id	sid	tid	token	lemma	pos
ejpam-6135	1	1	european	european	PROPN
ejpam-6135	1	2	journal	journal	PROPN
ejpam-6135	1	3	of	of	ADP
ejpam-6135	1	4	pure	pure	ADJ
ejpam-6135	1	5	and	and	CCONJ
ejpam-6135	1	6	applied	applied	ADJ
ejpam-6135	1	7	mathematics	mathematic	NOUN
ejpam-6135	1	8	2025	2025	NUM
ejpam-6135	1	9	,	,	PUNCT
ejpam-6135	1	10	vol	vol	NOUN
ejpam-6135	1	11	.	.	PROPN
ejpam-6135	1	12	18	18	NUM
ejpam-6135	1	13	,	,	PUNCT
ejpam-6135	1	14	issue	issue	NOUN
ejpam-6135	1	15	2	2	NUM
ejpam-6135	1	16	,	,	PUNCT
ejpam-6135	1	17	article	article	NOUN
ejpam-6135	1	18	number	number	NOUN
ejpam-6135	1	19	6135	6135	NUM
ejpam-6135	1	20	issn	issn	VERB
ejpam-6135	1	21	1307	1307	NUM
ejpam-6135	1	22	-	-	SYM
ejpam-6135	1	23	5543	5543	NUM
ejpam-6135	1	24	–	–	PUNCT
ejpam-6135	1	25	ejpam.com	ejpam.com	X
ejpam-6135	1	26	published	publish	VERB
ejpam-6135	1	27	by	by	ADP
ejpam-6135	1	28	new	new	PROPN
ejpam-6135	1	29	york	york	PROPN
ejpam-6135	1	30	business	business	PROPN
ejpam-6135	1	31	global	global	PROPN
ejpam-6135	1	32	a	a	DET
ejpam-6135	1	33	study	study	NOUN
ejpam-6135	1	34	on	on	ADP
ejpam-6135	1	35	(	(	PUNCT
ejpam-6135	1	36	c	c	X
ejpam-6135	1	37	,	,	PUNCT
ejpam-6135	1	38	d	d	NOUN
ejpam-6135	1	39	)	)	PUNCT
ejpam-6135	1	40	if	if	SCONJ
ejpam-6135	1	41	−q	−q	ADJ
ejpam-6135	1	42	uniform	uniform	ADJ
ejpam-6135	1	43	ir∗	ir∗	NOUN
ejpam-6135	1	44	centred	centre	VERB
ejpam-6135	1	45	structure	structure	NOUN
ejpam-6135	1	46	compactification	compactification	NOUN
ejpam-6135	1	47	s.	s.	PROPN
ejpam-6135	1	48	thirukumaran1	thirukumaran1	PROPN
ejpam-6135	1	49	,	,	PUNCT
ejpam-6135	1	50	g.	g.	PROPN
ejpam-6135	1	51	k.	k.	PROPN
ejpam-6135	1	52	revathi∗1	revathi∗1	PROPN
ejpam-6135	1	53	1	1	PROPN
ejpam-6135	1	54	department	department	NOUN
ejpam-6135	1	55	of	of	ADP
ejpam-6135	1	56	mathematics	mathematic	NOUN
ejpam-6135	1	57	,	,	PUNCT
ejpam-6135	1	58	school	school	NOUN
ejpam-6135	1	59	of	of	ADP
ejpam-6135	1	60	advanced	advanced	ADJ
ejpam-6135	1	61	sciences	science	NOUN
ejpam-6135	1	62	,	,	PUNCT
ejpam-6135	1	63	vellore	vellore	PROPN
ejpam-6135	1	64	institute	institute	PROPN
ejpam-6135	1	65	of	of	ADP
ejpam-6135	1	66	technology	technology	PROPN
ejpam-6135	1	67	chennai	chennai	PROPN
ejpam-6135	1	68	,	,	PUNCT
ejpam-6135	1	69	chennai-127	chennai-127	NOUN
ejpam-6135	1	70	,	,	PUNCT
ejpam-6135	1	71	tamilnadu	tamilnadu	ADJ
ejpam-6135	1	72	abstract	abstract	NOUN
ejpam-6135	1	73	.	.	PUNCT
ejpam-6135	2	1	compactification	compactification	NOUN
ejpam-6135	2	2	is	be	AUX
ejpam-6135	2	3	one	one	NUM
ejpam-6135	2	4	of	of	ADP
ejpam-6135	2	5	the	the	DET
ejpam-6135	2	6	novel	novel	ADJ
ejpam-6135	2	7	extensions	extension	NOUN
ejpam-6135	2	8	in	in	ADP
ejpam-6135	2	9	topological	topological	ADJ
ejpam-6135	2	10	space	space	NOUN
ejpam-6135	2	11	.	.	PUNCT
ejpam-6135	3	1	nets	net	NOUN
ejpam-6135	3	2	and	and	CCONJ
ejpam-6135	3	3	filters	filter	NOUN
ejpam-6135	3	4	are	be	AUX
ejpam-6135	3	5	used	use	VERB
ejpam-6135	3	6	to	to	PART
ejpam-6135	3	7	study	study	VERB
ejpam-6135	3	8	the	the	DET
ejpam-6135	3	9	detailed	detailed	ADJ
ejpam-6135	3	10	characterization	characterization	NOUN
ejpam-6135	3	11	of	of	ADP
ejpam-6135	3	12	compactness	compactness	NOUN
ejpam-6135	3	13	and	and	CCONJ
ejpam-6135	3	14	convergence	convergence	NOUN
ejpam-6135	3	15	in	in	ADP
ejpam-6135	3	16	topological	topological	ADJ
ejpam-6135	3	17	spaces	space	NOUN
ejpam-6135	3	18	.	.	PUNCT
ejpam-6135	4	1	the	the	DET
ejpam-6135	4	2	major	major	ADJ
ejpam-6135	4	3	framework	framework	NOUN
ejpam-6135	4	4	of	of	ADP
ejpam-6135	4	5	this	this	DET
ejpam-6135	4	6	article	article	NOUN
ejpam-6135	4	7	delves	delve	VERB
ejpam-6135	4	8	into	into	ADP
ejpam-6135	4	9	(	(	PUNCT
ejpam-6135	4	10	c	c	NOUN
ejpam-6135	4	11	,	,	PUNCT
ejpam-6135	4	12	d	d	NOUN
ejpam-6135	4	13	)	)	PUNCT
ejpam-6135	4	14	if	if	SCONJ
ejpam-6135	4	15	−q	−q	ADJ
ejpam-6135	4	16	uniform	uniform	ADJ
ejpam-6135	4	17	ir∗	ir∗	NOUN
ejpam-6135	4	18	centred	centre	VERB
ejpam-6135	4	19	structure	structure	NOUN
ejpam-6135	4	20	compactification	compactification	NOUN
ejpam-6135	4	21	.	.	PUNCT
ejpam-6135	5	1	an	an	DET
ejpam-6135	5	2	innovative	innovative	ADJ
ejpam-6135	5	3	space	space	NOUN
ejpam-6135	5	4	that	that	PRON
ejpam-6135	5	5	integrates	integrate	VERB
ejpam-6135	5	6	a	a	DET
ejpam-6135	5	7	(	(	PUNCT
ejpam-6135	5	8	c	c	NOUN
ejpam-6135	5	9	,	,	PUNCT
ejpam-6135	5	10	d	d	NOUN
ejpam-6135	5	11	)	)	PUNCT
ejpam-6135	5	12	if	if	SCONJ
ejpam-6135	5	13	−q	−q	ADJ
ejpam-6135	5	14	uniform	uniform	ADJ
ejpam-6135	5	15	topological	topological	ADJ
ejpam-6135	5	16	space	space	NOUN
ejpam-6135	5	17	with	with	ADP
ejpam-6135	5	18	(	(	PUNCT
ejpam-6135	5	19	c	c	X
ejpam-6135	5	20	,	,	PUNCT
ejpam-6135	5	21	d	d	NOUN
ejpam-6135	5	22	)	)	PUNCT
ejpam-6135	5	23	if	if	SCONJ
ejpam-6135	5	24	−q	−q	ADJ
ejpam-6135	5	25	uniform	uniform	ADJ
ejpam-6135	5	26	ir∗	ir∗	PROPN
ejpam-6135	5	27	space	space	NOUN
ejpam-6135	5	28	.	.	PUNCT
ejpam-6135	6	1	it	it	PRON
ejpam-6135	6	2	explains	explain	VERB
ejpam-6135	6	3	about	about	ADP
ejpam-6135	6	4	the	the	DET
ejpam-6135	6	5	irreducibility	irreducibility	NOUN
ejpam-6135	6	6	in	in	ADP
ejpam-6135	6	7	(	(	PUNCT
ejpam-6135	6	8	c	c	X
ejpam-6135	6	9	,	,	PUNCT
ejpam-6135	6	10	d	d	NOUN
ejpam-6135	6	11	)	)	PUNCT
ejpam-6135	6	12	if	if	SCONJ
ejpam-6135	6	13	−q	−q	ADJ
ejpam-6135	6	14	uniform	uniform	ADJ
ejpam-6135	6	15	topological	topological	ADJ
ejpam-6135	6	16	space	space	NOUN
ejpam-6135	6	17	.	.	PUNCT
ejpam-6135	7	1	also	also	ADV
ejpam-6135	7	2	combines	combine	VERB
ejpam-6135	7	3	with	with	ADP
ejpam-6135	7	4	(	(	PUNCT
ejpam-6135	7	5	c	c	NOUN
ejpam-6135	7	6	,	,	PUNCT
ejpam-6135	7	7	d	d	NOUN
ejpam-6135	7	8	)	)	PUNCT
ejpam-6135	7	9	if	if	SCONJ
ejpam-6135	7	10	−q	−q	ADJ
ejpam-6135	7	11	uniform	uniform	ADJ
ejpam-6135	7	12	centred	centre	VERB
ejpam-6135	7	13	system	system	NOUN
ejpam-6135	7	14	that	that	PRON
ejpam-6135	7	15	deals	deal	VERB
ejpam-6135	7	16	the	the	DET
ejpam-6135	7	17	intersection	intersection	NOUN
ejpam-6135	7	18	of	of	ADP
ejpam-6135	7	19	open	open	ADJ
ejpam-6135	7	20	sets	set	NOUN
ejpam-6135	7	21	.	.	PUNCT
ejpam-6135	8	1	this	this	DET
ejpam-6135	8	2	study	study	NOUN
ejpam-6135	8	3	also	also	ADV
ejpam-6135	8	4	involves	involve	VERB
ejpam-6135	8	5	(	(	PUNCT
ejpam-6135	8	6	c	c	X
ejpam-6135	8	7	,	,	PUNCT
ejpam-6135	8	8	d	d	NOUN
ejpam-6135	8	9	)	)	PUNCT
ejpam-6135	8	10	if	if	SCONJ
ejpam-6135	8	11	−q	−q	ADJ
ejpam-6135	8	12	uniform	uniform	ADJ
ejpam-6135	8	13	ir∗	ir∗	NOUN
ejpam-6135	8	14	centred	centre	VERB
ejpam-6135	8	15	structure	structure	NOUN
ejpam-6135	8	16	filters	filter	NOUN
ejpam-6135	8	17	and	and	CCONJ
ejpam-6135	8	18	(	(	PUNCT
ejpam-6135	8	19	c	c	X
ejpam-6135	8	20	,	,	PUNCT
ejpam-6135	8	21	d	d	NOUN
ejpam-6135	8	22	)	)	PUNCT
ejpam-6135	8	23	if	if	SCONJ
ejpam-6135	8	24	−q	−q	ADJ
ejpam-6135	8	25	uniform	uniform	ADJ
ejpam-6135	8	26	ir∗	ir∗	NOUN
ejpam-6135	8	27	centred	centre	VERB
ejpam-6135	8	28	structure	structure	NOUN
ejpam-6135	8	29	nets	net	NOUN
ejpam-6135	8	30	which	which	PRON
ejpam-6135	8	31	explains	explain	VERB
ejpam-6135	8	32	a	a	DET
ejpam-6135	8	33	detailed	detailed	ADJ
ejpam-6135	8	34	analysis	analysis	NOUN
ejpam-6135	8	35	on	on	ADP
ejpam-6135	8	36	sequences	sequence	NOUN
ejpam-6135	8	37	and	and	CCONJ
ejpam-6135	8	38	its	its	PRON
ejpam-6135	8	39	convergence	convergence	NOUN
ejpam-6135	8	40	in	in	ADP
ejpam-6135	8	41	(	(	PUNCT
ejpam-6135	8	42	c	c	X
ejpam-6135	8	43	,	,	PUNCT
ejpam-6135	8	44	d	d	NOUN
ejpam-6135	8	45	)	)	PUNCT
ejpam-6135	8	46	if	if	SCONJ
ejpam-6135	8	47	−q	−q	ADJ
ejpam-6135	8	48	uniform	uniform	ADJ
ejpam-6135	8	49	topological	topological	ADJ
ejpam-6135	8	50	space	space	NOUN
ejpam-6135	8	51	.	.	PUNCT
ejpam-6135	9	1	2020	2020	NUM
ejpam-6135	9	2	mathematics	mathematic	NOUN
ejpam-6135	9	3	subject	subject	NOUN
ejpam-6135	9	4	classifications	classification	NOUN
ejpam-6135	9	5	:	:	PUNCT
ejpam-6135	9	6	54a40	54a40	NUM
ejpam-6135	9	7	,	,	PUNCT
ejpam-6135	9	8	03e72	03e72	X
ejpam-6135	9	9	key	key	ADJ
ejpam-6135	9	10	words	word	NOUN
ejpam-6135	9	11	and	and	CCONJ
ejpam-6135	9	12	phrases	phrase	NOUN
ejpam-6135	9	13	:	:	PUNCT
ejpam-6135	9	14	(	(	PUNCT
ejpam-6135	9	15	c	c	X
ejpam-6135	9	16	,	,	PUNCT
ejpam-6135	9	17	d	d	NOUN
ejpam-6135	9	18	)	)	PUNCT
ejpam-6135	10	1	if	if	SCONJ
ejpam-6135	10	2	−q	−q	ADJ
ejpam-6135	10	3	uniform	uniform	ADJ
ejpam-6135	10	4	ir∗	ir∗	NOUN
ejpam-6135	10	5	structure	structure	NOUN
ejpam-6135	10	6	space	space	NOUN
ejpam-6135	10	7	,	,	PUNCT
ejpam-6135	10	8	(	(	PUNCT
ejpam-6135	10	9	c	c	X
ejpam-6135	10	10	,	,	PUNCT
ejpam-6135	10	11	d	d	NOUN
ejpam-6135	10	12	)	)	PUNCT
ejpam-6135	10	13	if	if	SCONJ
ejpam-6135	10	14	−q	−q	ADJ
ejpam-6135	10	15	uniform	uniform	ADJ
ejpam-6135	10	16	ir∗	ir∗	NOUN
ejpam-6135	10	17	centred	centre	VERB
ejpam-6135	10	18	structure	structure	NOUN
ejpam-6135	10	19	space	space	NOUN
ejpam-6135	10	20	,	,	PUNCT
ejpam-6135	10	21	(	(	PUNCT
ejpam-6135	10	22	c	c	X
ejpam-6135	10	23	,	,	PUNCT
ejpam-6135	10	24	d	d	NOUN
ejpam-6135	10	25	)	)	PUNCT
ejpam-6135	10	26	if	if	SCONJ
ejpam-6135	10	27	−q	−q	ADJ
ejpam-6135	10	28	uniform	uniform	ADJ
ejpam-6135	10	29	ir∗	ir∗	NOUN
ejpam-6135	10	30	centred	centre	VERB
ejpam-6135	10	31	structure	structure	NOUN
ejpam-6135	10	32	filter	filter	NOUN
ejpam-6135	10	33	and	and	CCONJ
ejpam-6135	10	34	(	(	PUNCT
ejpam-6135	10	35	c	c	X
ejpam-6135	10	36	,	,	PUNCT
ejpam-6135	10	37	d	d	NOUN
ejpam-6135	10	38	)	)	PUNCT
ejpam-6135	10	39	if	if	SCONJ
ejpam-6135	10	40	−q	−q	ADJ
ejpam-6135	10	41	uniform	uniform	ADJ
ejpam-6135	10	42	ir∗	ir∗	NOUN
ejpam-6135	10	43	centred	centre	VERB
ejpam-6135	10	44	structure	structure	NOUN
ejpam-6135	10	45	net	net	NOUN
ejpam-6135	10	46	1	1	NUM
ejpam-6135	10	47	.	.	PUNCT
ejpam-6135	10	48	introduction	introduction	NOUN
ejpam-6135	10	49	l.	l.	PROPN
ejpam-6135	10	50	zadeh	zadeh	PROPN
ejpam-6135	10	51	in	in	ADP
ejpam-6135	10	52	1965	1965	NUM
ejpam-6135	10	53	,	,	PUNCT
ejpam-6135	10	54	[	[	X
ejpam-6135	10	55	1	1	X
ejpam-6135	10	56	]	]	PUNCT
ejpam-6135	10	57	had	have	AUX
ejpam-6135	10	58	proposed	propose	VERB
ejpam-6135	10	59	a	a	DET
ejpam-6135	10	60	set	set	NOUN
ejpam-6135	10	61	that	that	PRON
ejpam-6135	10	62	deals	deal	VERB
ejpam-6135	10	63	with	with	ADP
ejpam-6135	10	64	vagueness	vagueness	NOUN
ejpam-6135	10	65	,	,	PUNCT
ejpam-6135	10	66	imprecision	imprecision	NOUN
ejpam-6135	10	67	called	call	VERB
ejpam-6135	10	68	fuzzy	fuzzy	ADJ
ejpam-6135	10	69	set	set	VERB
ejpam-6135	10	70	from	from	ADP
ejpam-6135	10	71	universal	universal	ADJ
ejpam-6135	10	72	set	set	NOUN
ejpam-6135	10	73	x	x	PUNCT
ejpam-6135	10	74	and	and	CCONJ
ejpam-6135	10	75	[	[	X
ejpam-6135	10	76	2	2	NUM
ejpam-6135	10	77	]	]	PUNCT
ejpam-6135	10	78	give	give	VERB
ejpam-6135	10	79	a	a	DET
ejpam-6135	10	80	detailed	detailed	ADJ
ejpam-6135	10	81	explanation	explanation	NOUN
ejpam-6135	10	82	on	on	ADP
ejpam-6135	10	83	this	this	DET
ejpam-6135	10	84	fuzzy	fuzzy	ADJ
ejpam-6135	10	85	set	set	NOUN
ejpam-6135	10	86	.	.	PUNCT
ejpam-6135	11	1	fuzzy	fuzzy	ADJ
ejpam-6135	11	2	set	set	NOUN
ejpam-6135	11	3	explores	explore	VERB
ejpam-6135	11	4	the	the	DET
ejpam-6135	11	5	characterisation	characterisation	NOUN
ejpam-6135	11	6	using	use	VERB
ejpam-6135	11	7	parameter	parameter	NOUN
ejpam-6135	11	8	,	,	PUNCT
ejpam-6135	11	9	linguistic	linguistic	ADJ
ejpam-6135	11	10	variables	variable	NOUN
ejpam-6135	11	11	etc	etc	X
ejpam-6135	11	12	.	.	X
ejpam-6135	12	1	each	each	DET
ejpam-6135	12	2	elements	element	NOUN
ejpam-6135	12	3	in	in	ADP
ejpam-6135	12	4	fuzzy	fuzzy	ADJ
ejpam-6135	12	5	set	set	NOUN
ejpam-6135	12	6	is	be	AUX
ejpam-6135	12	7	represented	represent	VERB
ejpam-6135	12	8	as	as	ADP
ejpam-6135	12	9	membership	membership	NOUN
ejpam-6135	12	10	values	value	NOUN
ejpam-6135	12	11	from	from	ADP
ejpam-6135	12	12	the	the	DET
ejpam-6135	12	13	set	set	NOUN
ejpam-6135	12	14	x	x	PUNCT
ejpam-6135	12	15	to	to	ADP
ejpam-6135	12	16	[	[	X
ejpam-6135	12	17	0	0	NUM
ejpam-6135	12	18	,	,	PUNCT
ejpam-6135	12	19	1	1	NUM
ejpam-6135	12	20	]	]	PUNCT
ejpam-6135	12	21	.	.	PUNCT
ejpam-6135	13	1	it	it	PRON
ejpam-6135	13	2	had	have	VERB
ejpam-6135	13	3	various	various	ADJ
ejpam-6135	13	4	applications	application	NOUN
ejpam-6135	13	5	in	in	ADP
ejpam-6135	13	6	image	image	NOUN
ejpam-6135	13	7	processing	processing	NOUN
ejpam-6135	13	8	,	,	PUNCT
ejpam-6135	13	9	decision	decision	NOUN
ejpam-6135	13	10	making	making	NOUN
ejpam-6135	13	11	,	,	PUNCT
ejpam-6135	13	12	fuzzy	fuzzy	ADJ
ejpam-6135	13	13	logics	logic	NOUN
ejpam-6135	13	14	and	and	CCONJ
ejpam-6135	13	15	fuzzy	fuzzy	ADJ
ejpam-6135	13	16	inference	inference	NOUN
ejpam-6135	13	17	systems	system	NOUN
ejpam-6135	13	18	etc	etc	X
ejpam-6135	13	19	.	.	PUNCT
ejpam-6135	13	20	k.	k.	PROPN
ejpam-6135	13	21	atanassov	atanassov	PROPN
ejpam-6135	13	22	in	in	ADP
ejpam-6135	13	23	1986	1986	NUM
ejpam-6135	13	24	,	,	PUNCT
ejpam-6135	13	25	[	[	X
ejpam-6135	13	26	3	3	NUM
ejpam-6135	13	27	]	]	PUNCT
ejpam-6135	13	28	enhances	enhance	VERB
ejpam-6135	13	29	a	a	DET
ejpam-6135	13	30	unique	unique	ADJ
ejpam-6135	13	31	concept	concept	NOUN
ejpam-6135	13	32	called	call	VERB
ejpam-6135	13	33	intuitionistic	intuitionistic	ADJ
ejpam-6135	13	34	fuzzy	fuzzy	ADJ
ejpam-6135	13	35	sets	set	NOUN
ejpam-6135	13	36	.	.	PUNCT
ejpam-6135	14	1	it	it	PRON
ejpam-6135	14	2	ensures	ensure	VERB
ejpam-6135	14	3	the	the	DET
ejpam-6135	14	4	both	both	CCONJ
ejpam-6135	14	5	membership	membership	NOUN
ejpam-6135	14	6	and	and	CCONJ
ejpam-6135	14	7	non	non	ADJ
ejpam-6135	14	8	-	-	ADJ
ejpam-6135	14	9	membership	membership	ADJ
ejpam-6135	14	10	values	value	NOUN
ejpam-6135	14	11	in	in	ADP
ejpam-6135	14	12	intuitionistic	intuitionistic	ADJ
ejpam-6135	14	13	fuzzy	fuzzy	ADJ
ejpam-6135	14	14	sets	set	NOUN
ejpam-6135	14	15	.	.	PUNCT
ejpam-6135	15	1	mathematical	mathematical	ADJ
ejpam-6135	15	2	analysis	analysis	NOUN
ejpam-6135	15	3	explores	explore	VERB
ejpam-6135	15	4	the	the	DET
ejpam-6135	15	5	concepts	concept	NOUN
ejpam-6135	15	6	of	of	ADP
ejpam-6135	15	7	limits	limit	NOUN
ejpam-6135	15	8	,	,	PUNCT
ejpam-6135	15	9	contuinity	contuinity	NOUN
