpam-6598	523	4	.	.	PUNCT
ejpam-6598	524	1	fuzzy	fuzzy	ADJ
ejpam-6598	524	2	sets	set	NOUN
ejpam-6598	524	3	and	and	CCONJ
ejpam-6598	524	4	systems	system	NOUN
ejpam-6598	524	5	,	,	PUNCT
ejpam-6598	524	6	20(1):87–96	20(1):87–96	NUM
ejpam-6598	524	7	,	,	PUNCT
ejpam-6598	524	8	1986	1986	NUM
ejpam-6598	524	9	.	.	PUNCT