ejpam-6135	15	10	,	,	PUNCT
ejpam-6135	15	11	open	open	ADJ
ejpam-6135	15	12	sets	set	NOUN
ejpam-6135	15	13	,	,	PUNCT
ejpam-6135	15	14	closed	closed	ADJ
ejpam-6135	15	15	sets	set	NOUN
ejpam-6135	15	16	,	,	PUNCT
ejpam-6135	15	17	compactness	compactness	NOUN
ejpam-6135	15	18	are	be	AUX
ejpam-6135	15	19	discussed	discuss	VERB
ejpam-6135	15	20	in	in	ADP
ejpam-6135	15	21	real	real	ADJ
ejpam-6135	15	22	numbers	number	NOUN
ejpam-6135	15	23	.	.	PUNCT
ejpam-6135	16	1	after	after	ADP
ejpam-6135	16	2	that	that	PRON
ejpam-6135	16	3	,	,	PUNCT
ejpam-6135	16	4	various	various	ADJ
ejpam-6135	16	5	mathematicians	mathematician	NOUN
ejpam-6135	16	6	convey	convey	VERB
ejpam-6135	16	7	his	his	PRON
ejpam-6135	16	8	ideas	idea	NOUN
ejpam-6135	16	9	and	and	CCONJ
ejpam-6135	16	10	explores	explore	VERB
ejpam-6135	16	11	his	his	PRON
ejpam-6135	16	12	conception	conception	NOUN
ejpam-6135	16	13	to	to	ADP
ejpam-6135	16	14	different	different	ADJ
ejpam-6135	16	15	geometrical	geometrical	ADJ
ejpam-6135	16	16	space	space	NOUN
ejpam-6135	16	17	is	be	AUX
ejpam-6135	16	18	represented	represent	VERB
ejpam-6135	16	19	as	as	ADP
ejpam-6135	16	20	topology	topology	NOUN
ejpam-6135	16	21	.	.	PUNCT
ejpam-6135	17	1	∗corresponding	∗corresponde	VERB
ejpam-6135	17	2	author	author	NOUN
ejpam-6135	17	3	.	.	PUNCT
ejpam-6135	18	1	doi	doi	NOUN
ejpam-6135	18	2	:	:	PUNCT
ejpam-6135	18	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6135	https://doi.org/10.29020/nybg.ejpam.v18i2.6135	NOUN
ejpam-6135	18	4	email	email	NOUN
ejpam-6135	18	5	addresses	address	NOUN
ejpam-6135	18	6	:	:	PUNCT
ejpam-6135	18	7	thirumaths1996@gmail.com	thirumaths1996@gmail.com	NOUN
ejpam-6135	18	8	(	(	PUNCT
ejpam-6135	18	9	s.	s.	PROPN
ejpam-6135	18	10	thirukumaran	thirukumaran	PROPN
ejpam-6135	18	11	)	)	PUNCT
ejpam-6135	18	12	,	,	PUNCT
ejpam-6135	18	13	gk	gk	PROPN
ejpam-6135	18	14	revathi@yahoo.co.in	revathi@yahoo.co.in	PROPN
ejpam-6135	18	15	(	(	PUNCT
ejpam-6135	19	1	g.	g.	PROPN
ejpam-6135	19	2	k.	k.	PROPN
ejpam-6135	19	3	revathi	revathi	PROPN
ejpam-6135	19	4	)	)	PUNCT
ejpam-6135	19	5	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6135	20	1	1	1	NUM
ejpam-6135	20	2	copyright	copyright	NOUN
ejpam-6135	20	3	:	:	PUNCT
ejpam-6135	20	4	©	©	PROPN
ejpam-6135	20	5	2025	2025	NUM
ejpam-6135	20	6	the	the	DET
ejpam-6135	20	7	author(s	author(s	NOUN
ejpam-6135	20	8	)	)	PUNCT
ejpam-6135	20	9	.	.	PUNCT
ejpam-6135	21	1	(	(	PUNCT
ejpam-6135	21	2	cc	cc	NOUN
ejpam-6135	21	3	by	by	ADP
ejpam-6135	21	4	-	-	PUNCT
ejpam-6135	21	5	nc	nc	PROPN
ejpam-6135	21	6	4.0	4.0	NUM
ejpam-6135	21	7	)	)	PUNCT
ejpam-6135	21	8	s.	s.	PROPN
ejpam-6135	21	9	thirukumaran	thirukumaran	PROPN
ejpam-6135	21	10	,	,	PUNCT
ejpam-6135	21	11	g.	g.	PROPN
ejpam-6135	21	12	k.	k.	PROPN
ejpam-6135	21	13	revathi	revathi	PROPN
ejpam-6135	21	14	/	/	SYM
ejpam-6135	21	15	eur	eur	PROPN
ejpam-6135	21	16	.	.	PUNCT
ejpam-6135	22	1	j.	j.	PROPN
ejpam-6135	22	2	pure	pure	PROPN
ejpam-6135	22	3	appl	appl	PROPN
ejpam-6135	22	4	.	.	PROPN
ejpam-6135	22	5	math	math	PROPN
ejpam-6135	22	6	,	,	PUNCT
ejpam-6135	22	7	18	18	NUM
ejpam-6135	22	8	(	(	PUNCT
ejpam-6135	22	9	2	2	NUM
ejpam-6135	22	10	)	)	PUNCT
ejpam-6135	22	11	(	(	PUNCT
ejpam-6135	22	12	2025	2025	NUM
ejpam-6135	22	13	)	)	PUNCT
ejpam-6135	22	14	,	,	PUNCT
ejpam-6135	22	15	6135	6135	NUM
ejpam-6135	22	16	2	2	NUM
ejpam-6135	22	17	of	of	ADP
ejpam-6135	22	18	17	17	NUM
ejpam-6135	22	19	topological	topological	ADJ
ejpam-6135	22	20	space	space	NOUN
ejpam-6135	22	21	is	be	AUX
ejpam-6135	22	22	other	other	ADJ
ejpam-6135	22	23	wise	wise	ADV
ejpam-6135	22	24	expressed	express	VERB
ejpam-6135	22	25	as	as	ADP
ejpam-6135	22	26	rubbersheet	rubbersheet	ADJ
ejpam-6135	22	27	geometry	geometry	NOUN
ejpam-6135	22	28	,	,	PUNCT
ejpam-6135	22	29	it	it	PRON
ejpam-6135	22	30	characterizes	characterize	VERB
ejpam-6135	22	31	the	the	DET
ejpam-6135	22	32	shapes	shape	NOUN
ejpam-6135	22	33	and	and	CCONJ
ejpam-6135	22	34	its	its	PRON
ejpam-6135	22	35	deformations	deformation	NOUN
ejpam-6135	22	36	.	.	PUNCT
ejpam-6135	23	1	connectedness	connectedness	NOUN
ejpam-6135	23	2	,	,	PUNCT
ejpam-6135	23	3	compactness	compactness	NOUN
ejpam-6135	23	4	and	and	CCONJ
ejpam-6135	23	5	continuity	continuity	NOUN
ejpam-6135	23	6	are	be	AUX
ejpam-6135	23	7	major	major	ADJ
ejpam-6135	23	8	three	three	NUM
ejpam-6135	23	9	c	c	NOUN
ejpam-6135	23	10	’s	’s	NOUN
ejpam-6135	23	11	in	in	ADP
ejpam-6135	23	12	topological	topological	ADJ
ejpam-6135	23	13	space	space	NOUN
ejpam-6135	23	14	.	.	PUNCT
ejpam-6135	24	1	among	among	ADP
ejpam-6135	24	2	these	these	PRON
ejpam-6135	24	3	,	,	PUNCT
ejpam-6135	24	4	compactness	compactness	NOUN
ejpam-6135	24	5	ensures	ensure	VERB
ejpam-6135	24	6	about	about	ADP
ejpam-6135	24	7	the	the	DET
ejpam-6135	24	8	open	open	ADJ
ejpam-6135	24	9	coverings	covering	NOUN
ejpam-6135	24	10	in	in	ADP
ejpam-6135	24	11	a	a	DET
ejpam-6135	24	12	give	give	NOUN
ejpam-6135	24	13	topological	topological	ADJ
ejpam-6135	24	14	spaces	space	NOUN
ejpam-6135	24	15	.	.	PUNCT
ejpam-6135	25	1	this	this	PRON
ejpam-6135	25	2	also	also	ADV
ejpam-6135	25	3	leads	lead	VERB
ejpam-6135	25	4	to	to	ADP
ejpam-6135	25	5	a	a	DET
ejpam-6135	25	6	higher	high	ADJ
ejpam-6135	25	7	dimension	dimension	NOUN
ejpam-6135	25	8	topological	topological	ADJ
ejpam-6135	25	9	space	space	NOUN
ejpam-6135	25	10	called	call	VERB
ejpam-6135	25	11	large	large	ADJ
ejpam-6135	25	12	inductive	inductive	ADJ
ejpam-6135	25	13	dimension	dimension	NOUN
ejpam-6135	25	14	,	,	PUNCT
ejpam-6135	25	15	short	short	ADJ
ejpam-6135	25	16	inductive	inductive	ADJ
ejpam-6135	25	17	covering	covering	NOUN
ejpam-6135	25	18	dimensions	dimension	NOUN
ejpam-6135	25	19	,	,	PUNCT
ejpam-6135	25	20	embeddings	embedding	NOUN
ejpam-6135	25	21	,	,	PUNCT
ejpam-6135	25	22	manifolds	manifold	NOUN
ejpam-6135	25	23	,	,	PUNCT
ejpam-6135	25	24	functions	function	NOUN
ejpam-6135	25	25	spaces	space	NOUN
ejpam-6135	25	26	,	,	PUNCT
ejpam-6135	25	27	and	and	CCONJ
ejpam-6135	25	28	also	also	ADV
ejpam-6135	25	29	it	it	PRON
ejpam-6135	25	30	leads	lead	VERB
ejpam-6135	25	31	to	to	ADP
ejpam-6135	25	32	a	a	DET
ejpam-6135	25	33	another	another	DET
ejpam-6135	25	34	dimensional	dimensional	ADJ
ejpam-6135	25	35	concept	concept	NOUN
ejpam-6135	25	36	as	as	ADP
ejpam-6135	25	37	algebraic	algebraic	ADJ
ejpam-6135	25	38	topology	topology	NOUN
ejpam-6135	25	39	.	.	PUNCT
ejpam-6135	26	1	c.	c.	PROPN
ejpam-6135	26	2	l.	l.	PROPN
ejpam-6135	26	3	chang	chang	PROPN
ejpam-6135	26	4	in	in	ADP
ejpam-6135	26	5	1968	1968	NUM
ejpam-6135	26	6	,	,	PUNCT
ejpam-6135	27	1	[	[	X
ejpam-6135	27	2	4	4	NUM
ejpam-6135	27	3	]	]	PUNCT
ejpam-6135	27	4	,	,	PUNCT
ejpam-6135	27	5	defines	define	VERB
ejpam-6135	27	6	fuzzy	fuzzy	ADJ
ejpam-6135	27	7	topological	topological	ADJ
ejpam-6135	27	8	spaces	space	NOUN
ejpam-6135	27	9	.	.	PUNCT
ejpam-6135	28	1	it	it	PRON
ejpam-6135	28	2	enhances	enhance	VERB
ejpam-6135	28	3	a	a	DET
ejpam-6135	28	4	various	various	ADJ
ejpam-6135	28	5	ideas	idea	NOUN
ejpam-6135	28	6	on	on	ADP
ejpam-6135	28	7	structures	structure	NOUN
ejpam-6135	28	8	and	and	CCONJ
ejpam-6135	28	9	spaces	space	NOUN
ejpam-6135	28	10	also	also	ADV
ejpam-6135	28	11	its	its	PRON
ejpam-6135	28	12	properties	property	NOUN
ejpam-6135	28	13	.	.	PUNCT
ejpam-6135	29	1	later	later	ADV
ejpam-6135	29	2	,	,	PUNCT
ejpam-6135	29	3	intuitionistic	intuitionistic	ADJ
ejpam-6135	29	4	fuzzy	fuzzy	ADJ
ejpam-6135	29	5	topological	topological	ADJ
ejpam-6135	29	6	space	space	NOUN
ejpam-6135	29	7	was	be	AUX
ejpam-6135	29	8	defined	define	VERB
ejpam-6135	29	9	by	by	ADP
ejpam-6135	29	10	d.	d.	PROPN
ejpam-6135	29	11	coker	coker	NOUN
ejpam-6135	29	12	in	in	ADP
ejpam-6135	29	13	1997	1997	NUM
ejpam-6135	29	14	[	[	X
ejpam-6135	29	15	5	5	NUM
ejpam-6135	29	16	]	]	PUNCT
ejpam-6135	29	17	.	.	PUNCT
ejpam-6135	30	1	in	in	ADP
ejpam-6135	30	2	both	both	CCONJ
ejpam-6135	30	3	fuzzy	fuzzy	ADJ
ejpam-6135	30	4	topological	topological	ADJ
ejpam-6135	30	5	space	space	NOUN
ejpam-6135	30	6	and	and	CCONJ
ejpam-6135	30	7	intuitionistic	intuitionistic	ADJ
ejpam-6135	30	8	fuzzy	fuzzy	ADJ
ejpam-6135	30	9	topological	topological	ADJ
ejpam-6135	30	10	space	space	NOUN
ejpam-6135	30	11	leads	lead	VERB
ejpam-6135	30	12	to	to	ADP
ejpam-6135	30	13	an	an	DET
ejpam-6135	30	14	concepts	concept	NOUN
ejpam-6135	30	15	for	for	ADP
ejpam-6135	30	16	connectedness	connectedness	NOUN
ejpam-6135	30	17	,	,	PUNCT
ejpam-6135	30	18	compactness	compactness	NOUN
ejpam-6135	30	19	etc	etc	X
ejpam-6135	30	20	.	.	PUNCT
ejpam-6135	30	21	b.	b.	PROPN
ejpam-6135	30	22	hutton	hutton	PROPN
ejpam-6135	30	23	in	in	ADP
ejpam-6135	30	24	1975	1975	NUM
ejpam-6135	30	25	and	and	CCONJ
ejpam-6135	30	26	1977	1977	NUM
ejpam-6135	30	27	[	[	X
ejpam-6135	30	28	6	6	NUM
ejpam-6135	30	29	,	,	PUNCT
ejpam-6135	30	30	7	7	NUM
ejpam-6135	30	31	]	]	PUNCT
ejpam-6135	30	32	notion	notion	NOUN
ejpam-6135	30	33	on	on	ADP
ejpam-6135	30	34	uniformities	uniformity	NOUN
ejpam-6135	30	35	and	and	CCONJ
ejpam-6135	30	36	normalities	normality	NOUN
ejpam-6135	30	37	in	in	ADP
ejpam-6135	30	38	fuzzy	fuzzy	ADJ
ejpam-6135	30	39	topological	topological	ADJ
ejpam-6135	30	40	space	space	NOUN
ejpam-6135	30	41	.	.	PUNCT
ejpam-6135	31	1	among	among	ADP
ejpam-6135	31	2	all	all	PRON
ejpam-6135	31	3	,	,	PUNCT
ejpam-6135	31	4	the	the	DET
ejpam-6135	31	5	main	main	ADJ
ejpam-6135	31	6	aim	aim	NOUN
ejpam-6135	31	7	in	in	ADP
ejpam-6135	31	8	this	this	DET
ejpam-6135	31	9	article	article	NOUN
ejpam-6135	31	10	is	be	AUX
ejpam-6135	31	11	to	to	PART
ejpam-6135	31	12	explores	explore	VERB
ejpam-6135	31	13	a	a	DET
ejpam-6135	31	14	new	new	ADJ
ejpam-6135	31	15	essence	essence	NOUN
ejpam-6135	31	16	called	call	VERB
ejpam-6135	31	17	(	(	PUNCT
ejpam-6135	31	18	c	c	X
ejpam-6135	31	19	,	,	PUNCT
ejpam-6135	31	20	d	d	NOUN
ejpam-6135	31	21	)	)	PUNCT
ejpam-6135	31	22	if	if	SCONJ
ejpam-6135	31	23	−q	−q	ADJ
ejpam-6135	31	24	uniform	uniform	ADJ
ejpam-6135	31	25	ir∗	ir∗	NOUN
ejpam-6135	31	26	centred	centre	VERB
ejpam-6135	31	27	structure	structure	NOUN
ejpam-6135	31	28	compactification	compactification	NOUN
ejpam-6135	31	29	using	use	VERB
ejpam-6135	31	30	(	(	PUNCT
ejpam-6135	31	31	c	c	NOUN
ejpam-6135	31	32	,	,	PUNCT
ejpam-6135	31	33	d	d	NOUN
ejpam-6135	31	34	)	)	PUNCT
ejpam-6135	31	35	if	if	SCONJ
ejpam-6135	31	36	−q	−q	ADJ
ejpam-6135	31	37	uniform	uniform	ADJ
ejpam-6135	31	38	ir∗	ir∗	NOUN
ejpam-6135	31	39	centred	centre	VERB
ejpam-6135	31	40	structure	structure	NOUN
ejpam-6135	31	41	filters	filter	NOUN
ejpam-6135	31	42	and	and	CCONJ
ejpam-6135	31	43	(	(	PUNCT
ejpam-6135	31	44	c	c	X
ejpam-6135	31	45	,	,	PUNCT
ejpam-6135	31	46	d	d	NOUN
ejpam-6135	31	47	)	)	PUNCT
ejpam-6135	31	48	if	if	SCONJ
ejpam-6135	31	49	−q	−q	ADJ
ejpam-6135	31	50	uniform	uniform	ADJ
ejpam-6135	31	51	ir∗	ir∗	NOUN
ejpam-6135	31	52	centred	centre	VERB
ejpam-6135	31	53	structue	structue	NOUN
ejpam-6135	31	54	nets	net	NOUN
ejpam-6135	31	55	.	.	PUNCT
ejpam-6135	32	1	in	in	ADP
ejpam-6135	32	2	this	this	DET
ejpam-6135	32	3	concept	concept	NOUN
ejpam-6135	32	4	,	,	PUNCT
ejpam-6135	32	5	various	various	ADJ
ejpam-6135	32	6	results	result	NOUN
ejpam-6135	32	7	regarding	regard	VERB
ejpam-6135	32	8	compactifications	compactification	NOUN
ejpam-6135	32	9	and	and	CCONJ
ejpam-6135	32	10	its	its	PRON
ejpam-6135	32	11	properties	property	NOUN
ejpam-6135	32	12	are	be	AUX
ejpam-6135	32	13	explored	explore	VERB
ejpam-6135	32	14	.	.	PUNCT
ejpam-6135	33	1	the	the	DET
ejpam-6135	33	2	relationship	relationship	NOUN
ejpam-6135	33	3	between	between	ADP
ejpam-6135	33	4	nets	net	NOUN
ejpam-6135	33	5	and	and	CCONJ
ejpam-6135	33	6	filters	filter	NOUN
ejpam-6135	33	7	in	in	ADP
ejpam-6135	33	8	topological	topological	ADJ
ejpam-6135	33	9	spaces	space	NOUN
ejpam-6135	33	10	is	be	AUX
ejpam-6135	33	11	to	to	PART
ejpam-6135	33	12	understand	understand	VERB
ejpam-6135	33	13	the	the	DET
ejpam-6135	33	14	compact	compact	ADJ
ejpam-6135	33	15	spaces	space	NOUN
ejpam-6135	33	16	and	and	CCONJ
ejpam-6135	33	17	its	its	PRON
ejpam-6135	33	18	characteristics	characteristic	NOUN
ejpam-6135	33	19	.	.	PUNCT
ejpam-6135	34	1	the	the	DET
ejpam-6135	34	2	(	(	PUNCT
ejpam-6135	34	3	c	c	NOUN
ejpam-6135	34	4	,	,	PUNCT
ejpam-6135	34	5	d	d	NOUN
ejpam-6135	34	6	)	)	PUNCT
ejpam-6135	34	7	if	if	SCONJ
ejpam-6135	34	8	−q	−q	ADJ
ejpam-6135	34	9	uniform	uniform	ADJ
ejpam-6135	34	10	ir∗	ir∗	NOUN
ejpam-6135	34	11	centred	centre	VERB
ejpam-6135	34	12	structure	structure	NOUN
ejpam-6135	34	13	compactification	compactification	NOUN
ejpam-6135	34	14	is	be	AUX
ejpam-6135	34	15	motivated	motivate	VERB
ejpam-6135	34	16	by	by	ADP
ejpam-6135	34	17	a	a	DET
ejpam-6135	34	18	need	need	NOUN
ejpam-6135	34	19	to	to	PART
ejpam-6135	34	20	bridge	bridge	VERB
ejpam-6135	34	21	certain	certain	ADJ
ejpam-6135	34	22	gaps	gap	NOUN
ejpam-6135	34	23	in	in	ADP
ejpam-6135	34	24	the	the	DET
ejpam-6135	34	25	theory	theory	NOUN
ejpam-6135	34	26	of	of	ADP
ejpam-6135	34	27	compactifications	compactification	NOUN
ejpam-6135	34	28	of	of	ADP
ejpam-6135	34	29	uniform	uniform	ADJ
ejpam-6135	34	30	spaces	space	NOUN
ejpam-6135	34	31	,	,	PUNCT
ejpam-6135	34	32	particularly	particularly	ADV
ejpam-6135	34	33	those	those	PRON
ejpam-6135	34	34	involving	involve	VERB
ejpam-6135	34	35	irregular	irregular	ADJ
ejpam-6135	34	36	and	and	CCONJ
ejpam-6135	34	37	quasi	quasi	ADJ
ejpam-6135	34	38	-	-	ADJ
ejpam-6135	34	39	uniform	uniform	ADJ
ejpam-6135	34	40	structures	structure	NOUN
ejpam-6135	34	41	.	.	PUNCT
ejpam-6135	35	1	traditional	traditional	ADJ
ejpam-6135	35	2	compactifications	compactification	NOUN
ejpam-6135	35	3	,	,	PUNCT
ejpam-6135	35	4	such	such	ADJ
ejpam-6135	35	5	as	as	ADP
ejpam-6135	35	6	stone	stone	NOUN
ejpam-6135	35	7	–	–	PUNCT
ejpam-6135	35	8	čech	čech	PUNCT
ejpam-6135	35	9	and	and	CCONJ
ejpam-6135	35	10	samuel	samuel	PROPN
ejpam-6135	35	11	compactifications	compactification	NOUN
ejpam-6135	35	12	,	,	PUNCT
ejpam-6135	35	13	are	be	AUX
ejpam-6135	35	14	largely	largely	ADV
ejpam-6135	35	15	constructed	construct	VERB
ejpam-6135	35	16	under	under	ADP
ejpam-6135	35	17	assumptions	assumption	NOUN
ejpam-6135	35	18	of	of	ADP
ejpam-6135	35	19	regularity	regularity	NOUN
ejpam-6135	35	20	,	,	PUNCT
ejpam-6135	35	21	symmetry	symmetry	NOUN
ejpam-6135	35	22	,	,	PUNCT
ejpam-6135	35	23	or	or	CCONJ
ejpam-6135	35	24	completeness	completeness	NOUN
ejpam-6135	35	25	.	.	PUNCT
ejpam-6135	36	1	however	however	ADV
ejpam-6135	36	2	,	,	PUNCT
ejpam-6135	36	3	many	many	ADJ
ejpam-6135	36	4	natural	natural	ADJ
ejpam-6135	36	5	and	and	CCONJ
ejpam-6135	36	6	important	important	ADJ
ejpam-6135	36	7	spaces	space	NOUN
ejpam-6135	36	8	in	in	ADP
ejpam-6135	36	9	both	both	DET
ejpam-6135	36	10	topology	topology	NOUN
ejpam-6135	36	11	and	and	CCONJ
ejpam-6135	36	12	analysis	analysis	NOUN
ejpam-6135	36	13	,	,	PUNCT
ejpam-6135	36	14	especially	especially	ADV
ejpam-6135	36	15	quasi	quasi	ADJ
ejpam-6135	36	16	-	-	ADJ
ejpam-6135	36	17	uniform	uniform	ADJ
ejpam-6135	36	18	spaces	space	NOUN
ejpam-6135	36	19	and	and	CCONJ
ejpam-6135	36	20	structures	structure	NOUN
ejpam-6135	36	21	arising	arise	VERB
ejpam-6135	36	22	in	in	ADP
ejpam-6135	36	23	generalized	generalized	ADJ
ejpam-6135	36	24	function	function	NOUN
ejpam-6135	36	25	theory	theory	NOUN
ejpam-6135	36	26	,	,	PUNCT
ejpam-6135	36	27	lack	lack	VERB
ejpam-6135	36	28	these	these	DET
ejpam-6135	36	29	properties	property	NOUN
ejpam-6135	36	30	.	.	PUNCT
ejpam-6135	37	1	the	the	DET
ejpam-6135	37	2	extension	extension	NOUN
ejpam-6135	37	3	of	of	ADP
ejpam-6135	37	4	(	(	PUNCT
ejpam-6135	37	5	c	c	X
ejpam-6135	37	6	,	,	PUNCT
ejpam-6135	37	7	d	d	NOUN
ejpam-6135	37	8	)	)	PUNCT
ejpam-6135	37	9	if	if	SCONJ
ejpam-6135	37	10	−q	−q	ADJ
ejpam-6135	37	11	uniform	uniform	ADJ
ejpam-6135	37	12	ir∗	ir∗	NOUN
ejpam-6135	37	13	centred	centre	VERB
ejpam-6135	37	14	structure	structure	NOUN
ejpam-6135	37	15	compactification	compactification	NOUN
ejpam-6135	37	16	more	more	ADV
ejpam-6135	37	17	flexible	flexible	ADJ
ejpam-6135	37	18	treatment	treatment	NOUN
ejpam-6135	37	19	of	of	ADP
ejpam-6135	37	20	quasi	quasi	NOUN
ejpam-6135	37	21	-	-	NOUN
ejpam-6135	37	22	uniformities	uniformity	NOUN
ejpam-6135	37	23	that	that	PRON
ejpam-6135	37	24	do	do	AUX
ejpam-6135	37	25	not	not	PART
ejpam-6135	37	26	necessarily	necessarily	ADV
ejpam-6135	37	27	satisfy	satisfy	VERB
ejpam-6135	37	28	classical	classical	ADJ
ejpam-6135	37	29	uniform	uniform	ADJ
ejpam-6135	37	30	conditions	condition	NOUN
ejpam-6135	37	31	,	,	PUNCT
ejpam-6135	37	32	enabling	enable	VERB
ejpam-6135	37	33	a	a	DET
ejpam-6135	37	34	broader	broad	ADJ
ejpam-6135	37	35	class	class	NOUN
ejpam-6135	37	36	of	of	ADP
ejpam-6135	37	37	spaces	space	NOUN
ejpam-6135	37	38	to	to	PART
ejpam-6135	37	39	be	be	AUX
ejpam-6135	37	40	compactified	compactifie	VERB
ejpam-6135	37	41	meaningfully	meaningfully	ADV
ejpam-6135	37	42	.	.	PUNCT
ejpam-6135	38	1	also	also	ADV
ejpam-6135	38	2	the	the	DET
ejpam-6135	38	3	broader	broad	ADJ
ejpam-6135	38	4	field	field	NOUN
ejpam-6135	38	5	of	of	ADP
ejpam-6135	38	6	topology	topology	NOUN
ejpam-6135	38	7	,	,	PUNCT
ejpam-6135	38	8	this	this	DET
ejpam-6135	38	9	research	research	NOUN
ejpam-6135	38	10	positions	position	VERB
ejpam-6135	38	11	itself	itself	PRON
ejpam-6135	38	12	at	at	ADP
ejpam-6135	38	13	the	the	DET
ejpam-6135	38	14	intersection	intersection	NOUN
ejpam-6135	38	15	of	of	ADP
ejpam-6135	38	16	compactification	compactification	NOUN
ejpam-6135	38	17	theory	theory	NOUN
ejpam-6135	38	18	,	,	PUNCT
ejpam-6135	38	19	uniform	uniform	ADJ
ejpam-6135	38	20	space	space	NOUN
ejpam-6135	38	21	theory	theory	NOUN
ejpam-6135	38	22	,	,	PUNCT
ejpam-6135	38	23	and	and	CCONJ
ejpam-6135	38	24	generalized	generalized	ADJ
ejpam-6135	38	25	convergence	convergence	NOUN
ejpam-6135	38	26	structures	structure	NOUN
ejpam-6135	38	27	.	.	PUNCT
ejpam-6135	39	1	it	it	PRON
ejpam-6135	39	2	contributes	contribute	VERB
ejpam-6135	39	3	to	to	ADP
ejpam-6135	39	4	the	the	DET
ejpam-6135	39	5	ongoing	ongoing	ADJ
ejpam-6135	39	6	effort	effort	NOUN
ejpam-6135	39	7	to	to	PART
ejpam-6135	39	8	generalize	generalize	VERB
ejpam-6135	39	9	classical	classical	ADJ
ejpam-6135	39	10	results	result	NOUN
ejpam-6135	39	11	to	to	ADP
ejpam-6135	39	12	more	more	ADV
ejpam-6135	39	13	flexible	flexible	ADJ
ejpam-6135	39	14	,	,	PUNCT
ejpam-6135	39	15	non	non	ADJ
ejpam-6135	39	16	-	-	ADJ
ejpam-6135	39	17	standard	standard	ADJ
ejpam-6135	39	18	settings	setting	NOUN
ejpam-6135	39	19	,	,	PUNCT
ejpam-6135	39	20	which	which	PRON
ejpam-6135	39	21	are	be	AUX
ejpam-6135	39	22	increasingly	increasingly	ADV
ejpam-6135	39	23	relevant	relevant	ADJ
ejpam-6135	39	24	in	in	ADP
ejpam-6135	39	25	modern	modern	ADJ
ejpam-6135	39	26	applications	application	NOUN
ejpam-6135	39	27	such	such	ADJ
ejpam-6135	39	28	as	as	ADP
ejpam-6135	39	29	rigid	rigid	ADJ
ejpam-6135	39	30	motions	motion	NOUN
ejpam-6135	39	31	in	in	ADP
ejpam-6135	39	32	theoretical	theoretical	ADJ
ejpam-6135	39	33	physics	physics	NOUN
ejpam-6135	39	34	,	,	PUNCT
ejpam-6135	39	35	other	other	ADJ
ejpam-6135	39	36	higher	high	ADJ
ejpam-6135	39	37	dimension	dimension	NOUN
ejpam-6135	39	38	topological	topological	ADJ
ejpam-6135	39	39	spaces	space	NOUN
ejpam-6135	39	40	,	,	PUNCT
ejpam-6135	39	41	and	and	CCONJ
ejpam-6135	39	42	the	the	DET
ejpam-6135	39	43	study	study	NOUN
ejpam-6135	39	44	of	of	ADP
ejpam-6135	39	45	generalized	generalized	ADJ
ejpam-6135	39	46	metric	metric	ADJ
ejpam-6135	39	47	spaces	space	NOUN
ejpam-6135	39	48	.	.	PUNCT
ejpam-6135	40	1	an	an	DET
ejpam-6135	40	2	filters	filter	NOUN
ejpam-6135	40	3	can	can	AUX
ejpam-6135	40	4	associate	associate	VERB
ejpam-6135	40	5	with	with	ADP
ejpam-6135	40	6	nets	net	NOUN
ejpam-6135	40	7	and	and	CCONJ
ejpam-6135	40	8	vice	vice	ADV
ejpam-6135	40	9	versa	versa	ADV
ejpam-6135	40	10	to	to	PART
ejpam-6135	40	11	analyze	analyze	VERB
ejpam-6135	40	12	convergence	convergence	NOUN
ejpam-6135	40	13	and	and	CCONJ
ejpam-6135	40	14	compactness	compactness	NOUN
ejpam-6135	40	15	.	.	PUNCT
ejpam-6135	41	1	among	among	ADP
ejpam-6135	41	2	that	that	PRON
ejpam-6135	41	3	the	the	DET
ejpam-6135	41	4	relationship	relationship	NOUN
ejpam-6135	41	5	between	between	ADP
ejpam-6135	41	6	nets	net	NOUN
ejpam-6135	41	7	,	,	PUNCT
ejpam-6135	41	8	filters	filter	NOUN
ejpam-6135	41	9	and	and	CCONJ
ejpam-6135	41	10	compactifications	compactification	NOUN
ejpam-6135	41	11	are	be	AUX
ejpam-6135	41	12	also	also	ADV
ejpam-6135	41	13	associated	associate	VERB
ejpam-6135	41	14	with	with	ADP
ejpam-6135	41	15	each	each	DET
ejpam-6135	41	16	other	other	ADJ
ejpam-6135	41	17	.	.	PUNCT
ejpam-6135	42	1	filters	filter	NOUN
ejpam-6135	42	2	are	be	AUX
ejpam-6135	42	3	used	use	VERB
ejpam-6135	42	4	to	to	PART
ejpam-6135	42	5	analyse	analyse	VERB
ejpam-6135	42	6	the	the	DET
ejpam-6135	42	7	compact	compact	ADJ
ejpam-6135	42	8	spaces	space	NOUN
ejpam-6135	42	9	and	and	CCONJ
ejpam-6135	42	10	construct	construct	VERB
ejpam-6135	42	11	compactifications	compactification	NOUN
ejpam-6135	42	12	.	.	PUNCT
ejpam-6135	43	1	likewise	likewise	ADV
ejpam-6135	43	2	,	,	PUNCT
ejpam-6135	43	3	the	the	DET
ejpam-6135	43	4	nets	net	NOUN
ejpam-6135	43	5	are	be	AUX
ejpam-6135	43	6	tedious	tedious	ADJ
ejpam-6135	43	7	to	to	PART
ejpam-6135	43	8	ensure	ensure	VERB
ejpam-6135	43	9	the	the	DET
ejpam-6135	43	10	convergence	convergence	NOUN
ejpam-6135	43	11	in	in	ADP
ejpam-6135	43	12	compactified	compactified	ADJ
ejpam-6135	43	13	space	space	NOUN
ejpam-6135	43	14	.	.	PUNCT
ejpam-6135	44	1	2	2	X
ejpam-6135	44	2	.	.	X
ejpam-6135	44	3	literature	literature	PROPN
ejpam-6135	44	4	review	review	PROPN
ejpam-6135	44	5	e.	e.	PROPN
ejpam-6135	44	6	narmada	narmada	PROPN
ejpam-6135	44	7	and	and	CCONJ
ejpam-6135	44	8	et	et	PROPN
ejpam-6135	44	9	.	.	PUNCT
ejpam-6135	45	1	al	al	PROPN
ejpam-6135	46	1	[	[	X
ejpam-6135	46	2	8	8	NUM
ejpam-6135	46	3	]	]	PUNCT
ejpam-6135	46	4	had	have	AUX
ejpam-6135	46	5	framed	frame	VERB
ejpam-6135	46	6	a	a	DET
ejpam-6135	46	7	c	c	NOUN
ejpam-6135	46	8	structure	structure	NOUN
ejpam-6135	46	9	to	to	PART
ejpam-6135	46	10	define	define	VERB
ejpam-6135	46	11	an	an	DET
ejpam-6135	46	12	compactification	compactification	NOUN
ejpam-6135	46	13	in	in	ADP
ejpam-6135	46	14	intuitionistic	intuitionistic	ADJ
ejpam-6135	46	15	fuzzy	fuzzy	ADJ
ejpam-6135	46	16	topological	topological	ADJ
ejpam-6135	46	17	spaces	space	NOUN
ejpam-6135	46	18	.	.	PUNCT
ejpam-6135	47	1	the	the	DET
ejpam-6135	47	2	article	article	NOUN
ejpam-6135	47	3	,	,	PUNCT
ejpam-6135	47	4	explores	explore	VERB
ejpam-6135	47	5	an	an	DET
ejpam-6135	47	6	detailed	detailed	ADJ
ejpam-6135	47	7	analysis	analysis	NOUN
ejpam-6135	47	8	of	of	ADP
ejpam-6135	47	9	c	c	NOUN
ejpam-6135	47	10	structure	structure	NOUN
ejpam-6135	47	11	spaces	space	NOUN
ejpam-6135	47	12	using	use	VERB
ejpam-6135	47	13	tc	tc	NOUN
ejpam-6135	47	14	filters	filter	NOUN
ejpam-6135	47	15	for	for	ADP
ejpam-6135	47	16	compactification	compactification	NOUN
ejpam-6135	47	17	.	.	PUNCT
ejpam-6135	48	1	in	in	ADP
ejpam-6135	48	2	2014	2014	NUM
ejpam-6135	48	3	,	,	PUNCT
ejpam-6135	48	4	g.	g.	PROPN
ejpam-6135	48	5	k.	k.	PROPN
ejpam-6135	48	6	revathi	revathi	PROPN
ejpam-6135	48	7	et	et	PROPN
ejpam-6135	48	8	.	.	PUNCT
ejpam-6135	49	1	al	al	PROPN
ejpam-6135	50	1	[	[	X
ejpam-6135	50	2	9	9	NUM
ejpam-6135	50	3	]	]	PUNCT
ejpam-6135	50	4	had	have	AUX
ejpam-6135	50	5	researched	research	VERB
ejpam-6135	50	6	a	a	DET
ejpam-6135	50	7	new	new	ADJ
ejpam-6135	50	8	approach	approach	NOUN
ejpam-6135	50	9	on	on	ADP
ejpam-6135	50	10	wallman	wallman	ADJ
ejpam-6135	50	11	-	-	PUNCT
ejpam-6135	50	12	type	type	NOUN
ejpam-6135	50	13	compactification	compactification	NOUN
ejpam-6135	50	14	via	via	ADP
ejpam-6135	50	15	intuitionistic	intuitionistic	ADJ
ejpam-6135	50	16	fuzzy	fuzzy	ADJ
ejpam-6135	50	17	s.	s.	PROPN
ejpam-6135	50	18	thirukumaran	thirukumaran	PROPN
ejpam-6135	50	19	,	,	PUNCT
ejpam-6135	50	20	g.	g.	PROPN
ejpam-6135	50	21	k.	k.	PROPN
ejpam-6135	50	22	revathi	revathi	PROPN
ejpam-6135	50	23	/	/	SYM
ejpam-6135	50	24	eur	eur	PROPN
ejpam-6135	50	25	.	.	PUNCT
ejpam-6135	51	1	j.	j.	PROPN
ejpam-6135	51	2	pure	pure	PROPN
ejpam-6135	51	3	appl	appl	PROPN
ejpam-6135	51	4	.	.	PROPN
ejpam-6135	51	5	math	math	PROPN
ejpam-6135	51	6	,	,	PUNCT
ejpam-6135	51	7	18	18	NUM
ejpam-6135	51	8	(	(	PUNCT
ejpam-6135	51	9	2	2	NUM
ejpam-6135	51	10	)	)	PUNCT
ejpam-6135	51	11	(	(	PUNCT
ejpam-6135	51	12	2025	2025	NUM
ejpam-6135	51	13	)	)	PUNCT
ejpam-6135	51	14	,	,	PUNCT
ejpam-6135	51	15	6135	6135	NUM
ejpam-6135	51	16	3	3	NUM
ejpam-6135	51	17	of	of	ADP
ejpam-6135	51	18	17	17	NUM
ejpam-6135	51	19	rough	rough	ADJ
ejpam-6135	51	20	centred	centred	ADJ
ejpam-6135	51	21	texture	texture	ADJ
ejpam-6135	51	22	spaces	space	NOUN
ejpam-6135	51	23	.	.	PUNCT
ejpam-6135	52	1	also	also	ADV
ejpam-6135	52	2	in	in	ADP
ejpam-6135	52	3	2015	2015	NUM
ejpam-6135	52	4	,	,	PUNCT
ejpam-6135	52	5	g.	g.	PROPN
ejpam-6135	52	6	k.	k.	PROPN
ejpam-6135	52	7	revathi	revathi	PROPN
ejpam-6135	52	8	et	et	PROPN
ejpam-6135	52	9	.	.	PUNCT
ejpam-6135	53	1	al	al	PROPN
ejpam-6135	54	1	[	[	X
ejpam-6135	54	2	10	10	NUM
ejpam-6135	54	3	]	]	X
ejpam-6135	54	4	express	express	VERB
ejpam-6135	54	5	an	an	DET
ejpam-6135	54	6	novel	novel	ADJ
ejpam-6135	54	7	idea	idea	NOUN
ejpam-6135	54	8	of	of	ADP
ejpam-6135	54	9	compactification	compactification	NOUN
ejpam-6135	54	10	via	via	ADP
ejpam-6135	54	11	semigroup	semigroup	PROPN
ejpam-6135	54	12	and	and	CCONJ
ejpam-6135	54	13	intuitionistic	intuitionistic	ADJ
ejpam-6135	54	14	fuzzy	fuzzy	ADJ
ejpam-6135	54	15	convergence	convergence	NOUN
ejpam-6135	54	16	topological	topological	ADJ
ejpam-6135	54	17	spaces	space	NOUN
ejpam-6135	54	18	.	.	PUNCT
ejpam-6135	55	1	later	later	ADV
ejpam-6135	55	2	on	on	ADP
ejpam-6135	55	3	that	that	PRON
ejpam-6135	55	4	,	,	PUNCT
ejpam-6135	55	5	in	in	ADP
ejpam-6135	55	6	2015	2015	NUM
ejpam-6135	55	7	,	,	PUNCT
ejpam-6135	55	8	ridvan	ridvan	NOUN
ejpam-6135	55	9	sahin	sahin	PROPN
ejpam-6135	55	10	developed	develop	VERB
ejpam-6135	55	11	his	his	PRON
ejpam-6135	55	12	ideas	idea	NOUN
ejpam-6135	55	13	to	to	ADP
ejpam-6135	55	14	soft	soft	ADJ
ejpam-6135	55	15	set	set	NOUN
ejpam-6135	55	16	.	.	PUNCT
ejpam-6135	56	1	soft	soft	ADJ
ejpam-6135	56	2	sets	set	NOUN
ejpam-6135	56	3	deals	deal	NOUN
ejpam-6135	56	4	with	with	ADP
ejpam-6135	56	5	paramaters	paramater	NOUN
ejpam-6135	56	6	.	.	PUNCT
ejpam-6135	57	1	the	the	DET
ejpam-6135	57	2	author	author	NOUN
ejpam-6135	57	3	had	have	AUX
ejpam-6135	57	4	define	define	VERB
ejpam-6135	57	5	a	a	DET
ejpam-6135	57	6	compactification	compactification	NOUN
ejpam-6135	57	7	and	and	CCONJ
ejpam-6135	57	8	its	its	PRON
ejpam-6135	57	9	properties	property	NOUN
ejpam-6135	57	10	on	on	ADP
ejpam-6135	57	11	soft	soft	ADJ
ejpam-6135	57	12	sets	set	NOUN
ejpam-6135	57	13	.	.	PUNCT
ejpam-6135	58	1	in	in	ADP
ejpam-6135	58	2	2019	2019	NUM
ejpam-6135	58	3	,	,	PUNCT
ejpam-6135	58	4	ceren	ceren	PROPN
ejpam-6135	58	5	sultan	sultan	PROPN
ejpam-6135	58	6	elimali	elimali	PROPN
ejpam-6135	58	7	et	et	PROPN
ejpam-6135	58	8	.	.	PUNCT
ejpam-6135	59	1	al	al	PROPN
ejpam-6135	60	1	[	[	X
ejpam-6135	60	2	11	11	NUM
ejpam-6135	60	3	]	]	PUNCT
ejpam-6135	60	4	defined	define	VERB
ejpam-6135	60	5	an	an	DET
ejpam-6135	60	6	fan	fan	NOUN
ejpam-6135	60	7	-	-	PUNCT
ejpam-6135	60	8	gottesman	gottesman	NOUN
ejpam-6135	60	9	compactifications	compactification	NOUN
ejpam-6135	60	10	and	and	CCONJ
ejpam-6135	60	11	stone	stone	NOUN
ejpam-6135	60	12	spaces	space	NOUN
ejpam-6135	60	13	along	along	ADP
ejpam-6135	60	14	with	with	ADP
ejpam-6135	60	15	properties	property	NOUN
ejpam-6135	60	16	are	be	AUX
ejpam-6135	60	17	discussed	discuss	VERB
ejpam-6135	60	18	.	.	PUNCT
ejpam-6135	61	1	likewise	likewise	ADV
ejpam-6135	61	2	[	[	X
ejpam-6135	61	3	12]the	12]the	NUM
ejpam-6135	61	4	topological	topological	ADJ
ejpam-6135	61	5	group	group	NOUN
ejpam-6135	61	6	of	of	ADP
ejpam-6135	61	7	transformations	transformation	NOUN
ejpam-6135	61	8	explain	explain	VERB
ejpam-6135	61	9	about	about	ADP
ejpam-6135	61	10	the	the	DET
ejpam-6135	61	11	pointwise	pointwise	PROPN
ejpam-6135	61	12	convergence	convergence	NOUN
ejpam-6135	61	13	topology	topology	NOUN
ejpam-6135	61	14	and	and	CCONJ
ejpam-6135	61	15	admissible	admissible	ADJ
ejpam-6135	61	16	group	group	NOUN
ejpam-6135	61	17	topology	topology	NOUN
ejpam-6135	61	18	with	with	ADP
ejpam-6135	61	19	the	the	DET
ejpam-6135	61	20	structure	structure	NOUN
ejpam-6135	61	21	equivariant	equivariant	PROPN
ejpam-6135	61	22	compactifications	compactification	NOUN
ejpam-6135	61	23	.	.	PUNCT
ejpam-6135	62	1	also	also	ADV
ejpam-6135	62	2	[	[	X
ejpam-6135	62	3	13	13	NUM
ejpam-6135	62	4	]	]	PUNCT
ejpam-6135	62	5	introduced	introduce	VERB
ejpam-6135	62	6	the	the	DET
ejpam-6135	62	7	category	category	NOUN
ejpam-6135	62	8	of	of	ADP
ejpam-6135	62	9	stable	stable	ADJ
ejpam-6135	62	10	compactifications	compactification	NOUN
ejpam-6135	62	11	and	and	CCONJ
ejpam-6135	62	12	raney	raney	NOUN
ejpam-6135	62	13	extensions	extension	NOUN
ejpam-6135	62	14	of	of	ADP
ejpam-6135	62	15	proximity	proximity	NOUN
ejpam-6135	62	16	frames	frame	NOUN
ejpam-6135	62	17	in	in	ADP
ejpam-6135	62	18	duality	duality	NOUN
ejpam-6135	62	19	spaces	space	NOUN
ejpam-6135	62	20	.	.	PUNCT
ejpam-6135	63	1	in	in	ADP
ejpam-6135	63	2	this	this	DET
ejpam-6135	63	3	articles	article	NOUN
ejpam-6135	63	4	,	,	PUNCT
ejpam-6135	63	5	the	the	DET
ejpam-6135	63	6	author	author	NOUN
ejpam-6135	63	7	defines	define	VERB
ejpam-6135	63	8	an	an	DET
ejpam-6135	63	9	comparitive	comparitive	NOUN
ejpam-6135	63	10	analysis	analysis	NOUN
ejpam-6135	63	11	on	on	ADP
ejpam-6135	63	12	other	other	ADJ
ejpam-6135	63	13	type	type	NOUN
ejpam-6135	63	14	of	of	ADP
ejpam-6135	63	15	compactifications	compactification	NOUN
ejpam-6135	63	16	.	.	PUNCT
ejpam-6135	64	1	also	also	ADV
ejpam-6135	64	2	they	they	PRON
ejpam-6135	64	3	explore	explore	VERB
ejpam-6135	64	4	his	his	PRON
ejpam-6135	64	5	ideas	idea	NOUN
ejpam-6135	64	6	in	in	ADP
ejpam-6135	64	7	clopen	clopen	ADJ
ejpam-6135	64	8	sets	set	NOUN
ejpam-6135	64	9	,	,	PUNCT
ejpam-6135	64	10	ultrafilters	ultrafilter	NOUN
ejpam-6135	64	11	,	,	PUNCT
ejpam-6135	64	12	non	non	ADJ
ejpam-6135	64	13	-	-	ADJ
ejpam-6135	64	14	convergent	convergent	ADJ
ejpam-6135	64	15	spaces	space	NOUN
ejpam-6135	64	16	,	,	PUNCT
ejpam-6135	64	17	etc	etc	X
ejpam-6135	64	18	.	.	X
ejpam-6135	65	1	an	an	DET
ejpam-6135	65	2	application	application	NOUN
ejpam-6135	65	3	related	relate	VERB
ejpam-6135	65	4	to	to	ADP
ejpam-6135	65	5	compactifications	compactification	NOUN
ejpam-6135	65	6	[	[	X
ejpam-6135	65	7	14–16	14–16	NUM
ejpam-6135	65	8	]	]	PUNCT
ejpam-6135	65	9	are	be	AUX
ejpam-6135	65	10	used	use	VERB
ejpam-6135	65	11	in	in	ADP
ejpam-6135	65	12	both	both	CCONJ
ejpam-6135	65	13	the	the	DET
ejpam-6135	65	14	theoretical	theoretical	ADJ
ejpam-6135	65	15	approaches	approach	NOUN
ejpam-6135	65	16	like	like	ADP
ejpam-6135	65	17	lie	lie	NOUN
ejpam-6135	65	18	algebra	algebra	PROPN
ejpam-6135	65	19	,	,	PUNCT
ejpam-6135	65	20	bounded	bounded	ADJ
ejpam-6135	65	21	operators	operator	NOUN
ejpam-6135	65	22	,	,	PUNCT
ejpam-6135	65	23	etc	etc	X
ejpam-6135	65	24	,	,	PUNCT
ejpam-6135	65	25	.	.	PUNCT
ejpam-6135	66	1	and	and	CCONJ
ejpam-6135	66	2	also	also	ADV
ejpam-6135	66	3	applied	apply	VERB
ejpam-6135	66	4	in	in	ADP
ejpam-6135	66	5	different	different	ADJ
ejpam-6135	66	6	fields	field	NOUN
ejpam-6135	66	7	like	like	ADP
ejpam-6135	66	8	physics	physics	NOUN
ejpam-6135	66	9	,	,	PUNCT
ejpam-6135	66	10	robotics	robotic	NOUN
ejpam-6135	66	11	,	,	PUNCT
ejpam-6135	66	12	etc	etc	X
ejpam-6135	66	13	.	.	X
ejpam-6135	66	14	3	3	X
ejpam-6135	66	15	.	.	X
ejpam-6135	66	16	motivation	motivation	NOUN
ejpam-6135	66	17	and	and	CCONJ
ejpam-6135	66	18	contribution	contribution	NOUN
ejpam-6135	66	19	of	of	ADP
ejpam-6135	66	20	the	the	DET
ejpam-6135	66	21	study	study	NOUN
ejpam-6135	66	22	the	the	DET
ejpam-6135	66	23	major	major	ADJ
ejpam-6135	66	24	motivation	motivation	NOUN
ejpam-6135	66	25	behind	behind	ADP
ejpam-6135	66	26	the	the	DET
ejpam-6135	66	27	(	(	PUNCT
ejpam-6135	66	28	c	c	NOUN
ejpam-6135	66	29	,	,	PUNCT
ejpam-6135	66	30	d	d	NOUN
ejpam-6135	66	31	)	)	PUNCT
ejpam-6135	66	32	if	if	SCONJ
ejpam-6135	66	33	−q	−q	ADJ
ejpam-6135	66	34	uniform	uniform	ADJ
ejpam-6135	66	35	topological	topological	ADJ
ejpam-6135	66	36	space	space	NOUN
ejpam-6135	66	37	is	be	AUX
ejpam-6135	66	38	an	an	DET
ejpam-6135	66	39	major	major	ADJ
ejpam-6135	66	40	extension	extension	NOUN
ejpam-6135	66	41	of	of	ADP
ejpam-6135	66	42	intuitionsitic	intuitionsitic	ADJ
ejpam-6135	66	43	fuzzy	fuzzy	ADJ
ejpam-6135	66	44	topological	topological	ADJ
ejpam-6135	66	45	space	space	NOUN
ejpam-6135	66	46	.	.	PUNCT
ejpam-6135	67	1	a	a	DET
ejpam-6135	67	2	(	(	PUNCT
ejpam-6135	67	3	c	c	NOUN
ejpam-6135	67	4	,	,	PUNCT
ejpam-6135	67	5	d	d	NOUN
ejpam-6135	67	6	)	)	PUNCT
ejpam-6135	67	7	if	if	SCONJ
ejpam-6135	67	8	−q	−q	ADJ
ejpam-6135	67	9	uniform	uniform	ADJ
ejpam-6135	67	10	topological	topological	ADJ
ejpam-6135	67	11	space	space	NOUN
ejpam-6135	67	12	is	be	AUX
ejpam-6135	67	13	a	a	DET
ejpam-6135	67	14	highly	highly	ADV
ejpam-6135	67	15	generalized	generalized	ADJ
ejpam-6135	67	16	mathematical	mathematical	ADJ
ejpam-6135	67	17	structure	structure	NOUN
ejpam-6135	67	18	that	that	PRON
ejpam-6135	67	19	blends	blend	VERB
ejpam-6135	67	20	concepts	concept	NOUN
ejpam-6135	67	21	from	from	ADP
ejpam-6135	67	22	uniform	uniform	ADJ
ejpam-6135	67	23	topology	topology	NOUN
ejpam-6135	67	24	,	,	PUNCT
ejpam-6135	67	25	intuitionistic	intuitionistic	ADJ
ejpam-6135	67	26	fuzzy	fuzzy	ADJ
ejpam-6135	67	27	sets	set	NOUN
ejpam-6135	67	28	,	,	PUNCT
ejpam-6135	67	29	and	and	CCONJ
ejpam-6135	67	30	quasi	quasi	NOUN
ejpam-6135	67	31	-	-	NOUN
ejpam-6135	67	32	uniformity	uniformity	NOUN
ejpam-6135	67	33	.	.	PUNCT
ejpam-6135	68	1	it	it	PRON
ejpam-6135	68	2	is	be	AUX
ejpam-6135	68	3	designed	design	VERB
ejpam-6135	68	4	to	to	PART
ejpam-6135	68	5	model	model	VERB
ejpam-6135	68	6	uncertainity	uncertainity	NOUN
ejpam-6135	68	7	in	in	ADP
ejpam-6135	68	8	topological	topological	ADJ
ejpam-6135	68	9	spaces	space	NOUN
ejpam-6135	68	10	.	.	PUNCT
ejpam-6135	69	1	this	this	DET
ejpam-6135	69	2	space	space	NOUN
ejpam-6135	69	3	has	have	AUX
ejpam-6135	69	4	led	lead	VERB
ejpam-6135	69	5	to	to	ADP
ejpam-6135	69	6	the	the	DET
ejpam-6135	69	7	numerous	numerous	ADJ
ejpam-6135	69	8	concepts	concept	NOUN
ejpam-6135	69	9	in	in	ADP
ejpam-6135	69	10	topological	topological	ADJ
ejpam-6135	69	11	space	space	NOUN
ejpam-6135	69	12	is	be	AUX
ejpam-6135	69	13	functors	functor	NOUN
ejpam-6135	69	14	,	,	PUNCT
ejpam-6135	69	15	morphisms	morphism	NOUN
ejpam-6135	69	16	etc	etc	X
ejpam-6135	69	17	.	.	X
ejpam-6135	69	18	also	also	ADV
ejpam-6135	69	19	in	in	ADP
ejpam-6135	69	20	(	(	PUNCT
ejpam-6135	69	21	c	c	X
ejpam-6135	69	22	,	,	PUNCT
ejpam-6135	69	23	d	d	NOUN
ejpam-6135	69	24	)	)	PUNCT
ejpam-6135	69	25	if	if	SCONJ
ejpam-6135	69	26	−q	−q	ADJ
ejpam-6135	69	27	uniform	uniform	ADJ
ejpam-6135	69	28	ir∗	ir∗	NOUN
ejpam-6135	69	29	structure	structure	NOUN
ejpam-6135	69	30	space	space	NOUN
ejpam-6135	69	31	deals	deal	NOUN
ejpam-6135	69	32	with	with	ADP
ejpam-6135	69	33	the	the	DET
ejpam-6135	69	34	irreducibility	irreducibility	NOUN
ejpam-6135	69	35	in	in	ADP
ejpam-6135	69	36	topological	topological	ADJ
ejpam-6135	69	37	spaces	space	NOUN
ejpam-6135	69	38	.	.	PUNCT
ejpam-6135	70	1	this	this	PRON
ejpam-6135	70	2	leads	lead	VERB
ejpam-6135	70	3	to	to	ADP
ejpam-6135	70	4	zariski	zariski	NOUN
ejpam-6135	70	5	topology	topology	NOUN
ejpam-6135	70	6	,	,	PUNCT
ejpam-6135	70	7	spectral	spectral	ADJ
ejpam-6135	70	8	space	space	NOUN
ejpam-6135	70	9	and	and	CCONJ
ejpam-6135	70	10	jac	jac	PROPN
ejpam-6135	70	11	-	-	PUNCT
ejpam-6135	70	12	spectral	spectral	ADJ
ejpam-6135	70	13	space	space	NOUN
ejpam-6135	70	14	etc	etc	X
ejpam-6135	70	15	.	.	X
ejpam-6135	70	16	,	,	PUNCT
ejpam-6135	70	17	these	these	PRON
ejpam-6135	70	18	are	be	AUX
ejpam-6135	70	19	the	the	DET
ejpam-6135	70	20	higher	high	ADJ
ejpam-6135	70	21	dimension	dimension	NOUN
ejpam-6135	70	22	topological	topological	ADJ
ejpam-6135	70	23	space	space	NOUN
ejpam-6135	70	24	combined	combine	VERB
ejpam-6135	70	25	with	with	ADP
ejpam-6135	70	26	algebraic	algebraic	ADJ
ejpam-6135	70	27	geometry	geometry	NOUN
ejpam-6135	70	28	and	and	CCONJ
ejpam-6135	70	29	commutative	commutative	ADJ
ejpam-6135	70	30	algebra	algebra	NOUN
ejpam-6135	70	31	.	.	PUNCT
ejpam-6135	71	1	here	here	ADV
ejpam-6135	71	2	,	,	PUNCT
ejpam-6135	71	3	this	this	DET
ejpam-6135	71	4	motivate	motivate	NOUN
ejpam-6135	71	5	for	for	ADP
ejpam-6135	71	6	novel	novel	ADJ
ejpam-6135	71	7	research	research	NOUN
ejpam-6135	71	8	ideas	idea	NOUN
ejpam-6135	71	9	which	which	PRON
ejpam-6135	71	10	can	can	AUX
ejpam-6135	71	11	be	be	AUX
ejpam-6135	71	12	incorporated	incorporate	VERB
ejpam-6135	71	13	to	to	ADP
ejpam-6135	71	14	various	various	ADJ
ejpam-6135	71	15	domains	domain	NOUN
ejpam-6135	71	16	.	.	PUNCT
ejpam-6135	72	1	likewise	likewise	ADV
ejpam-6135	72	2	,	,	PUNCT
ejpam-6135	72	3	centred	centred	ADJ
ejpam-6135	72	4	systems	system	NOUN
ejpam-6135	72	5	deals	deal	NOUN
ejpam-6135	72	6	only	only	ADV
ejpam-6135	72	7	with	with	ADP
ejpam-6135	72	8	the	the	DET
ejpam-6135	72	9	collection	collection	NOUN
ejpam-6135	72	10	of	of	ADP
ejpam-6135	72	11	open	open	ADJ
ejpam-6135	72	12	sets	set	NOUN
ejpam-6135	72	13	in	in	ADP
ejpam-6135	72	14	the	the	DET
ejpam-6135	72	15	given	give	VERB
ejpam-6135	72	16	topological	topological	ADJ
ejpam-6135	72	17	space	space	NOUN
ejpam-6135	72	18	.	.	PUNCT
ejpam-6135	73	1	so	so	ADV
ejpam-6135	73	2	,	,	PUNCT
ejpam-6135	73	3	here	here	ADV
ejpam-6135	73	4	the	the	DET
ejpam-6135	73	5	reserach	reserach	NOUN
ejpam-6135	73	6	work	work	NOUN
ejpam-6135	73	7	incorporates	incorporate	VERB
ejpam-6135	73	8	the	the	DET
ejpam-6135	73	9	different	different	ADJ
ejpam-6135	73	10	spaces	space	NOUN
ejpam-6135	73	11	in	in	ADP
ejpam-6135	73	12	(	(	PUNCT
ejpam-6135	73	13	c	c	X
ejpam-6135	73	14	,	,	PUNCT
ejpam-6135	73	15	d	d	NOUN
ejpam-6135	73	16	)	)	PUNCT
ejpam-6135	73	17	if	if	SCONJ
ejpam-6135	73	18	−q	−q	ADJ
ejpam-6135	73	19	uniform	uniform	ADJ
ejpam-6135	73	20	topological	topological	ADJ
ejpam-6135	73	21	space	space	NOUN
ejpam-6135	73	22	.	.	PUNCT
ejpam-6135	74	1	based	base	VERB
ejpam-6135	74	2	on	on	ADP
ejpam-6135	74	3	the	the	DET
ejpam-6135	74	4	literature	literature	NOUN
ejpam-6135	74	5	survey	survey	NOUN
ejpam-6135	74	6	in	in	ADP
ejpam-6135	74	7	section-2	section-2	NUM
ejpam-6135	74	8	,	,	PUNCT
ejpam-6135	74	9	the	the	DET
ejpam-6135	74	10	authors	author	NOUN
ejpam-6135	74	11	introduced	introduce	VERB
ejpam-6135	74	12	the	the	DET
ejpam-6135	74	13	novel	novel	ADJ
ejpam-6135	74	14	idea	idea	NOUN
ejpam-6135	74	15	called	call	VERB
ejpam-6135	74	16	(	(	PUNCT
ejpam-6135	74	17	c	c	X
ejpam-6135	74	18	,	,	PUNCT
ejpam-6135	74	19	d	d	NOUN
ejpam-6135	74	20	)	)	PUNCT
ejpam-6135	74	21	if	if	SCONJ
ejpam-6135	74	22	−q	−q	ADJ
ejpam-6135	74	23	uniform	uniform	ADJ
ejpam-6135	74	24	ir	ir	PROPN
ejpam-6135	74	25	topological	topological	ADJ
ejpam-6135	74	26	space	space	NOUN
ejpam-6135	74	27	.	.	PUNCT
ejpam-6135	75	1	many	many	ADJ
ejpam-6135	75	2	researchers	researcher	NOUN
ejpam-6135	75	3	depicted	depict	VERB
ejpam-6135	75	4	and	and	CCONJ
ejpam-6135	75	5	applied	apply	VERB
ejpam-6135	75	6	compactifications	compactification	NOUN
ejpam-6135	75	7	in	in	ADP
ejpam-6135	75	8	robotics	robotic	NOUN
ejpam-6135	75	9	,	,	PUNCT
ejpam-6135	75	10	physics	physic	NOUN
ejpam-6135	75	11	,	,	PUNCT
ejpam-6135	75	12	lie	lie	NOUN
ejpam-6135	75	13	groups	group	NOUN
ejpam-6135	75	14	,	,	PUNCT
ejpam-6135	75	15	etc	etc	X
ejpam-6135	75	16	.	.	X
ejpam-6135	75	17	,	,	PUNCT
ejpam-6135	75	18	which	which	PRON
ejpam-6135	75	19	leads	lead	VERB
ejpam-6135	75	20	authors	author	NOUN
ejpam-6135	75	21	to	to	PART
ejpam-6135	75	22	study	study	VERB
ejpam-6135	75	23	(	(	PUNCT
ejpam-6135	75	24	c	c	X
ejpam-6135	75	25	,	,	PUNCT
ejpam-6135	75	26	d	d	NOUN
ejpam-6135	75	27	)	)	PUNCT
ejpam-6135	75	28	if	if	SCONJ
ejpam-6135	75	29	−q	−q	ADJ
ejpam-6135	75	30	uniform	uniform	ADJ
ejpam-6135	75	31	ir∗	ir∗	NOUN
ejpam-6135	75	32	centred	centre	VERB
ejpam-6135	75	33	structure	structure	NOUN
ejpam-6135	75	34	compactification	compactification	NOUN
ejpam-6135	75	35	.	.	PUNCT
ejpam-6135	76	1	to	to	PART
ejpam-6135	76	2	increase	increase	VERB
ejpam-6135	76	3	the	the	DET
ejpam-6135	76	4	readers	reader	NOUN
ejpam-6135	76	5	interest	interest	NOUN
ejpam-6135	76	6	,	,	PUNCT
ejpam-6135	76	7	the	the	DET
ejpam-6135	76	8	authors	author	NOUN
ejpam-6135	76	9	introduced	introduce	VERB
ejpam-6135	76	10	(	(	PUNCT
ejpam-6135	76	11	c	c	X
ejpam-6135	76	12	,	,	PUNCT
ejpam-6135	76	13	d	d	NOUN
ejpam-6135	76	14	)	)	PUNCT
ejpam-6135	76	15	if	if	SCONJ
ejpam-6135	76	16	−q	−q	ADJ
ejpam-6135	76	17	uniform	uniform	ADJ
ejpam-6135	76	18	ir∗	ir∗	NOUN
ejpam-6135	76	19	centred	centre	VERB
ejpam-6135	76	20	structure	structure	NOUN
ejpam-6135	76	21	filters	filter	NOUN
ejpam-6135	76	22	and	and	CCONJ
ejpam-6135	76	23	(	(	PUNCT
ejpam-6135	76	24	c	c	X
ejpam-6135	76	25	,	,	PUNCT
ejpam-6135	76	26	d	d	NOUN
ejpam-6135	76	27	)	)	PUNCT
ejpam-6135	76	28	if	if	SCONJ
ejpam-6135	76	29	−q	−q	ADJ
ejpam-6135	76	30	uniform	uniform	ADJ
ejpam-6135	76	31	ir∗	ir∗	NOUN
ejpam-6135	76	32	centred	centre	VERB
ejpam-6135	76	33	structure	structure	NOUN
ejpam-6135	76	34	nets	net	NOUN
ejpam-6135	76	35	which	which	PRON
ejpam-6135	76	36	supported	support	VERB
ejpam-6135	76	37	the	the	DET
ejpam-6135	76	38	study	study	NOUN
ejpam-6135	76	39	of	of	ADP
ejpam-6135	76	40	(	(	PUNCT
ejpam-6135	76	41	c	c	X
ejpam-6135	76	42	,	,	PUNCT
ejpam-6135	76	43	d	d	NOUN
ejpam-6135	76	44	)	)	PUNCT
ejpam-6135	76	45	if	if	SCONJ
ejpam-6135	76	46	−q	−q	ADJ
ejpam-6135	76	47	uniform	uniform	ADJ
ejpam-6135	76	48	ir∗	ir∗	NOUN
ejpam-6135	76	49	centred	centre	VERB
ejpam-6135	76	50	structure	structure	NOUN
ejpam-6135	76	51	compactification	compactification	NOUN
ejpam-6135	76	52	.	.	PUNCT
ejpam-6135	77	1	4	4	X
ejpam-6135	77	2	.	.	NUM
ejpam-6135	77	3	proposed	propose	VERB
ejpam-6135	77	4	structure	structure	NOUN
ejpam-6135	77	5	of	of	ADP
ejpam-6135	77	6	the	the	DET
ejpam-6135	77	7	paper	paper	NOUN
ejpam-6135	77	8	in	in	ADP
ejpam-6135	77	9	this	this	DET
ejpam-6135	77	10	article	article	NOUN
ejpam-6135	77	11	,	,	PUNCT
ejpam-6135	77	12	an	an	DET
ejpam-6135	77	13	idea	idea	NOUN
ejpam-6135	77	14	of	of	ADP
ejpam-6135	77	15	compactification	compactification	NOUN
ejpam-6135	77	16	on	on	ADP
ejpam-6135	77	17	(	(	PUNCT
ejpam-6135	77	18	c	c	X
ejpam-6135	77	19	,	,	PUNCT
ejpam-6135	77	20	d	d	NOUN
ejpam-6135	77	21	)	)	PUNCT
ejpam-6135	77	22	if	if	SCONJ
ejpam-6135	77	23	−q	−q	ADJ
ejpam-6135	77	24	uniform	uniform	ADJ
ejpam-6135	77	25	ir∗	ir∗	NOUN
ejpam-6135	77	26	centred	centre	VERB
ejpam-6135	77	27	structure	structure	NOUN
ejpam-6135	77	28	space	space	NOUN
ejpam-6135	77	29	is	be	AUX
ejpam-6135	77	30	defined	define	VERB
ejpam-6135	77	31	.	.	PUNCT
ejpam-6135	78	1	the	the	DET
ejpam-6135	78	2	below	below	PROPN
ejpam-6135	78	3	flowchart	flowchart	PROPN
ejpam-6135	78	4	shows	show	VERB
ejpam-6135	78	5	the	the	DET
ejpam-6135	78	6	process	process	NOUN
ejpam-6135	78	7	of	of	ADP
ejpam-6135	78	8	compactification	compactification	NOUN
ejpam-6135	78	9	is	be	AUX
ejpam-6135	78	10	executed	execute	VERB
ejpam-6135	78	11	via	via	ADP
ejpam-6135	78	12	(	(	PUNCT
ejpam-6135	78	13	c	c	X
ejpam-6135	78	14	,	,	PUNCT
ejpam-6135	78	15	d	d	NOUN
ejpam-6135	78	16	)	)	PUNCT
ejpam-6135	78	17	if	if	SCONJ
ejpam-6135	78	18	−q	−q	ADJ
ejpam-6135	78	19	uniform	uniform	ADJ
ejpam-6135	78	20	ir∗	ir∗	NOUN
ejpam-6135	78	21	centred	centre	VERB
ejpam-6135	78	22	filters	filter	NOUN
ejpam-6135	78	23	and	and	CCONJ
ejpam-6135	78	24	(	(	PUNCT
ejpam-6135	78	25	c	c	X
ejpam-6135	78	26	,	,	PUNCT
ejpam-6135	78	27	d	d	NOUN
ejpam-6135	78	28	)	)	PUNCT
ejpam-6135	78	29	if	if	SCONJ
ejpam-6135	78	30	−q	−q	ADJ
ejpam-6135	78	31	uniform	uniform	ADJ
ejpam-6135	78	32	nets	net	NOUN
ejpam-6135	78	33	.	.	PUNCT
ejpam-6135	79	1	s.	s.	PROPN
ejpam-6135	79	2	thirukumaran	thirukumaran	PROPN
ejpam-6135	79	3	,	,	PUNCT
ejpam-6135	79	4	g.	g.	PROPN
ejpam-6135	79	5	k.	k.	PROPN
ejpam-6135	79	6	revathi	revathi	PROPN
ejpam-6135	79	7	/	/	SYM
ejpam-6135	79	8	eur	eur	PROPN
ejpam-6135	79	9	.	.	PUNCT
ejpam-6135	80	1	j.	j.	PROPN
ejpam-6135	80	2	pure	pure	PROPN
ejpam-6135	80	3	appl	appl	PROPN
ejpam-6135	80	4	.	.	PROPN
ejpam-6135	80	5	math	math	PROPN
ejpam-6135	80	6	,	,	PUNCT
ejpam-6135	80	7	18	18	NUM
ejpam-6135	80	8	(	(	PUNCT
ejpam-6135	80	9	2	2	NUM
ejpam-6135	80	10	)	)	PUNCT
ejpam-6135	80	11	(	(	PUNCT
ejpam-6135	80	12	2025	2025	NUM
ejpam-6135	80	13	)	)	PUNCT
ejpam-6135	80	14	,	,	PUNCT
ejpam-6135	80	15	6135	6135	NUM
ejpam-6135	80	16	4	4	NUM
ejpam-6135	80	17	of	of	ADP
ejpam-6135	80	18	17	17	NUM
ejpam-6135	80	19	figure	figure	NOUN
ejpam-6135	80	20	1	1	NUM
ejpam-6135	80	21	:	:	PUNCT
ejpam-6135	80	22	a	a	DET
ejpam-6135	80	23	study	study	NOUN
ejpam-6135	80	24	on	on	ADP
ejpam-6135	80	25	(	(	PUNCT
ejpam-6135	80	26	c	c	X
ejpam-6135	80	27	,	,	PUNCT
ejpam-6135	80	28	d	d	NOUN
ejpam-6135	80	29	)	)	PUNCT
ejpam-6135	80	30	if	if	SCONJ
ejpam-6135	80	31	−q	−q	ADJ
ejpam-6135	80	32	uniform	uniform	ADJ
ejpam-6135	80	33	ir∗	ir∗	NOUN
ejpam-6135	80	34	centred	centre	VERB
ejpam-6135	80	35	structure	structure	NOUN
ejpam-6135	80	36	compactification	compactification	NOUN
ejpam-6135	80	37	5	5	NUM
ejpam-6135	80	38	.	.	PUNCT
ejpam-6135	80	39	preliminaries	preliminary	NOUN
ejpam-6135	80	40	here	here	ADV
ejpam-6135	80	41	if	if	SCONJ
ejpam-6135	80	42	denotes	denote	VERB
ejpam-6135	80	43	the	the	DET
ejpam-6135	80	44	intuitionistic	intuitionistic	ADJ
ejpam-6135	80	45	fuzzy	fuzzy	ADJ
ejpam-6135	80	46	set	set	NOUN
ejpam-6135	80	47	on	on	ADP
ejpam-6135	80	48	x	x	PUNCT
ejpam-6135	80	49	and	and	CCONJ
ejpam-6135	80	50	throughout	throughout	ADP
ejpam-6135	80	51	the	the	DET
ejpam-6135	80	52	article	article	NOUN
ejpam-6135	80	53	,	,	PUNCT
ejpam-6135	80	54	and	and	CCONJ
ejpam-6135	80	55	the	the	DET
ejpam-6135	80	56	universe	universe	NOUN
ejpam-6135	80	57	of	of	ADP
ejpam-6135	80	58	discourse	discourse	NOUN
ejpam-6135	80	59	x	x	VERB
ejpam-6135	80	60	is	be	AUX
ejpam-6135	80	61	a	a	DET
ejpam-6135	80	62	non	non	ADJ
ejpam-6135	80	63	-	-	ADJ
ejpam-6135	80	64	empty	empty	ADJ
ejpam-6135	80	65	set	set	NOUN
ejpam-6135	80	66	.	.	PUNCT
ejpam-6135	81	1	definition	definition	NOUN
ejpam-6135	81	2	1	1	NUM
ejpam-6135	81	3	.	.	PUNCT
ejpam-6135	82	1	[	[	X
ejpam-6135	82	2	3	3	X
ejpam-6135	82	3	]	]	X
ejpam-6135	82	4	let	let	VERB
ejpam-6135	82	5	x	x	PRON
ejpam-6135	82	6	be	be	AUX
ejpam-6135	82	7	a	a	DET
ejpam-6135	82	8	universal	universal	ADJ
ejpam-6135	82	9	set	set	NOUN
ejpam-6135	82	10	and	and	CCONJ
ejpam-6135	82	11	an	an	DET
ejpam-6135	82	12	if	if	SCONJ
ejpam-6135	82	13	set	set	VERB
ejpam-6135	82	14	a	a	DET
ejpam-6135	82	15	in	in	NOUN
ejpam-6135	82	16	x	x	SYM
ejpam-6135	82	17	is	be	AUX
ejpam-6135	82	18	defined	define	VERB
ejpam-6135	82	19	as	as	ADP
ejpam-6135	82	20	a	a	DET
ejpam-6135	82	21	=	=	X
ejpam-6135	82	22	{	{	PUNCT
ejpam-6135	82	23	⟨x	⟨x	NUM
ejpam-6135	82	24	,	,	PUNCT
ejpam-6135	82	25	µa(x	µa(x	ADV
ejpam-6135	82	26	)	)	PUNCT
ejpam-6135	82	27	,	,	PUNCT
ejpam-6135	82	28	νa(x)⟩	νa(x)⟩	VERB
ejpam-6135	82	29	:	:	PUNCT
ejpam-6135	82	30	x	x	PUNCT
ejpam-6135	82	31	∈	∈	NOUN
ejpam-6135	82	32	x	x	X
ejpam-6135	82	33	}	}	PUNCT
ejpam-6135	82	34	where	where	SCONJ
ejpam-6135	82	35	µa(x	µa(x	NOUN
ejpam-6135	82	36	)	)	PUNCT
ejpam-6135	82	37	:	:	PUNCT
ejpam-6135	82	38	x	x	X
ejpam-6135	82	39	→	→	PUNCT
ejpam-6135	83	1	[	[	X
ejpam-6135	83	2	0	0	NUM
ejpam-6135	83	3	,	,	PUNCT
ejpam-6135	83	4	1	1	NUM
ejpam-6135	83	5	]	]	PUNCT
ejpam-6135	83	6	and	and	CCONJ
ejpam-6135	83	7	νa(x	νa(x	NOUN
ejpam-6135	83	8	)	)	PUNCT
ejpam-6135	83	9	:	:	PUNCT
ejpam-6135	83	10	x	x	X
ejpam-6135	83	11	→	→	PUNCT
ejpam-6135	83	12	[	[	X
ejpam-6135	83	13	0	0	NUM
ejpam-6135	83	14	,	,	PUNCT
ejpam-6135	83	15	1	1	NUM
ejpam-6135	83	16	]	]	PUNCT
ejpam-6135	83	17	are	be	AUX
ejpam-6135	83	18	the	the	DET
ejpam-6135	83	19	membership	membership	NOUN
ejpam-6135	83	20	and	and	CCONJ
ejpam-6135	83	21	non	non	ADJ
ejpam-6135	83	22	-	-	ADJ
ejpam-6135	83	23	membership	membership	ADJ
ejpam-6135	83	24	functions	function	NOUN
ejpam-6135	83	25	respectively	respectively	ADV
ejpam-6135	83	26	for	for	ADP
ejpam-6135	83	27	every	every	DET
ejpam-6135	83	28	x	x	SYM
ejpam-6135	83	29	∈	∈	PROPN
ejpam-6135	83	30	x	x	NOUN
ejpam-6135	83	31	,	,	PUNCT
ejpam-6135	83	32	with	with	ADP
ejpam-6135	83	33	the	the	DET
ejpam-6135	83	34	condition	condition	NOUN
ejpam-6135	83	35	0	0	NUM
ejpam-6135	83	36	≤	≤	NOUN
ejpam-6135	83	37	µa(x	µa(x	ADP
ejpam-6135	83	38	)	)	PUNCT
ejpam-6135	84	1	+	+	CCONJ
ejpam-6135	84	2	νa(x	νa(x	NOUN
ejpam-6135	84	3	)	)	PUNCT
ejpam-6135	84	4	≤	≤	NUM
ejpam-6135	84	5	1	1	NUM
ejpam-6135	84	6	.	.	PUNCT
ejpam-6135	85	1	s.	s.	PROPN
ejpam-6135	85	2	thirukumaran	thirukumaran	PROPN
ejpam-6135	85	3	,	,	PUNCT
ejpam-6135	85	4	g.	g.	PROPN
ejpam-6135	85	5	k.	k.	PROPN
ejpam-6135	85	6	revathi	revathi	PROPN
ejpam-6135	85	7	/	/	SYM
ejpam-6135	85	8	eur	eur	PROPN
ejpam-6135	85	9	.	.	PUNCT
ejpam-6135	86	1	j.	j.	PROPN
ejpam-6135	86	2	pure	pure	PROPN
ejpam-6135	86	3	appl	appl	PROPN
ejpam-6135	86	4	.	.	PROPN
ejpam-6135	86	5	math	math	PROPN
ejpam-6135	86	6	,	,	PUNCT
ejpam-6135	86	7	18	18	NUM
ejpam-6135	86	8	(	(	PUNCT
ejpam-6135	86	9	2	2	NUM
ejpam-6135	86	10	)	)	PUNCT
ejpam-6135	86	11	(	(	PUNCT
ejpam-6135	86	12	2025	2025	NUM
ejpam-6135	86	13	)	)	PUNCT
ejpam-6135	86	14	,	,	PUNCT
ejpam-6135	86	15	6135	6135	NUM
ejpam-6135	86	16	5	5	NUM
ejpam-6135	86	17	of	of	ADP
ejpam-6135	86	18	17	17	NUM
ejpam-6135	86	19	definition	definition	NOUN
ejpam-6135	86	20	2	2	NUM
ejpam-6135	86	21	.	.	PUNCT
ejpam-6135	87	1	[	[	X
ejpam-6135	87	2	5	5	NUM
ejpam-6135	87	3	]	]	PUNCT
ejpam-6135	87	4	an	an	DET
ejpam-6135	87	5	if	if	SCONJ
ejpam-6135	87	6	topology	topology	NOUN
ejpam-6135	87	7	τ	τ	PROPN
ejpam-6135	87	8	on	on	ADP
ejpam-6135	87	9	x	x	SYM
ejpam-6135	87	10	is	be	AUX
ejpam-6135	87	11	a	a	DET
ejpam-6135	87	12	collection	collection	NOUN
ejpam-6135	87	13	of	of	ADP
ejpam-6135	87	14	intuitionistic	intuitionistic	ADJ
ejpam-6135	87	15	fuzzy	fuzzy	ADJ
ejpam-6135	87	16	sets	set	NOUN
ejpam-6135	87	17	,	,	PUNCT
ejpam-6135	87	18	the	the	DET
ejpam-6135	87	19	following	follow	VERB
ejpam-6135	87	20	assertion	assertion	NOUN
ejpam-6135	87	21	are	be	AUX
ejpam-6135	87	22	to	to	PART
ejpam-6135	87	23	be	be	AUX
ejpam-6135	87	24	hold	hold	VERB
ejpam-6135	87	25	:	:	PUNCT
ejpam-6135	87	26	(	(	PUNCT
ejpam-6135	87	27	i	i	NOUN
ejpam-6135	87	28	)	)	PUNCT
ejpam-6135	88	1	0∼,1∼	0∼,1∼	PROPN
ejpam-6135	88	2	∈	∈	PROPN
ejpam-6135	88	3	τ	τ	X
ejpam-6135	88	4	,	,	PUNCT
ejpam-6135	88	5	(	(	PUNCT
ejpam-6135	88	6	ii	ii	NOUN
ejpam-6135	88	7	)	)	PUNCT
ejpam-6135	88	8	each	each	PRON
ejpam-6135	88	9	ai	ai	VERB
ejpam-6135	88	10	∈	∈	PROPN
ejpam-6135	88	11	τ	τ	X
ejpam-6135	88	12	,	,	PUNCT
ejpam-6135	88	13	then	then	ADV
ejpam-6135	88	14	∩n	∩n	PROPN
ejpam-6135	88	15	i=1ai	i=1ai	ADV
ejpam-6135	88	16	∈	∈	PROPN
ejpam-6135	88	17	τ	τ	X
ejpam-6135	88	18	.	.	PUNCT
ejpam-6135	89	1	(	(	PUNCT
ejpam-6135	89	2	iii	iii	NOUN
ejpam-6135	89	3	)	)	PUNCT
ejpam-6135	89	4	for	for	ADP
ejpam-6135	89	5	all	all	PRON
ejpam-6135	89	6	ai	ai	VERB
ejpam-6135	89	7	∈	∈	PROPN
ejpam-6135	89	8	τ	τ	X
ejpam-6135	89	9	then	then	ADV
ejpam-6135	89	10	∪i	∪i	PROPN
ejpam-6135	89	11	∈	∈	PROPN
ejpam-6135	89	12	ja	ja	PROPN
ejpam-6135	89	13	∈	∈	PROPN
ejpam-6135	89	14	τ	τ	X
ejpam-6135	89	15	.	.	PUNCT
ejpam-6135	90	1	the	the	DET
ejpam-6135	90	2	pair	pair	NOUN
ejpam-6135	90	3	(	(	PUNCT
ejpam-6135	90	4	x	x	X
ejpam-6135	90	5	,	,	PUNCT
ejpam-6135	90	6	τ	τ	X
ejpam-6135	90	7	)	)	PUNCT
ejpam-6135	90	8	is	be	AUX
ejpam-6135	90	9	referred	refer	VERB
ejpam-6135	90	10	to	to	ADP
ejpam-6135	90	11	as	as	ADP
ejpam-6135	90	12	if	if	SCONJ
ejpam-6135	90	13	topological	topological	ADJ
ejpam-6135	90	14	space	space	NOUN
ejpam-6135	90	15	on	on	ADP
ejpam-6135	90	16	x	x	PUNCT
ejpam-6135	90	17	definition	definition	NOUN
ejpam-6135	90	18	3	3	NUM
ejpam-6135	90	19	.	.	PUNCT
ejpam-6135	91	1	[	[	X
ejpam-6135	91	2	17	17	NUM
ejpam-6135	91	3	]	]	PUNCT
ejpam-6135	91	4	suppose	suppose	VERB
ejpam-6135	91	5	ξx	ξx	PROPN
ejpam-6135	91	6	represents	represent	VERB
ejpam-6135	91	7	the	the	DET
ejpam-6135	91	8	collection	collection	NOUN
ejpam-6135	91	9	of	of	ADP
ejpam-6135	91	10	if	if	SCONJ
ejpam-6135	91	11	mappings	mapping	NOUN
ejpam-6135	91	12	,	,	PUNCT
ejpam-6135	91	13	g	g	NOUN
ejpam-6135	91	14	:	:	PUNCT
ejpam-6135	91	15	if	if	SCONJ
ejpam-6135	91	16	(	(	PUNCT
ejpam-6135	91	17	x	x	X
ejpam-6135	91	18	)	)	PUNCT
ejpam-6135	91	19	→	→	SYM
ejpam-6135	91	20	if	if	SCONJ
ejpam-6135	91	21	(	(	PUNCT
ejpam-6135	91	22	x	x	X
ejpam-6135	91	23	)	)	PUNCT
ejpam-6135	91	24	then	then	ADV
ejpam-6135	91	25	the	the	DET
ejpam-6135	91	26	following	following	NOUN
ejpam-6135	91	27	are	be	AUX
ejpam-6135	91	28	:	:	PUNCT
ejpam-6135	91	29	(	(	PUNCT
ejpam-6135	91	30	i	i	NOUN
ejpam-6135	91	31	)	)	PUNCT
ejpam-6135	91	32	g(0∼	g(0∼	NOUN
ejpam-6135	91	33	)	)	PUNCT
ejpam-6135	92	1	=	=	SYM
ejpam-6135	92	2	0∼	0∼	NUM
ejpam-6135	92	3	(	(	PUNCT
ejpam-6135	92	4	ii	ii	NOUN
ejpam-6135	92	5	)	)	PUNCT
ejpam-6135	92	6	a	a	DET
ejpam-6135	92	7	⊆	⊆	NUM
ejpam-6135	92	8	g(a	g(a	PROPN
ejpam-6135	92	9	)	)	PUNCT
ejpam-6135	92	10	,	,	PUNCT
ejpam-6135	92	11	∀a	∀a	X
ejpam-6135	92	12	∈	∈	PROPN
ejpam-6135	92	13	if(x	if(x	NOUN
ejpam-6135	92	14	)	)	PUNCT
ejpam-6135	92	15	(	(	PUNCT
ejpam-6135	92	16	iii	iii	X
ejpam-6135	92	17	)	)	PUNCT
ejpam-6135	92	18	g(∪ai)=	g(∪ai)=	NOUN
ejpam-6135	92	19	∪g(ai	∪g(ai	PROPN
ejpam-6135	92	20	)	)	PUNCT
ejpam-6135	92	21	,	,	PUNCT
ejpam-6135	92	22	∀ai	∀ai	PROPN
ejpam-6135	92	23	∈	∈	PROPN
ejpam-6135	92	24	if	if	SCONJ
ejpam-6135	92	25	(	(	PUNCT
ejpam-6135	92	26	x	x	X
ejpam-6135	92	27	)	)	PUNCT
ejpam-6135	92	28	,	,	PUNCT
ejpam-6135	92	29	i	i	PRON
ejpam-6135	92	30	∈	∈	PROPN
ejpam-6135	92	31	j	j	PROPN
ejpam-6135	92	32	for	for	ADP
ejpam-6135	92	33	g	g	PROPN
ejpam-6135	92	34	∈	∈	PROPN
ejpam-6135	92	35	ξx	ξx	NOUN
ejpam-6135	92	36	,	,	PUNCT
ejpam-6135	92	37	the	the	DET
ejpam-6135	92	38	function	function	NOUN
ejpam-6135	92	39	g−1(a)=	g−1(a)=	PROPN
ejpam-6135	92	40	∩{b	∩{b	X
ejpam-6135	92	41	:	:	PUNCT
ejpam-6135	92	42	g(b̄	g(b̄	X
ejpam-6135	92	43	)	)	PUNCT
ejpam-6135	92	44	⊆	⊆	NUM
ejpam-6135	92	45	ā	ā	ADJ
ejpam-6135	92	46	}	}	PUNCT
ejpam-6135	92	47	∈	∈	PROPN
ejpam-6135	92	48	ξx	ξx	NOUN
ejpam-6135	92	49	,	,	PUNCT
ejpam-6135	92	50	given	give	VERB
ejpam-6135	92	51	for	for	ADP
ejpam-6135	92	52	all	all	DET
ejpam-6135	92	53	a	a	DET
ejpam-6135	92	54	∈	∈	NOUN
ejpam-6135	92	55	if	if	SCONJ
ejpam-6135	92	56	(	(	PUNCT
ejpam-6135	92	57	x	x	X
ejpam-6135	92	58	)	)	PUNCT
ejpam-6135	92	59	,	,	PUNCT
ejpam-6135	92	60	g	g	PROPN
ejpam-6135	92	61	⊓	⊓	PROPN
ejpam-6135	92	62	g	g	NOUN
ejpam-6135	92	63	′	′	NUM
ejpam-6135	92	64	(	(	PUNCT
ejpam-6135	92	65	a)=∩{g(a1	a)=∩{g(a1	PROPN
ejpam-6135	92	66	)	)	PUNCT
ejpam-6135	92	67	∪	∪	ADP
ejpam-6135	92	68	g	g	PROPN
ejpam-6135	92	69	′	′	NUM
ejpam-6135	92	70	(	(	PUNCT
ejpam-6135	92	71	a2	a2	PROPN
ejpam-6135	92	72	)	)	PUNCT
ejpam-6135	92	73	:	:	PUNCT
ejpam-6135	92	74	a1	a1	VERB
ejpam-6135	92	75	∪a2	∪a2	PRON
ejpam-6135	93	1	=	=	SYM
ejpam-6135	93	2	a	a	NOUN
ejpam-6135	93	3	}	}	PUNCT
ejpam-6135	93	4	,	,	PUNCT
ejpam-6135	93	5	(	(	PUNCT
ejpam-6135	93	6	g	g	PROPN
ejpam-6135	93	7	◦	◦	NOUN
ejpam-6135	93	8	g′	g′	NOUN
ejpam-6135	93	9	)	)	PUNCT
ejpam-6135	93	10	(	(	PUNCT
ejpam-6135	93	11	a)=g(g	a)=g(g	PROPN
ejpam-6135	93	12	′	′	INTJ
ejpam-6135	93	13	(	(	PUNCT
ejpam-6135	93	14	a	a	NOUN
ejpam-6135	93	15	)	)	PUNCT
ejpam-6135	93	16	)	)	PUNCT
ejpam-6135	93	17	.	.	PUNCT
ejpam-6135	94	1	definition	definition	NOUN
ejpam-6135	94	2	4	4	NUM
ejpam-6135	94	3	.	.	PUNCT
ejpam-6135	95	1	[	[	X
ejpam-6135	95	2	17	17	NUM
ejpam-6135	95	3	]	]	PUNCT
ejpam-6135	95	4	let	let	VERB
ejpam-6135	95	5	υ	υ	NOUN
ejpam-6135	95	6	:	:	PUNCT
ejpam-6135	95	7	ξx	ξx	PROPN
ejpam-6135	96	1	→	→	PUNCT
ejpam-6135	96	2	i	i	PRON
ejpam-6135	96	3	×	×	VERB
ejpam-6135	97	1	i	i	PRON
ejpam-6135	97	2	be	be	VERB
ejpam-6135	97	3	an	an	DET
ejpam-6135	97	4	if	if	SCONJ
ejpam-6135	97	5	mapping	mapping	NOUN
ejpam-6135	97	6	.	.	PUNCT
ejpam-6135	98	1	then	then	ADV
ejpam-6135	98	2	υ	υ	PROPN
ejpam-6135	98	3	is	be	AUX
ejpam-6135	98	4	characterized	characterize	VERB
ejpam-6135	98	5	as	as	ADP
ejpam-6135	98	6	an	an	DET
ejpam-6135	98	7	if	if	SCONJ
ejpam-6135	98	8	quasi	quasi	ADJ
ejpam-6135	98	9	uniformity	uniformity	NOUN
ejpam-6135	98	10	on	on	ADP
ejpam-6135	98	11	x	x	NOUN
ejpam-6135	98	12	,	,	PUNCT
ejpam-6135	98	13	if	if	SCONJ
ejpam-6135	98	14	it	it	PRON
ejpam-6135	98	15	fulfills	fulfill	VERB
ejpam-6135	98	16	the	the	DET
ejpam-6135	98	17	circumstances	circumstance	NOUN
ejpam-6135	98	18	:	:	PUNCT
ejpam-6135	98	19	(	(	PUNCT
ejpam-6135	98	20	i	i	NOUN
ejpam-6135	98	21	)	)	PUNCT
ejpam-6135	98	22	υ(g1	υ(g1	NUM
ejpam-6135	98	23	⊓	⊓	PROPN
ejpam-6135	98	24	g2	g2	PROPN
ejpam-6135	98	25	)	)	PUNCT
ejpam-6135	98	26	⊇	⊇	NOUN
ejpam-6135	98	27	υ(g1	υ(g1	NUM
ejpam-6135	98	28	)	)	PUNCT
ejpam-6135	98	29	∩	∩	NOUN
ejpam-6135	98	30	υ(g2	υ(g2	X
ejpam-6135	98	31	)	)	PUNCT
ejpam-6135	98	32	for	for	ADP
ejpam-6135	98	33	g1	g1	NOUN
ejpam-6135	98	34	,	,	PUNCT
ejpam-6135	98	35	g2	g2	PROPN
ejpam-6135	98	36	∈	∈	PROPN
ejpam-6135	98	37	ξx	ξx	PROPN
ejpam-6135	98	38	(	(	PUNCT
ejpam-6135	98	39	ii	ii	NOUN
ejpam-6135	98	40	)	)	PUNCT
ejpam-6135	98	41	g	g	PROPN
ejpam-6135	98	42	∈	∈	PROPN
ejpam-6135	98	43	ξx	ξx	NOUN
ejpam-6135	98	44	we	we	PRON
ejpam-6135	98	45	have	have	VERB
ejpam-6135	98	46	∪{υ(g1	∪{υ(g1	PUNCT
ejpam-6135	98	47	)	)	PUNCT
ejpam-6135	98	48	:	:	PUNCT
ejpam-6135	98	49	g1	g1	VERB
ejpam-6135	98	50	◦	◦	NOUN
ejpam-6135	98	51	g1	g1	PROPN
ejpam-6135	98	52	⊆	⊆	NUM
ejpam-6135	98	53	g	g	PROPN
ejpam-6135	98	54	}	}	PUNCT
ejpam-6135	98	55	⊇	⊇	PROPN
ejpam-6135	98	56	υ(g	υ(g	NOUN
ejpam-6135	98	57	)	)	PUNCT
ejpam-6135	98	58	(	(	PUNCT
ejpam-6135	98	59	iii	iii	X
ejpam-6135	98	60	)	)	PUNCT
ejpam-6135	98	61	g1	g1	PROPN
ejpam-6135	98	62	⊇	⊇	PROPN
ejpam-6135	98	63	g	g	PROPN
ejpam-6135	98	64	then	then	ADV
ejpam-6135	98	65	υ(g1	υ(g1	NUM
ejpam-6135	98	66	)	)	PUNCT
ejpam-6135	98	67	⊇	⊇	PROPN
ejpam-6135	98	68	υ(g	υ(g	NOUN
ejpam-6135	98	69	)	)	PUNCT
ejpam-6135	98	70	(	(	PUNCT
ejpam-6135	98	71	iv	iv	X
ejpam-6135	98	72	)	)	PUNCT
ejpam-6135	98	73	g	g	PROPN
ejpam-6135	98	74	∈	∈	PROPN
ejpam-6135	98	75	ξx	ξx	NOUN
ejpam-6135	98	76	then	then	ADV
ejpam-6135	98	77	υ(f)=1∼.	υ(f)=1∼.	VERB
ejpam-6135	98	78	a	a	DET
ejpam-6135	98	79	pair	pair	NOUN
ejpam-6135	98	80	(	(	PUNCT
ejpam-6135	98	81	x	x	NOUN
ejpam-6135	98	82	,	,	PUNCT
ejpam-6135	98	83	υ	υ	NOUN
ejpam-6135	98	84	)	)	PUNCT
ejpam-6135	98	85	is	be	AUX
ejpam-6135	98	86	claimed	claim	VERB
ejpam-6135	98	87	as	as	ADP
ejpam-6135	98	88	if	if	SCONJ
ejpam-6135	98	89	−q	−q	ADJ
ejpam-6135	98	90	uniform	uniform	ADJ
ejpam-6135	98	91	space	space	NOUN
ejpam-6135	98	92	.	.	PUNCT
ejpam-6135	99	1	definition	definition	NOUN
ejpam-6135	99	2	5	5	NUM
ejpam-6135	99	3	.	.	PUNCT
ejpam-6135	100	1	[	[	X
ejpam-6135	100	2	17	17	NUM
ejpam-6135	100	3	]	]	PUNCT
ejpam-6135	100	4	a	a	DET
ejpam-6135	100	5	pair	pair	NOUN
ejpam-6135	100	6	(	(	PUNCT
ejpam-6135	100	7	x	x	NOUN
ejpam-6135	100	8	,	,	PUNCT
ejpam-6135	100	9	υ	υ	NOUN
ejpam-6135	100	10	)	)	PUNCT
ejpam-6135	100	11	be	be	AUX
ejpam-6135	100	12	an	an	DET
ejpam-6135	100	13	if	if	SCONJ
ejpam-6135	100	14	−q	−q	ADJ
ejpam-6135	100	15	uniform	uniform	ADJ
ejpam-6135	100	16	space	space	NOUN
ejpam-6135	100	17	.	.	PUNCT
ejpam-6135	101	1	let	let	VERB
ejpam-6135	101	2	c	c	NOUN
ejpam-6135	101	3	∈	∈	PROPN
ejpam-6135	101	4	(	(	PUNCT
ejpam-6135	101	5	0	0	NUM
ejpam-6135	101	6	,	,	PUNCT
ejpam-6135	101	7	1	1	NUM
ejpam-6135	101	8	]	]	PUNCT
ejpam-6135	101	9	=	=	X
ejpam-6135	101	10	i0	i0	PROPN
ejpam-6135	101	11	and	and	CCONJ
ejpam-6135	101	12	d	d	ADP
ejpam-6135	101	13	∈	∈	PROPN
ejpam-6135	102	1	[	[	X
ejpam-6135	102	2	0	0	NUM
ejpam-6135	102	3	,	,	PUNCT
ejpam-6135	102	4	1	1	NUM
ejpam-6135	102	5	)	)	PUNCT
ejpam-6135	102	6	=	=	NOUN
ejpam-6135	102	7	i1	i1	NOUN
ejpam-6135	102	8	with	with	ADP
ejpam-6135	102	9	c	c	PROPN
ejpam-6135	102	10	+	+	CCONJ
ejpam-6135	102	11	d	d	PROPN
ejpam-6135	102	12	≤	≤	NUM
ejpam-6135	102	13	1	1	NUM
ejpam-6135	102	14	and	and	CCONJ
ejpam-6135	102	15	a	a	DET
ejpam-6135	102	16	∈	∈	NOUN
ejpam-6135	102	17	if	if	SCONJ
ejpam-6135	102	18	(	(	PUNCT
ejpam-6135	102	19	x	x	NOUN
ejpam-6135	102	20	)	)	PUNCT
ejpam-6135	102	21	.	.	PUNCT
ejpam-6135	103	1	(	(	PUNCT
ejpam-6135	103	2	c	c	X
ejpam-6135	103	3	,	,	PUNCT
ejpam-6135	103	4	d)ifqiυ(a	d)ifqiυ(a	ADJ
ejpam-6135	103	5	)	)	PUNCT
ejpam-6135	103	6	=	=	X
ejpam-6135	104	1	∪{b	∪{b	NOUN
ejpam-6135	104	2	:	:	PUNCT
ejpam-6135	104	3	f(b	f(b	X
ejpam-6135	104	4	)	)	PUNCT
ejpam-6135	104	5	⊆	⊆	NUM
ejpam-6135	104	6	a	a	PRON
ejpam-6135	104	7	,	,	PUNCT
ejpam-6135	104	8	some	some	PRON
ejpam-6135	104	9	of	of	ADP
ejpam-6135	104	10	f	f	PROPN
ejpam-6135	104	11	∈	∈	PROPN
ejpam-6135	104	12	ξ(x	ξ(x	PROPN
ejpam-6135	104	13	)	)	PUNCT
ejpam-6135	104	14	and	and	CCONJ
ejpam-6135	104	15	υ(f	υ(f	PROPN
ejpam-6135	104	16	)	)	PUNCT
ejpam-6135	104	17	>	>	X
ejpam-6135	105	1	(	(	PUNCT
ejpam-6135	105	2	c	c	X
ejpam-6135	105	3	,	,	PUNCT
ejpam-6135	105	4	d	d	NOUN
ejpam-6135	105	5	)	)	PUNCT
ejpam-6135	105	6	}	}	PUNCT
ejpam-6135	105	7	definition	definition	NOUN
ejpam-6135	105	8	6	6	NUM
ejpam-6135	105	9	.	.	PUNCT
ejpam-6135	106	1	[	[	X
ejpam-6135	106	2	17	17	NUM
ejpam-6135	106	3	]	]	PUNCT
ejpam-6135	106	4	consider	consider	VERB
ejpam-6135	106	5	(	(	PUNCT
ejpam-6135	106	6	x	x	NOUN
ejpam-6135	106	7	,	,	PUNCT
ejpam-6135	106	8	υ	υ	NOUN
ejpam-6135	106	9	)	)	PUNCT
ejpam-6135	106	10	be	be	AUX
ejpam-6135	106	11	an	an	DET
ejpam-6135	106	12	if	if	SCONJ
ejpam-6135	106	13	−q	−q	ADJ
ejpam-6135	106	14	uniform	uniform	ADJ
ejpam-6135	106	15	space	space	NOUN
ejpam-6135	106	16	the	the	DET
ejpam-6135	106	17	mapping	mapping	NOUN
ejpam-6135	106	18	τυ	τυ	PRON
ejpam-6135	106	19	is	be	AUX
ejpam-6135	106	20	defined	define	VERB
ejpam-6135	106	21	by	by	ADP
ejpam-6135	106	22	:	:	PUNCT
ejpam-6135	106	23	if	if	SCONJ
ejpam-6135	106	24	(	(	PUNCT
ejpam-6135	106	25	x)→	x)→	PROPN
ejpam-6135	107	1	i	i	PRON
ejpam-6135	107	2	×	×	VERB
ejpam-6135	107	3	i	i	PRON
ejpam-6135	107	4	is	be	AUX
ejpam-6135	107	5	defined	define	VERB
ejpam-6135	107	6	by	by	ADP
ejpam-6135	107	7	τυ(a	τυ(a	NOUN
ejpam-6135	107	8	)	)	PUNCT
ejpam-6135	108	1	=	=	SYM
ejpam-6135	108	2	∪{(c	∪{(c	NOUN
ejpam-6135	108	3	,	,	PUNCT
ejpam-6135	108	4	d	d	NOUN
ejpam-6135	108	5	)	)	PUNCT
ejpam-6135	108	6	:	:	PUNCT
ejpam-6135	108	7	(	(	PUNCT
ejpam-6135	108	8	c	c	X
ejpam-6135	108	9	,	,	PUNCT
ejpam-6135	108	10	d	d	NOUN
ejpam-6135	108	11	)	)	PUNCT
ejpam-6135	108	12	ifqiυ(a)=a	ifqiυ(a)=a	NOUN
ejpam-6135	108	13	,	,	PUNCT
ejpam-6135	108	14	c	c	PROPN
ejpam-6135	108	15	∈	∈	PROPN
ejpam-6135	108	16	i0	i0	PROPN
ejpam-6135	108	17	,	,	PUNCT
ejpam-6135	108	18	d	d	PROPN
ejpam-6135	108	19	∈	∈	PROPN
ejpam-6135	108	20	i1	i1	PROPN
ejpam-6135	108	21	with	with	ADP
ejpam-6135	108	22	c	c	PROPN
ejpam-6135	108	23	+	+	CCONJ
ejpam-6135	108	24	d	d	PROPN
ejpam-6135	108	25	≤	≤	ADJ
ejpam-6135	108	26	1}.hence	1}.hence	NUM
ejpam-6135	108	27	,	,	PUNCT
ejpam-6135	108	28	a	a	DET
ejpam-6135	108	29	pair	pair	NOUN
ejpam-6135	108	30	(	(	PUNCT
ejpam-6135	108	31	x	x	X
ejpam-6135	108	32	,	,	PUNCT
ejpam-6135	108	33	τυ	τυ	NUM
ejpam-6135	108	34	)	)	PUNCT
ejpam-6135	108	35	is	be	AUX
ejpam-6135	108	36	called	call	VERB
ejpam-6135	108	37	if	if	SCONJ
ejpam-6135	108	38	−q	−q	ADJ
ejpam-6135	108	39	uniform	uniform	ADJ
ejpam-6135	108	40	topological	topological	ADJ
ejpam-6135	108	41	space	space	NOUN
ejpam-6135	108	42	.	.	PUNCT
ejpam-6135	109	1	the	the	DET
ejpam-6135	109	2	elements	element	NOUN
ejpam-6135	109	3	of	of	ADP
ejpam-6135	109	4	(	(	PUNCT
ejpam-6135	109	5	x	x	NOUN
ejpam-6135	109	6	,	,	PUNCT
ejpam-6135	109	7	τυ	τυ	NUM
ejpam-6135	109	8	)	)	PUNCT
ejpam-6135	109	9	is	be	AUX
ejpam-6135	109	10	called	call	VERB
ejpam-6135	109	11	(	(	PUNCT
ejpam-6135	109	12	c	c	X
ejpam-6135	109	13	,	,	PUNCT
ejpam-6135	109	14	d	d	NOUN
ejpam-6135	109	15	)	)	PUNCT
ejpam-6135	109	16	if	if	SCONJ
ejpam-6135	109	17	−q	−q	ADJ
ejpam-6135	109	18	uniform	uniform	ADJ
ejpam-6135	109	19	open	open	ADJ
ejpam-6135	109	20	sets	set	NOUN
ejpam-6135	109	21	and	and	CCONJ
ejpam-6135	109	22	its	its	PRON
ejpam-6135	109	23	complement	complement	NOUN
ejpam-6135	109	24	is	be	AUX
ejpam-6135	109	25	(	(	PUNCT
ejpam-6135	109	26	c	c	X
ejpam-6135	109	27	,	,	PUNCT
ejpam-6135	109	28	d	d	NOUN
ejpam-6135	109	29	)	)	PUNCT
ejpam-6135	109	30	if	if	SCONJ
ejpam-6135	109	31	−q	−q	ADJ
ejpam-6135	109	32	uniform	uniform	NOUN
ejpam-6135	109	33	closed	close	VERB
ejpam-6135	109	34	sets	set	NOUN
ejpam-6135	109	35	.	.	PUNCT
ejpam-6135	110	1	example	example	NOUN
ejpam-6135	110	2	1	1	NUM
ejpam-6135	110	3	.	.	X
ejpam-6135	111	1	assume	assume	VERB
ejpam-6135	111	2	x	x	X
ejpam-6135	111	3	=	=	PRON
ejpam-6135	111	4	{	{	PUNCT
ejpam-6135	111	5	w	w	PROPN
ejpam-6135	111	6	,	,	PUNCT
ejpam-6135	111	7	y	y	PROPN
ejpam-6135	111	8	}	}	PUNCT
ejpam-6135	111	9	.	.	PUNCT
ejpam-6135	112	1	a	a	DET
ejpam-6135	112	2	=	=	PUNCT
ejpam-6135	112	3	〈	〈	NOUN
ejpam-6135	112	4	x	x	NOUN
ejpam-6135	112	5	,	,	PUNCT
ejpam-6135	112	6	(	(	PUNCT
ejpam-6135	112	7	w	w	NOUN
ejpam-6135	112	8	0.3	0.3	NUM
ejpam-6135	112	9	,	,	PUNCT
ejpam-6135	112	10	y	y	PROPN
ejpam-6135	112	11	0.5	0.5	NUM
ejpam-6135	112	12	)	)	PUNCT
ejpam-6135	112	13	,	,	PUNCT
ejpam-6135	112	14	(	(	PUNCT
ejpam-6135	112	15	w	w	ADP
ejpam-6135	112	16	0.4	0.4	NUM
ejpam-6135	112	17	,	,	PUNCT
ejpam-6135	112	18	y	y	PROPN
ejpam-6135	112	19	0.1	0.1	NUM
ejpam-6135	112	20	)	)	PUNCT
ejpam-6135	112	21	〉	〉	NOUN
ejpam-6135	112	22	,	,	PUNCT
ejpam-6135	112	23	b	b	NOUN
ejpam-6135	112	24	=	=	SYM
ejpam-6135	112	25	〈	〈	PROPN
ejpam-6135	112	26	x	x	NOUN
ejpam-6135	112	27	,	,	PUNCT
ejpam-6135	112	28	(	(	PUNCT
ejpam-6135	112	29	w	w	NOUN
ejpam-6135	112	30	0.1	0.1	NUM
ejpam-6135	112	31	,	,	PUNCT
ejpam-6135	112	32	y	y	PROPN
ejpam-6135	112	33	0.2	0.2	NUM
ejpam-6135	112	34	)	)	PUNCT
ejpam-6135	112	35	,	,	PUNCT
ejpam-6135	112	36	(	(	PUNCT
ejpam-6135	112	37	w	w	PROPN
ejpam-6135	112	38	0.5	0.5	NUM
ejpam-6135	112	39	,	,	PUNCT
ejpam-6135	112	40	y	y	PROPN
ejpam-6135	112	41	0.6	0.6	NUM
ejpam-6135	112	42	)	)	PUNCT
ejpam-6135	112	43	〉	〉	NOUN
ejpam-6135	112	44	and	and	CCONJ
ejpam-6135	112	45	c	c	NOUN
ejpam-6135	112	46	=	=	SYM
ejpam-6135	112	47	〈	〈	PROPN
ejpam-6135	112	48	x	x	NOUN
ejpam-6135	112	49	,	,	PUNCT
ejpam-6135	112	50	(	(	PUNCT
ejpam-6135	112	51	w	w	NOUN
ejpam-6135	112	52	0.3	0.3	NUM
ejpam-6135	112	53	,	,	PUNCT
ejpam-6135	112	54	y	y	PROPN
ejpam-6135	112	55	0.2	0.2	NUM
ejpam-6135	112	56	)	)	PUNCT
ejpam-6135	112	57	,	,	PUNCT
ejpam-6135	112	58	(	(	PUNCT
ejpam-6135	112	59	w	w	ADP
ejpam-6135	112	60	0.4	0.4	NUM
ejpam-6135	112	61	,	,	PUNCT
ejpam-6135	112	62	y	y	PROPN
ejpam-6135	112	63	0.3	0.3	NUM
ejpam-6135	112	64	)	)	PUNCT
ejpam-6135	112	65	〉	〉	NOUN
ejpam-6135	112	66	be	be	VERB
ejpam-6135	112	67	any	any	DET
ejpam-6135	112	68	three	three	NUM
ejpam-6135	112	69	if	if	SCONJ
ejpam-6135	112	70	sets	set	VERB
ejpam-6135	112	71	on	on	ADP
ejpam-6135	112	72	x	x	PUNCT
ejpam-6135	112	73	and	and	CCONJ
ejpam-6135	112	74	let	let	VERB
ejpam-6135	112	75	e	e	NOUN
ejpam-6135	112	76	is	be	AUX
ejpam-6135	112	77	a	a	DET
ejpam-6135	112	78	non	non	ADJ
ejpam-6135	112	79	-	-	NOUN
ejpam-6135	112	80	void	void	ADJ
ejpam-6135	112	81	if	if	SCONJ
ejpam-6135	112	82	set	set	VERB
ejpam-6135	112	83	.	.	PUNCT
ejpam-6135	113	1	s.	s.	PROPN
ejpam-6135	113	2	thirukumaran	thirukumaran	PROPN
ejpam-6135	113	3	,	,	PUNCT
ejpam-6135	113	4	g.	g.	PROPN
ejpam-6135	113	5	k.	k.	PROPN
ejpam-6135	113	6	revathi	revathi	PROPN
ejpam-6135	113	7	/	/	SYM
ejpam-6135	113	8	eur	eur	PROPN
ejpam-6135	113	9	.	.	PUNCT
ejpam-6135	114	1	j.	j.	PROPN
ejpam-6135	114	2	pure	pure	PROPN
ejpam-6135	114	3	appl	appl	PROPN
ejpam-6135	114	4	.	.	PROPN
ejpam-6135	114	5	math	math	PROPN
ejpam-6135	114	6	,	,	PUNCT
ejpam-6135	114	7	18	18	NUM
ejpam-6135	114	8	(	(	PUNCT
ejpam-6135	114	9	2	2	NUM
ejpam-6135	114	10	)	)	PUNCT
ejpam-6135	114	11	(	(	PUNCT
ejpam-6135	114	12	2025	2025	NUM
ejpam-6135	114	13	)	)	PUNCT
ejpam-6135	114	14	,	,	PUNCT
ejpam-6135	114	15	6135	6135	NUM
ejpam-6135	114	16	6	6	NUM
ejpam-6135	114	17	of	of	ADP
ejpam-6135	114	18	17	17	NUM
ejpam-6135	114	19	let	let	VERB
ejpam-6135	114	20	ξx	ξx	NOUN
ejpam-6135	114	21	:	:	PUNCT
ejpam-6135	114	22	if	if	SCONJ
ejpam-6135	114	23	(	(	PUNCT
ejpam-6135	114	24	x	x	X
ejpam-6135	114	25	)	)	PUNCT
ejpam-6135	114	26	→	→	SYM
ejpam-6135	114	27	if	if	SCONJ
ejpam-6135	114	28	(	(	PUNCT
ejpam-6135	114	29	x	x	X
ejpam-6135	114	30	)	)	PUNCT
ejpam-6135	114	31	be	be	AUX
ejpam-6135	114	32	an	an	DET
ejpam-6135	114	33	if	if	SCONJ
ejpam-6135	114	34	mapping	mapping	NOUN
ejpam-6135	114	35	.	.	PUNCT
ejpam-6135	115	1	let	let	VERB
ejpam-6135	115	2	g1	g1	PROPN
ejpam-6135	115	3	,	,	PUNCT
ejpam-6135	115	4	g2	g2	PROPN
ejpam-6135	115	5	,	,	PUNCT
ejpam-6135	115	6	g3	g3	NOUN
ejpam-6135	115	7	and	and	CCONJ
ejpam-6135	115	8	g4	g4	PROPN
ejpam-6135	115	9	∈	∈	PROPN
ejpam-6135	115	10	ξx	ξx	NOUN
ejpam-6135	115	11	be	be	AUX
ejpam-6135	115	12	defined	define	VERB
ejpam-6135	115	13	as	as	ADP
ejpam-6135	115	14	:	:	PUNCT
ejpam-6135	115	15	g1(e	g1(e	PROPN
ejpam-6135	115	16	)	)	PUNCT
ejpam-6135	115	17	=	=	NOUN
ejpam-6135	116	1	{	{	PUNCT
ejpam-6135	116	2	0∼	0∼	ADP
ejpam-6135	116	3	,	,	PUNCT
ejpam-6135	116	4	ife	ife	PROPN
ejpam-6135	116	5	=	=	PUNCT
ejpam-6135	116	6	0∼	0∼	NUM
ejpam-6135	116	7	1∼	1∼	NUM
ejpam-6135	116	8	,	,	PUNCT
ejpam-6135	116	9	otherwise	otherwise	ADV
ejpam-6135	116	10	g2(e	g2(e	PROPN
ejpam-6135	116	11	)	)	PUNCT
ejpam-6135	116	12	=	=	SYM
ejpam-6135	117	1			NOUN
ejpam-6135	117	2	0∼	0∼	ADP
ejpam-6135	117	3	,	,	PUNCT
ejpam-6135	117	4	ife	ife	PROPN
ejpam-6135	117	5	=	=	PUNCT
ejpam-6135	117	6	0∼	0∼	NUM
ejpam-6135	117	7	a	a	X
ejpam-6135	117	8	,	,	PUNCT
ejpam-6135	117	9	ife	ife	PROPN
ejpam-6135	117	10	⊆	⊆	NUM
ejpam-6135	117	11	a	a	DET
ejpam-6135	117	12	1∼	1∼	NUM
ejpam-6135	117	13	,	,	PUNCT
ejpam-6135	117	14	otherwise	otherwise	ADV
ejpam-6135	117	15	.	.	PUNCT
ejpam-6135	118	1	g3(e	g3(e	NUM
ejpam-6135	118	2	)	)	PUNCT
ejpam-6135	119	1	=	=	SYM
ejpam-6135	119	2			PRON
ejpam-6135	119	3	0∼	0∼	ADP
ejpam-6135	119	4	,	,	PUNCT
ejpam-6135	119	5	ife	ife	PROPN
ejpam-6135	119	6	=	=	PUNCT
ejpam-6135	119	7	0∼	0∼	NUM
ejpam-6135	119	8	b	b	NOUN
ejpam-6135	119	9	,	,	PUNCT
ejpam-6135	119	10	ife	ife	PROPN
ejpam-6135	119	11	⊆	⊆	NUM
ejpam-6135	119	12	b	b	PROPN
ejpam-6135	119	13	1∼	1∼	NUM
ejpam-6135	119	14	,	,	PUNCT
ejpam-6135	119	15	otherwise	otherwise	ADV
ejpam-6135	119	16	.	.	PUNCT
ejpam-6135	120	1	g4(e	g4(e	X
ejpam-6135	120	2	)	)	PUNCT
ejpam-6135	121	1	=	=	SYM
ejpam-6135	121	2			NOUN
ejpam-6135	121	3	0∼	0∼	ADP
ejpam-6135	121	4	,	,	PUNCT
ejpam-6135	121	5	ife	ife	PROPN
ejpam-6135	121	6	=	=	PUNCT
ejpam-6135	121	7	0∼	0∼	NUM
ejpam-6135	121	8	c	c	X
ejpam-6135	121	9	,	,	PUNCT
ejpam-6135	121	10	ife	ife	PROPN
ejpam-6135	121	11	⊆	⊆	NUM
ejpam-6135	121	12	c	c	NOUN
ejpam-6135	121	13	1∼	1∼	NUM
ejpam-6135	121	14	,	,	PUNCT
ejpam-6135	121	15	otherwise	otherwise	ADV
ejpam-6135	121	16	.	.	PUNCT
ejpam-6135	122	1	υ(g	υ(g	NOUN
ejpam-6135	122	2	)	)	PUNCT
ejpam-6135	122	3	=	=	SYM
ejpam-6135	122	4			X
ejpam-6135	122	5	(	(	PUNCT
ejpam-6135	122	6	1	1	NUM
ejpam-6135	122	7	,	,	PUNCT
ejpam-6135	122	8	0	0	NUM
ejpam-6135	122	9	)	)	PUNCT
ejpam-6135	122	10	,	,	PUNCT
ejpam-6135	122	11	ifg	ifg	PROPN
ejpam-6135	122	12	=	=	PUNCT
ejpam-6135	122	13	g1	g1	PROPN
ejpam-6135	122	14	(	(	PUNCT
ejpam-6135	122	15	2/7	2/7	NUM
ejpam-6135	122	16	,	,	PUNCT
ejpam-6135	122	17	5/8	5/8	NUM
ejpam-6135	122	18	)	)	PUNCT
ejpam-6135	122	19	,	,	PUNCT
ejpam-6135	122	20	ifg	ifg	VERB
ejpam-6135	122	21	=	=	PUNCT
ejpam-6135	122	22	g2	g2	PROPN
ejpam-6135	122	23	(	(	PUNCT
ejpam-6135	122	24	3/6	3/6	NUM
ejpam-6135	122	25	,	,	PUNCT
ejpam-6135	122	26	1/5	1/5	NUM
ejpam-6135	122	27	)	)	PUNCT
ejpam-6135	122	28	,	,	PUNCT
ejpam-6135	122	29	ifg	ifg	PROPN
ejpam-6135	122	30	=	=	PROPN
ejpam-6135	122	31	g3	g3	PROPN
ejpam-6135	122	32	(	(	PUNCT
ejpam-6135	122	33	5/9	5/9	NUM
ejpam-6135	122	34	,	,	PUNCT
ejpam-6135	122	35	9/11	9/11	NUM
ejpam-6135	122	36	)	)	PUNCT
ejpam-6135	122	37	,	,	PUNCT
ejpam-6135	122	38	ifg	ifg	VERB
ejpam-6135	122	39	=	=	PUNCT
ejpam-6135	122	40	g4	g4	NOUN
ejpam-6135	122	41	(	(	PUNCT
ejpam-6135	122	42	4/7	4/7	NUM
ejpam-6135	122	43	,	,	PUNCT
ejpam-6135	122	44	1/9	1/9	NUM
ejpam-6135	122	45	)	)	PUNCT
ejpam-6135	122	46	,	,	PUNCT
ejpam-6135	122	47	ifg	ifg	VERB
ejpam-6135	122	48	=	=	PUNCT
ejpam-6135	122	49	g2	g2	PROPN
ejpam-6135	122	50	⊓	⊓	PROPN
ejpam-6135	122	51	g3	g3	PROPN
ejpam-6135	122	52	(	(	PUNCT
ejpam-6135	122	53	5/7	5/7	NUM
ejpam-6135	122	54	,	,	PUNCT
ejpam-6135	122	55	8/9	8/9	NUM
ejpam-6135	122	56	)	)	PUNCT
ejpam-6135	122	57	,	,	PUNCT
ejpam-6135	122	58	ifg	ifg	VERB
ejpam-6135	122	59	=	=	PUNCT
ejpam-6135	122	60	g2	g2	PROPN
ejpam-6135	122	61	⊓	⊓	NOUN
ejpam-6135	122	62	g4	g4	NOUN
ejpam-6135	122	63	(	(	PUNCT
ejpam-6135	122	64	5/9	5/9	NUM
ejpam-6135	122	65	,	,	PUNCT
ejpam-6135	122	66	6/7	6/7	NUM
ejpam-6135	122	67	)	)	PUNCT
ejpam-6135	122	68	,	,	PUNCT
ejpam-6135	122	69	ifg	ifg	PROPN
ejpam-6135	122	70	=	=	SYM
ejpam-6135	122	71	g3	g3	ADJ
ejpam-6135	122	72	⊓	⊓	NOUN
ejpam-6135	122	73	g4	g4	NOUN
ejpam-6135	122	74	(	(	PUNCT
ejpam-6135	122	75	0	0	NUM
ejpam-6135	122	76	,	,	PUNCT
ejpam-6135	122	77	1	1	NUM
ejpam-6135	122	78	)	)	PUNCT
ejpam-6135	122	79	,	,	PUNCT
ejpam-6135	122	80	otherwise	otherwise	ADV
ejpam-6135	122	81	clearly	clearly	ADV
ejpam-6135	122	82	,	,	PUNCT
ejpam-6135	122	83	(	(	PUNCT
ejpam-6135	122	84	x	x	NOUN
ejpam-6135	122	85	,	,	PUNCT
ejpam-6135	122	86	υ	υ	NOUN
ejpam-6135	122	87	)	)	PUNCT
ejpam-6135	122	88	is	be	AUX
ejpam-6135	122	89	an	an	DET
ejpam-6135	122	90	if	if	SCONJ
ejpam-6135	122	91	−q	−q	ADJ
ejpam-6135	122	92	uniform	uniform	ADJ
ejpam-6135	122	93	space	space	NOUN
ejpam-6135	122	94	,	,	PUNCT
ejpam-6135	122	95	for	for	ADP
ejpam-6135	122	96	c=0.02	c=0.02	PROPN
ejpam-6135	122	97	and	and	CCONJ
ejpam-6135	122	98	d=0.05	d=0.05	NOUN
ejpam-6135	122	99	.	.	PUNCT
ejpam-6135	123	1	define	define	VERB
ejpam-6135	123	2	intuitionistic	intuitionistic	ADJ
ejpam-6135	123	3	fuzzy	fuzzy	ADJ
ejpam-6135	123	4	mapping	mapping	NOUN
ejpam-6135	123	5	,	,	PUNCT
ejpam-6135	123	6	τυ	τυ	ADP
ejpam-6135	123	7	:	:	PUNCT
ejpam-6135	123	8	if	if	SCONJ
ejpam-6135	123	9	(	(	PUNCT
ejpam-6135	123	10	x	x	X
ejpam-6135	123	11	)	)	PUNCT
ejpam-6135	123	12	→	→	PUNCT
ejpam-6135	124	1	i	i	PRON
ejpam-6135	124	2	×	×	VERB
ejpam-6135	124	3	i	i	PRON
ejpam-6135	124	4	as	as	ADP
ejpam-6135	124	5	τυ(e	τυ(e	NUM
ejpam-6135	124	6	)	)	PUNCT
ejpam-6135	124	7	=	=	VERB
ejpam-6135	124	8			X
ejpam-6135	124	9	(	(	PUNCT
ejpam-6135	124	10	0	0	NUM
ejpam-6135	124	11	,	,	PUNCT
ejpam-6135	124	12	1	1	NUM
ejpam-6135	124	13	)	)	PUNCT
ejpam-6135	124	14	,	,	PUNCT
ejpam-6135	124	15	ife	ife	PROPN
ejpam-6135	124	16	=	=	PUNCT
ejpam-6135	124	17	0∼	0∼	NUM
ejpam-6135	124	18	(	(	PUNCT
ejpam-6135	124	19	4/5	4/5	NOUN
ejpam-6135	124	20	,	,	PUNCT
ejpam-6135	124	21	2/7	2/7	NUM
ejpam-6135	124	22	)	)	PUNCT
ejpam-6135	124	23	,	,	PUNCT
ejpam-6135	124	24	ife	ife	PROPN
ejpam-6135	124	25	=	=	PUNCT
ejpam-6135	124	26	a	a	PRON
ejpam-6135	124	27	(	(	PUNCT
ejpam-6135	124	28	2/5	2/5	NUM
ejpam-6135	124	29	,	,	PUNCT
ejpam-6135	124	30	3/7	3/7	NUM
ejpam-6135	124	31	)	)	PUNCT
ejpam-6135	124	32	,	,	PUNCT
ejpam-6135	124	33	ife	ife	PROPN
ejpam-6135	124	34	=	=	SYM
ejpam-6135	124	35	b	b	PROPN
ejpam-6135	124	36	(	(	PUNCT
ejpam-6135	124	37	1/8	1/8	NUM
ejpam-6135	124	38	,	,	PUNCT
ejpam-6135	124	39	2/7	2/7	NUM
ejpam-6135	124	40	)	)	PUNCT
ejpam-6135	124	41	,	,	PUNCT
ejpam-6135	124	42	ife	ife	PROPN
ejpam-6135	124	43	=	=	PUNCT
ejpam-6135	124	44	c	c	PROPN
ejpam-6135	124	45	(	(	PUNCT
ejpam-6135	124	46	1	1	NUM
ejpam-6135	124	47	,	,	PUNCT
ejpam-6135	124	48	0	0	NUM
ejpam-6135	124	49	)	)	PUNCT
ejpam-6135	124	50	,	,	PUNCT
ejpam-6135	124	51	otherwise	otherwise	ADV
ejpam-6135	124	52	hence	hence	ADV
ejpam-6135	124	53	τυ={a	τυ={a	ADP
ejpam-6135	124	54	,	,	PUNCT
ejpam-6135	124	55	b	b	NOUN
ejpam-6135	124	56	,	,	PUNCT
ejpam-6135	124	57	c	c	NOUN
ejpam-6135	124	58	,	,	PUNCT
ejpam-6135	124	59	0∼	0∼	NOUN
ejpam-6135	124	60	,	,	PUNCT
ejpam-6135	124	61	1∼	1∼	NUM
ejpam-6135	124	62	}	}	PUNCT
ejpam-6135	124	63	.	.	PUNCT
ejpam-6135	125	1	clearly	clearly	ADV
ejpam-6135	125	2	(	(	PUNCT
ejpam-6135	125	3	x	x	X
ejpam-6135	125	4	,	,	PUNCT
ejpam-6135	125	5	τυ	τυ	NUM
ejpam-6135	125	6	)	)	PUNCT
ejpam-6135	125	7	is	be	AUX
ejpam-6135	125	8	an	an	DET
ejpam-6135	125	9	if	if	SCONJ
ejpam-6135	125	10	−q	−q	ADJ
ejpam-6135	125	11	uniform	uniform	ADJ
ejpam-6135	125	12	topological	topological	ADJ
ejpam-6135	125	13	space	space	NOUN
ejpam-6135	125	14	.	.	PUNCT
ejpam-6135	126	1	definition	definition	NOUN
ejpam-6135	126	2	7	7	NUM
ejpam-6135	126	3	.	.	PUNCT
ejpam-6135	127	1	[	[	X
ejpam-6135	127	2	17	17	NUM
ejpam-6135	127	3	]	]	PUNCT
ejpam-6135	127	4	a	a	DET
ejpam-6135	127	5	pair	pair	NOUN
ejpam-6135	127	6	(	(	PUNCT
ejpam-6135	127	7	x	x	X
ejpam-6135	127	8	,	,	PUNCT
ejpam-6135	127	9	τυ	τυ	NUM
ejpam-6135	127	10	)	)	PUNCT
ejpam-6135	127	11	be	be	AUX
ejpam-6135	127	12	an	an	DET
ejpam-6135	127	13	if	if	SCONJ
ejpam-6135	127	14	−q	−q	ADJ
ejpam-6135	127	15	uniform	uniform	ADJ
ejpam-6135	127	16	topological	topological	ADJ
ejpam-6135	127	17	space	space	NOUN
ejpam-6135	127	18	and	and	CCONJ
ejpam-6135	127	19	a	a	DET
ejpam-6135	127	20	be	be	AUX
ejpam-6135	127	21	an	an	DET
ejpam-6135	127	22	if	if	NOUN
ejpam-6135	127	23	set	set	VERB
ejpam-6135	127	24	.	.	PUNCT
ejpam-6135	128	1	the	the	DET
ejpam-6135	128	2	if	if	SCONJ
ejpam-6135	128	3	−q	−q	ADJ
ejpam-6135	128	4	uniform	uniform	ADJ
ejpam-6135	128	5	interior	interior	NOUN
ejpam-6135	128	6	of	of	ADP
ejpam-6135	128	7	a	a	PRON
ejpam-6135	128	8	is	be	AUX
ejpam-6135	128	9	then	then	ADV
ejpam-6135	128	10	described	describe	VERB
ejpam-6135	128	11	as	as	ADP
ejpam-6135	128	12	(	(	PUNCT
ejpam-6135	128	13	c	c	NOUN
ejpam-6135	128	14	,	,	PUNCT
ejpam-6135	128	15	d)ifqintυ(a)=∪{b	d)ifqintυ(a)=∪{b	NOUN
ejpam-6135	128	16	:	:	PUNCT
ejpam-6135	128	17	b	b	X
ejpam-6135	128	18	⊆	⊆	NUM
ejpam-6135	128	19	a	a	PRON
ejpam-6135	128	20	and	and	CCONJ
ejpam-6135	128	21	b	b	NOUN
ejpam-6135	128	22	is	be	AUX
ejpam-6135	128	23	a	a	DET
ejpam-6135	128	24	(	(	PUNCT
ejpam-6135	128	25	c	c	NOUN
ejpam-6135	128	26	,	,	PUNCT
ejpam-6135	128	27	d	d	NOUN
ejpam-6135	128	28	)	)	PUNCT
ejpam-6135	128	29	if	if	SCONJ
ejpam-6135	128	30	−q	−q	ADJ
ejpam-6135	128	31	uniform	uniform	NOUN
ejpam-6135	128	32	open	open	ADJ
ejpam-6135	128	33	set	set	VERB
ejpam-6135	128	34	where	where	SCONJ
ejpam-6135	128	35	c	c	PROPN
ejpam-6135	128	36	∈	∈	PROPN
ejpam-6135	128	37	i0	i0	PROPN
ejpam-6135	128	38	,	,	PUNCT
ejpam-6135	128	39	d	d	PROPN
ejpam-6135	128	40	∈	∈	PROPN
ejpam-6135	128	41	i1	i1	PROPN
ejpam-6135	128	42	,	,	PUNCT
ejpam-6135	128	43	and	and	CCONJ
ejpam-6135	128	44	c+d	c+d	PROPN
ejpam-6135	128	45	≤	≤	ADV
ejpam-6135	128	46	1	1	NUM
ejpam-6135	128	47	}	}	PUNCT
ejpam-6135	128	48	.	.	PUNCT
ejpam-6135	129	1	s.	s.	PROPN
ejpam-6135	129	2	thirukumaran	thirukumaran	PROPN
ejpam-6135	129	3	,	,	PUNCT
ejpam-6135	129	4	g.	g.	PROPN
ejpam-6135	129	5	k.	k.	PROPN
ejpam-6135	129	6	revathi	revathi	PROPN
ejpam-6135	129	7	/	/	SYM
ejpam-6135	129	8	eur	eur	PROPN
ejpam-6135	129	9	.	.	PUNCT
ejpam-6135	130	1	j.	j.	PROPN
ejpam-6135	130	2	pure	pure	PROPN
ejpam-6135	130	3	appl	appl	PROPN
ejpam-6135	130	4	.	.	PROPN
ejpam-6135	130	5	math	math	PROPN
ejpam-6135	130	6	,	,	PUNCT
ejpam-6135	130	7	18	18	NUM
ejpam-6135	130	8	(	(	PUNCT
ejpam-6135	130	9	2	2	NUM
ejpam-6135	130	10	)	)	PUNCT
ejpam-6135	130	11	(	(	PUNCT
ejpam-6135	130	12	2025	2025	NUM
ejpam-6135	130	13	)	)	PUNCT
ejpam-6135	130	14	,	,	PUNCT
ejpam-6135	130	15	6135	6135	NUM
ejpam-6135	130	16	7	7	NUM
ejpam-6135	130	17	of	of	ADP
ejpam-6135	130	18	17	17	NUM
ejpam-6135	130	19	definition	definition	NOUN
ejpam-6135	130	20	8	8	NUM
ejpam-6135	130	21	.	.	PUNCT
ejpam-6135	131	1	[	[	X
ejpam-6135	131	2	17	17	NUM
ejpam-6135	131	3	]	]	X
ejpam-6135	131	4	let	let	VERB
ejpam-6135	131	5	(	(	PUNCT
ejpam-6135	131	6	x	x	NOUN
ejpam-6135	131	7	,	,	PUNCT
ejpam-6135	131	8	τυ	τυ	NUM
ejpam-6135	131	9	)	)	PUNCT
ejpam-6135	131	10	be	be	AUX
ejpam-6135	131	11	an	an	DET
ejpam-6135	131	12	if	if	SCONJ
ejpam-6135	131	13	−q	−q	ADJ
ejpam-6135	131	14	uniform	uniform	ADJ
ejpam-6135	131	15	topological	topological	ADJ
ejpam-6135	131	16	space	space	NOUN
ejpam-6135	131	17	and	and	CCONJ
ejpam-6135	131	18	a	a	DET
ejpam-6135	131	19	be	be	AUX
ejpam-6135	131	20	a	a	DET
ejpam-6135	131	21	if	if	NOUN
ejpam-6135	131	22	set	set	VERB
ejpam-6135	131	23	.	.	PUNCT
ejpam-6135	132	1	then	then	ADV
ejpam-6135	132	2	the	the	DET
ejpam-6135	132	3	if	if	SCONJ
ejpam-6135	132	4	−q	−q	ADJ
ejpam-6135	132	5	uniform	uniform	ADJ
ejpam-6135	132	6	closure	closure	NOUN
ejpam-6135	132	7	of	of	ADP
ejpam-6135	132	8	a	a	PRON
ejpam-6135	132	9	is	be	AUX
ejpam-6135	132	10	expressed	express	VERB
ejpam-6135	132	11	as	as	ADP
ejpam-6135	132	12	(	(	PUNCT
ejpam-6135	132	13	c	c	NOUN
ejpam-6135	132	14	,	,	PUNCT
ejpam-6135	132	15	d)ifqclυ(a)=∩{b	d)ifqclυ(a)=∩{b	X
ejpam-6135	132	16	:	:	PUNCT
ejpam-6135	132	17	b	b	X
ejpam-6135	132	18	⊇	⊇	NOUN
ejpam-6135	132	19	a	a	PROPN
ejpam-6135	132	20	and	and	CCONJ
ejpam-6135	132	21	b	b	NOUN
ejpam-6135	132	22	is	be	AUX
ejpam-6135	132	23	an	an	DET
ejpam-6135	132	24	(	(	PUNCT
ejpam-6135	132	25	c	c	NOUN
ejpam-6135	132	26	,	,	PUNCT
ejpam-6135	132	27	d	d	NOUN
ejpam-6135	132	28	)	)	PUNCT
ejpam-6135	132	29	if	if	SCONJ
ejpam-6135	132	30	−q	−q	ADJ
ejpam-6135	132	31	uniform	uniform	NOUN
ejpam-6135	132	32	closed	close	VERB
ejpam-6135	132	33	set	set	VERB
ejpam-6135	132	34	where	where	SCONJ
ejpam-6135	132	35	c	c	PROPN
ejpam-6135	132	36	∈	∈	PROPN
ejpam-6135	132	37	i0	i0	PROPN
ejpam-6135	132	38	,	,	PUNCT
ejpam-6135	132	39	d	d	PROPN
ejpam-6135	132	40	∈	∈	PROPN
ejpam-6135	132	41	i1	i1	PROPN
ejpam-6135	132	42	with	with	ADP
ejpam-6135	132	43	c+d	c+d	PROPN
ejpam-6135	132	44	≤	≤	ADV
ejpam-6135	132	45	1	1	NUM
ejpam-6135	132	46	}	}	SYM
ejpam-6135	132	47	6	6	NUM
ejpam-6135	132	48	.	.	PUNCT
ejpam-6135	133	1	compactification	compactification	NOUN
ejpam-6135	133	2	in	in	ADP
ejpam-6135	133	3	(	(	PUNCT
ejpam-6135	133	4	c	c	X
ejpam-6135	133	5	,	,	PUNCT
ejpam-6135	133	6	d	d	NOUN
ejpam-6135	133	7	)	)	PUNCT
ejpam-6135	133	8	if	if	SCONJ
ejpam-6135	133	9	−q	−q	ADJ
ejpam-6135	133	10	uniform	uniform	ADJ
ejpam-6135	133	11	ir∗-structure	ir∗-structure	NOUN
ejpam-6135	133	12	space	space	NOUN
ejpam-6135	133	13	throughout	throughout	ADP
ejpam-6135	133	14	the	the	DET
ejpam-6135	133	15	article	article	NOUN
ejpam-6135	133	16	the	the	DET
ejpam-6135	133	17	word	word	NOUN
ejpam-6135	133	18	”	"	PUNCT
ejpam-6135	133	19	bounded	bound	VERB
ejpam-6135	133	20	”	"	PUNCT
ejpam-6135	133	21	is	be	AUX
ejpam-6135	133	22	represented	represent	VERB
ejpam-6135	133	23	as	as	ADP
ejpam-6135	133	24	”	"	PUNCT
ejpam-6135	133	25	bdd	bdd	PROPN
ejpam-6135	133	26	”	"	PUNCT
ejpam-6135	133	27	.	.	PUNCT
ejpam-6135	134	1	6.1	6.1	NUM
ejpam-6135	134	2	.	.	X
ejpam-6135	134	3	irreducibility	irreducibility	NOUN
ejpam-6135	134	4	and	and	CCONJ
ejpam-6135	134	5	(	(	PUNCT
ejpam-6135	134	6	c	c	X
ejpam-6135	134	7	,	,	PUNCT
ejpam-6135	134	8	d	d	NOUN
ejpam-6135	134	9	)	)	PUNCT
ejpam-6135	134	10	if	if	SCONJ
ejpam-6135	134	11	−q	−q	ADJ
ejpam-6135	134	12	uniform	uniform	ADJ
ejpam-6135	134	13	ir∗	ir∗	NOUN
ejpam-6135	134	14	centred	centre	VERB
ejpam-6135	134	15	structure	structure	NOUN
ejpam-6135	134	16	space	space	NOUN
ejpam-6135	134	17	in	in	ADP
ejpam-6135	134	18	if	if	SCONJ
ejpam-6135	134	19	−q	−q	ADJ
ejpam-6135	134	20	uniform	uniform	ADJ
ejpam-6135	134	21	topological	topological	ADJ
ejpam-6135	134	22	space	space	NOUN
ejpam-6135	134	23	definition	definition	NOUN
ejpam-6135	134	24	9	9	NUM
ejpam-6135	134	25	.	.	PUNCT
ejpam-6135	135	1	let	let	AUX
ejpam-6135	135	2	(	(	PUNCT
ejpam-6135	135	3	x	x	X
ejpam-6135	135	4	,	,	PUNCT
ejpam-6135	135	5	τυ	τυ	NOUN
ejpam-6135	135	6	)	)	PUNCT
ejpam-6135	135	7	represents	represent	VERB
ejpam-6135	135	8	an	an	DET
ejpam-6135	135	9	if	if	SCONJ
ejpam-6135	135	10	−q	−q	ADJ
ejpam-6135	135	11	uniform	uniform	ADJ
ejpam-6135	135	12	topological	topological	ADJ
ejpam-6135	135	13	space	space	NOUN
ejpam-6135	135	14	.	.	PUNCT
ejpam-6135	136	1	a	a	DET
ejpam-6135	136	2	,	,	PUNCT
ejpam-6135	136	3	b	b	NOUN
ejpam-6135	136	4	and	and	CCONJ
ejpam-6135	136	5	c	c	NOUN
ejpam-6135	136	6	∈	∈	PROPN
ejpam-6135	137	1	if	if	SCONJ
ejpam-6135	137	2	(	(	PUNCT
ejpam-6135	137	3	x	x	NOUN
ejpam-6135	137	4	)	)	PUNCT
ejpam-6135	137	5	.	.	PUNCT
ejpam-6135	138	1	an	an	DET
ejpam-6135	138	2	if	if	SCONJ
ejpam-6135	138	3	set	set	VERB
ejpam-6135	138	4	a	a	PRON
ejpam-6135	138	5	is	be	AUX
ejpam-6135	138	6	said	say	VERB
ejpam-6135	138	7	to	to	PART
ejpam-6135	138	8	be	be	AUX
ejpam-6135	138	9	irreducible	irreducible	ADJ
ejpam-6135	138	10	iff	iff	VERB
ejpam-6135	138	11	a	a	DET
ejpam-6135	138	12	⊆	⊆	NUM
ejpam-6135	138	13	b	b	NOUN
ejpam-6135	138	14	∪	∪	X
ejpam-6135	138	15	c	c	NOUN
ejpam-6135	138	16	,	,	PUNCT
ejpam-6135	138	17	such	such	ADJ
ejpam-6135	138	18	that	that	SCONJ
ejpam-6135	138	19	a	a	DET
ejpam-6135	138	20	⊆	⊆	NUM
ejpam-6135	138	21	b	b	NOUN
ejpam-6135	138	22	or	or	CCONJ
ejpam-6135	138	23	a	a	DET
ejpam-6135	138	24	⊆	⊆	NUM
ejpam-6135	138	25	c	c	NOUN
ejpam-6135	138	26	with	with	ADP
ejpam-6135	138	27	b	b	PROPN
ejpam-6135	138	28	̸=	̸=	PROPN
ejpam-6135	138	29	1∼	1∼	NUM
ejpam-6135	138	30	and	and	CCONJ
ejpam-6135	138	31	c	c	PROPN
ejpam-6135	138	32	̸=	̸=	PROPN
ejpam-6135	138	33	1∼	1∼	NUM
ejpam-6135	138	34	definition	definition	NOUN
ejpam-6135	138	35	10	10	NUM
ejpam-6135	138	36	.	.	PUNCT
ejpam-6135	139	1	a	a	DET
ejpam-6135	139	2	pair	pair	NOUN
ejpam-6135	139	3	(	(	PUNCT
ejpam-6135	139	4	x	x	NOUN
ejpam-6135	139	5	,	,	PUNCT
ejpam-6135	139	6	τυ	τυ	NUM
ejpam-6135	139	7	)	)	PUNCT
ejpam-6135	139	8	be	be	AUX
ejpam-6135	139	9	if	if	SCONJ
ejpam-6135	139	10	−q	−q	ADJ
ejpam-6135	139	11	uniform	uniform	ADJ
ejpam-6135	139	12	topological	topological	ADJ
ejpam-6135	139	13	space	space	NOUN
ejpam-6135	139	14	and	and	CCONJ
ejpam-6135	139	15	a	a	DET
ejpam-6135	139	16	,	,	PUNCT
ejpam-6135	139	17	b	b	NOUN
ejpam-6135	139	18	,	,	PUNCT
ejpam-6135	139	19	c	c	X
ejpam-6135	139	20	be	be	AUX
ejpam-6135	139	21	any	any	DET
ejpam-6135	139	22	(	(	PUNCT
ejpam-6135	139	23	c	c	NOUN
ejpam-6135	139	24	,	,	PUNCT
ejpam-6135	139	25	d	d	NOUN
ejpam-6135	139	26	)	)	PUNCT
ejpam-6135	139	27	if	if	SCONJ
ejpam-6135	139	28	−q	−q	ADJ
ejpam-6135	139	29	uniform	uniform	NOUN
ejpam-6135	139	30	open	open	ADJ
ejpam-6135	139	31	sets	set	NOUN
ejpam-6135	139	32	is	be	AUX
ejpam-6135	139	33	said	say	VERB
ejpam-6135	139	34	be	be	AUX
ejpam-6135	139	35	to	to	ADP
ejpam-6135	139	36	irreducible	irreducible	ADJ
ejpam-6135	139	37	,	,	PUNCT
ejpam-6135	139	38	iff	iff	VERB
ejpam-6135	139	39	a	a	DET
ejpam-6135	139	40	⊆	⊆	NUM
ejpam-6135	139	41	b	b	NOUN
ejpam-6135	139	42	∪	∪	NOUN
ejpam-6135	139	43	c	c	NOUN
ejpam-6135	139	44	such	such	ADJ
ejpam-6135	139	45	that	that	SCONJ
ejpam-6135	139	46	a	a	DET
ejpam-6135	139	47	⊆	⊆	NUM
ejpam-6135	139	48	b	b	NOUN
ejpam-6135	139	49	or	or	CCONJ
ejpam-6135	139	50	a	a	DET
ejpam-6135	139	51	⊆	⊆	NUM
ejpam-6135	139	52	c.	c.	NOUN
ejpam-6135	139	53	then	then	ADV
ejpam-6135	139	54	a	a	PRON
ejpam-6135	139	55	is	be	AUX
ejpam-6135	139	56	said	say	VERB
ejpam-6135	139	57	to	to	PART
ejpam-6135	139	58	be	be	AUX
ejpam-6135	139	59	(	(	PUNCT
ejpam-6135	139	60	c	c	X
ejpam-6135	139	61	,	,	PUNCT
ejpam-6135	139	62	d	d	NOUN
ejpam-6135	139	63	)	)	PUNCT
ejpam-6135	139	64	if	if	SCONJ
ejpam-6135	139	65	−q	−q	ADJ
ejpam-6135	139	66	uniform	uniform	NOUN
ejpam-6135	139	67	irreducible	irreducible	ADJ
ejpam-6135	139	68	open	open	ADJ
ejpam-6135	139	69	set	set	NOUN
ejpam-6135	139	70	.	.	PUNCT
ejpam-6135	140	1	the	the	DET
ejpam-6135	140	2	complement	complement	NOUN
ejpam-6135	140	3	of	of	ADP
ejpam-6135	140	4	(	(	PUNCT
ejpam-6135	140	5	c	c	X
ejpam-6135	140	6	,	,	PUNCT
ejpam-6135	140	7	d	d	NOUN
ejpam-6135	140	8	)	)	PUNCT
ejpam-6135	140	9	if	if	SCONJ
ejpam-6135	140	10	−q	−q	ADJ
ejpam-6135	140	11	uniform	uniform	NOUN
ejpam-6135	140	12	irreducible	irreducible	ADJ
ejpam-6135	140	13	open	open	ADJ
ejpam-6135	140	14	sets	set	NOUN
ejpam-6135	140	15	is	be	AUX
ejpam-6135	140	16	said	say	VERB
ejpam-6135	140	17	to	to	PART
ejpam-6135	140	18	be	be	AUX
ejpam-6135	140	19	(	(	PUNCT
ejpam-6135	140	20	c	c	X
ejpam-6135	140	21	,	,	PUNCT
ejpam-6135	140	22	d	d	NOUN
ejpam-6135	140	23	)	)	PUNCT
ejpam-6135	140	24	if	if	SCONJ
ejpam-6135	140	25	−q	−q	ADJ
ejpam-6135	140	26	uniform	uniform	NOUN
ejpam-6135	140	27	irreducible	irreducible	ADJ
ejpam-6135	140	28	closed	close	VERB
ejpam-6135	140	29	set	set	NOUN
ejpam-6135	140	30	.	.	PUNCT
ejpam-6135	141	1	example	example	NOUN
ejpam-6135	142	1	2	2	NUM
ejpam-6135	142	2	.	.	PUNCT
ejpam-6135	142	3	let	let	VERB
ejpam-6135	142	4	x	x	PUNCT
ejpam-6135	142	5	=	=	PRON
ejpam-6135	142	6	{	{	PUNCT
ejpam-6135	142	7	g	g	PROPN
ejpam-6135	142	8	,	,	PUNCT
ejpam-6135	142	9	h	h	NOUN
ejpam-6135	142	10	}	}	PUNCT
ejpam-6135	142	11	be	be	AUX
ejpam-6135	142	12	a	a	DET
ejpam-6135	142	13	non	non	X
ejpam-6135	142	14	empty	empty	ADJ
ejpam-6135	142	15	set	set	NOUN
ejpam-6135	142	16	,	,	PUNCT
ejpam-6135	142	17	a	a	DET
ejpam-6135	142	18	=	=	X
ejpam-6135	142	19	〈	〈	NOUN
ejpam-6135	142	20	x	x	NOUN
ejpam-6135	142	21	,	,	PUNCT
ejpam-6135	142	22	(	(	PUNCT
ejpam-6135	142	23	g	g	PROPN
ejpam-6135	142	24	0.1	0.1	NUM
ejpam-6135	142	25	,	,	PUNCT
ejpam-6135	142	26	h	h	NOUN
ejpam-6135	142	27	0.2	0.2	NUM
ejpam-6135	142	28	)	)	PUNCT
ejpam-6135	142	29	,	,	PUNCT
ejpam-6135	142	30	(	(	PUNCT
ejpam-6135	142	31	g	g	PROPN
ejpam-6135	142	32	0.3	0.3	NUM
ejpam-6135	142	33	,	,	PUNCT
ejpam-6135	142	34	h	h	NOUN
ejpam-6135	142	35	0.5	0.5	NUM
ejpam-6135	142	36	)	)	PUNCT
ejpam-6135	142	37	〉	〉	NOUN
ejpam-6135	142	38	b	b	NOUN
ejpam-6135	142	39	=	=	SYM
ejpam-6135	142	40	〈	〈	PROPN
ejpam-6135	142	41	x	x	NOUN
ejpam-6135	142	42	,	,	PUNCT
ejpam-6135	142	43	(	(	PUNCT
ejpam-6135	142	44	g	g	PROPN
ejpam-6135	142	45	0.2	0.2	NUM
ejpam-6135	142	46	,	,	PUNCT
ejpam-6135	142	47	h	h	NOUN
ejpam-6135	142	48	0.3	0.3	NUM
ejpam-6135	142	49	)	)	PUNCT
ejpam-6135	142	50	,	,	PUNCT
ejpam-6135	142	51	(	(	PUNCT
ejpam-6135	142	52	g	g	NOUN
ejpam-6135	142	53	0.2	0.2	NUM
ejpam-6135	142	54	,	,	PUNCT
ejpam-6135	142	55	h	h	NOUN
ejpam-6135	142	56	0.2	0.2	NUM
ejpam-6135	142	57	)	)	PUNCT
ejpam-6135	142	58	〉	〉	NOUN
ejpam-6135	142	59	,	,	PUNCT
ejpam-6135	142	60	c	c	NOUN
ejpam-6135	142	61	=	=	SYM
ejpam-6135	142	62	〈	〈	PROPN
ejpam-6135	142	63	x	x	NOUN
ejpam-6135	142	64	,	,	PUNCT
ejpam-6135	142	65	(	(	PUNCT
ejpam-6135	142	66	g	g	PROPN
ejpam-6135	142	67	0.4	0.4	NUM
ejpam-6135	142	68	,	,	PUNCT
ejpam-6135	142	69	h	h	PROPN
ejpam-6135	142	70	0.4	0.4	NUM
ejpam-6135	142	71	)	)	PUNCT
ejpam-6135	142	72	,	,	PUNCT
ejpam-6135	142	73	(	(	PUNCT
ejpam-6135	142	74	h	h	NOUN
ejpam-6135	142	75	0.1	0.1	NUM
ejpam-6135	142	76	,	,	PUNCT
ejpam-6135	142	77	h	h	NOUN
ejpam-6135	142	78	0.1	0.1	NUM
ejpam-6135	142	79	)	)	PUNCT
ejpam-6135	142	80	〉	〉	NOUN
ejpam-6135	142	81	and	and	CCONJ
ejpam-6135	142	82	d	d	NOUN
ejpam-6135	142	83	=	=	SYM
ejpam-6135	142	84	〈	〈	PROPN
ejpam-6135	142	85	x	x	NOUN
ejpam-6135	142	86	,	,	PUNCT
ejpam-6135	142	87	(	(	PUNCT
ejpam-6135	142	88	g	g	PROPN
ejpam-6135	142	89	0.8	0.8	NUM
ejpam-6135	142	90	,	,	PUNCT
ejpam-6135	142	91	h	h	NOUN
ejpam-6135	142	92	0.1	0.1	NUM
ejpam-6135	142	93	)	)	PUNCT
ejpam-6135	142	94	,	,	PUNCT
ejpam-6135	142	95	(	(	PUNCT
ejpam-6135	142	96	g	g	PROPN
ejpam-6135	142	97	0.03	0.03	NUM
ejpam-6135	142	98	,	,	PUNCT
ejpam-6135	142	99	h	h	NOUN
ejpam-6135	142	100	0.01	0.01	NUM
ejpam-6135	142	101	)	)	PUNCT
ejpam-6135	142	102	〉	〉	NOUN
ejpam-6135	142	103	be	be	VERB
ejpam-6135	142	104	any	any	DET
ejpam-6135	142	105	four	four	NUM
ejpam-6135	142	106	if	if	SCONJ
ejpam-6135	142	107	sets	set	VERB
ejpam-6135	142	108	on	on	ADP
ejpam-6135	142	109	x	x	PUNCT
ejpam-6135	142	110	and	and	CCONJ
ejpam-6135	142	111	let	let	VERB
ejpam-6135	142	112	e	e	NOUN
ejpam-6135	142	113	is	be	AUX
ejpam-6135	142	114	a	a	DET
ejpam-6135	142	115	non	non	ADJ
ejpam-6135	142	116	-	-	ADJ
ejpam-6135	142	117	empty	empty	ADJ
ejpam-6135	142	118	if	if	SCONJ
ejpam-6135	142	119	set	set	VERB
ejpam-6135	142	120	on	on	ADP
ejpam-6135	142	121	x.	x.	NOUN
ejpam-6135	142	122	consider	consider	VERB
ejpam-6135	142	123	the	the	DET
ejpam-6135	142	124	if	if	SCONJ
ejpam-6135	142	125	mapping	mapping	NOUN
ejpam-6135	142	126	,	,	PUNCT
ejpam-6135	142	127	ξx	ξx	NOUN
ejpam-6135	142	128	:	:	PUNCT
ejpam-6135	142	129	if	if	SCONJ
ejpam-6135	142	130	(	(	PUNCT
ejpam-6135	142	131	x	x	X
ejpam-6135	142	132	)	)	PUNCT
ejpam-6135	142	133	→	→	SYM
ejpam-6135	142	134	if	if	SCONJ
ejpam-6135	142	135	(	(	PUNCT
ejpam-6135	142	136	x	x	NOUN
ejpam-6135	142	137	)	)	PUNCT
ejpam-6135	142	138	g1	g1	NOUN
ejpam-6135	142	139	,	,	PUNCT
ejpam-6135	142	140	g2	g2	PROPN
ejpam-6135	142	141	,	,	PUNCT
ejpam-6135	142	142	g3	g3	NOUN
ejpam-6135	142	143	,	,	PUNCT
ejpam-6135	142	144	g4	g4	NOUN
ejpam-6135	142	145	and	and	CCONJ
ejpam-6135	142	146	g5	g5	PROPN
ejpam-6135	142	147	∈	∈	PROPN
ejpam-6135	142	148	ξx	ξx	NOUN
ejpam-6135	142	149	be	be	AUX
ejpam-6135	142	150	defined	define	VERB
ejpam-6135	142	151	as	as	ADP
ejpam-6135	142	152	:	:	PUNCT
ejpam-6135	142	153	g1(e	g1(e	PROPN
ejpam-6135	142	154	)	)	PUNCT
ejpam-6135	142	155	=	=	NOUN
ejpam-6135	142	156	{	{	PUNCT
ejpam-6135	142	157	0∼	0∼	ADP
ejpam-6135	142	158	,	,	PUNCT
ejpam-6135	142	159	ife	ife	PROPN
ejpam-6135	142	160	=	=	PUNCT
ejpam-6135	142	161	0∼	0∼	NUM
ejpam-6135	142	162	1∼	1∼	NUM
ejpam-6135	142	163	,	,	PUNCT
ejpam-6135	142	164	otherwise	otherwise	ADV
ejpam-6135	142	165	.	.	PUNCT
ejpam-6135	143	1	g2(e	g2(e	X
ejpam-6135	143	2	)	)	PUNCT
ejpam-6135	144	1	=	=	SYM
ejpam-6135	144	2			NOUN
ejpam-6135	144	3	0∼	0∼	ADP
ejpam-6135	144	4	,	,	PUNCT
ejpam-6135	144	5	ife	ife	PROPN
ejpam-6135	144	6	=	=	PUNCT
ejpam-6135	144	7	0∼	0∼	NUM
ejpam-6135	144	8	a	a	X
ejpam-6135	144	9	,	,	PUNCT
ejpam-6135	144	10	ife	ife	PROPN
ejpam-6135	144	11	⊆	⊆	NUM
ejpam-6135	144	12	a	a	DET
ejpam-6135	144	13	1∼	1∼	NUM
ejpam-6135	144	14	,	,	PUNCT
ejpam-6135	144	15	otherwise	otherwise	ADV
ejpam-6135	144	16	.	.	PUNCT
ejpam-6135	145	1	g3(e	g3(e	NUM
ejpam-6135	145	2	)	)	PUNCT
ejpam-6135	146	1	=	=	SYM
ejpam-6135	146	2			PRON
ejpam-6135	146	3	0∼	0∼	ADP
ejpam-6135	146	4	,	,	PUNCT
ejpam-6135	146	5	ife	ife	PROPN
ejpam-6135	146	6	=	=	PUNCT
ejpam-6135	146	7	0∼	0∼	NUM
ejpam-6135	146	8	b	b	NOUN
ejpam-6135	146	9	,	,	PUNCT
ejpam-6135	146	10	ife	ife	PROPN
ejpam-6135	146	11	⊆	⊆	NUM
ejpam-6135	146	12	b	b	PROPN
ejpam-6135	146	13	1∼	1∼	NUM
ejpam-6135	146	14	,	,	PUNCT
ejpam-6135	146	15	otherwise	otherwise	ADV
ejpam-6135	146	16	.	.	PUNCT
ejpam-6135	147	1	g4(e	g4(e	X
ejpam-6135	147	2	)	)	PUNCT
ejpam-6135	148	1	=	=	SYM
ejpam-6135	148	2			NOUN
ejpam-6135	148	3	0∼	0∼	ADP
ejpam-6135	148	4	,	,	PUNCT
ejpam-6135	148	5	ife	ife	PROPN
ejpam-6135	148	6	=	=	PUNCT
ejpam-6135	148	7	0∼	0∼	NUM
ejpam-6135	148	8	c	c	X
ejpam-6135	148	9	,	,	PUNCT
ejpam-6135	148	10	ife	ife	PROPN
ejpam-6135	148	11	⊆	⊆	NUM
ejpam-6135	148	12	c	c	NOUN
ejpam-6135	148	13	1∼	1∼	NUM
ejpam-6135	148	14	,	,	PUNCT
ejpam-6135	148	15	otherwise	otherwise	ADV
ejpam-6135	148	16	.	.	PUNCT
ejpam-6135	149	1	s.	s.	PROPN
ejpam-6135	149	2	thirukumaran	thirukumaran	PROPN
ejpam-6135	149	3	,	,	PUNCT
ejpam-6135	149	4	g.	g.	PROPN
ejpam-6135	149	5	k.	k.	PROPN
ejpam-6135	149	6	revathi	revathi	PROPN
ejpam-6135	149	7	/	/	SYM
ejpam-6135	149	8	eur	eur	PROPN
ejpam-6135	149	9	.	.	PUNCT
ejpam-6135	150	1	j.	j.	PROPN
ejpam-6135	150	2	pure	pure	PROPN
ejpam-6135	150	3	appl	appl	PROPN
ejpam-6135	150	4	.	.	PROPN
ejpam-6135	150	5	math	math	PROPN
ejpam-6135	150	6	,	,	PUNCT
ejpam-6135	150	7	18	18	NUM
ejpam-6135	150	8	(	(	PUNCT
ejpam-6135	150	9	2	2	NUM
ejpam-6135	150	10	)	)	PUNCT
ejpam-6135	150	11	(	(	PUNCT
ejpam-6135	150	12	2025	2025	NUM
ejpam-6135	150	13	)	)	PUNCT
ejpam-6135	150	14	,	,	PUNCT
ejpam-6135	150	15	6135	6135	NUM
ejpam-6135	150	16	8	8	NUM
ejpam-6135	150	17	of	of	ADP
ejpam-6135	150	18	17	17	NUM
ejpam-6135	150	19	g5(e	g5(e	NUM
ejpam-6135	150	20	)	)	PUNCT
ejpam-6135	150	21	=	=	SYM
ejpam-6135	151	1			NOUN
ejpam-6135	151	2	0∼	0∼	ADP
ejpam-6135	151	3	,	,	PUNCT
ejpam-6135	151	4	ife	ife	PROPN
ejpam-6135	151	5	=	=	PUNCT
ejpam-6135	151	6	0∼	0∼	NUM
ejpam-6135	152	1	d	d	NOUN
ejpam-6135	152	2	,	,	PUNCT
ejpam-6135	152	3	ife	ife	PROPN
ejpam-6135	152	4	⊆	⊆	NUM
ejpam-6135	152	5	d	d	PROPN
ejpam-6135	152	6	1∼	1∼	NUM
ejpam-6135	152	7	,	,	PUNCT
ejpam-6135	152	8	otherwise	otherwise	ADV
ejpam-6135	152	9	.	.	PUNCT
ejpam-6135	153	1	υ(g	υ(g	NOUN
ejpam-6135	153	2	)	)	PUNCT
ejpam-6135	153	3	=	=	SYM
ejpam-6135	153	4			NOUN
ejpam-6135	153	5	(	(	PUNCT
ejpam-6135	153	6	1	1	NUM
ejpam-6135	153	7	,	,	PUNCT
ejpam-6135	153	8	0	0	NUM
ejpam-6135	153	9	)	)	PUNCT
ejpam-6135	153	10	,	,	PUNCT
ejpam-6135	153	11	ifg	ifg	PROPN
ejpam-6135	153	12	=	=	PUNCT
ejpam-6135	153	13	g1	g1	PROPN
ejpam-6135	153	14	(	(	PUNCT
ejpam-6135	153	15	2/7	2/7	NUM
ejpam-6135	153	16	,	,	PUNCT
ejpam-6135	153	17	5/8	5/8	NUM
ejpam-6135	153	18	)	)	PUNCT
ejpam-6135	153	19	,	,	PUNCT
ejpam-6135	153	20	ifg	ifg	VERB
ejpam-6135	153	21	=	=	PUNCT
ejpam-6135	153	22	g2	g2	PROPN
ejpam-6135	153	23	(	(	PUNCT
ejpam-6135	153	24	3/6	3/6	NUM
ejpam-6135	153	25	,	,	PUNCT
ejpam-6135	153	26	1/5	1/5	NUM
ejpam-6135	153	27	)	)	PUNCT
ejpam-6135	153	28	,	,	PUNCT
ejpam-6135	153	29	ifg	ifg	PROPN
ejpam-6135	153	30	=	=	PROPN
ejpam-6135	153	31	g3	g3	PROPN
ejpam-6135	153	32	(	(	PUNCT
ejpam-6135	153	33	3/7	3/7	NUM
ejpam-6135	153	34	,	,	PUNCT
ejpam-6135	153	35	1/6	1/6	NUM
ejpam-6135	153	36	)	)	PUNCT
ejpam-6135	153	37	,	,	PUNCT
ejpam-6135	153	38	ifg	ifg	VERB
ejpam-6135	153	39	=	=	PUNCT
ejpam-6135	153	40	g4	g4	NOUN
ejpam-6135	153	41	(	(	PUNCT
ejpam-6135	153	42	3/8	3/8	NUM
ejpam-6135	153	43	,	,	PUNCT
ejpam-6135	153	44	1/8	1/8	NUM
ejpam-6135	153	45	)	)	PUNCT
ejpam-6135	153	46	,	,	PUNCT
ejpam-6135	153	47	ifg	ifg	VERB
ejpam-6135	153	48	=	=	SYM
ejpam-6135	153	49	g5	g5	PROPN
ejpam-6135	153	50	(	(	PUNCT
ejpam-6135	153	51	4/9	4/9	NUM
ejpam-6135	153	52	,	,	PUNCT
ejpam-6135	153	53	1/9	1/9	NUM
ejpam-6135	153	54	)	)	PUNCT
ejpam-6135	153	55	,	,	PUNCT
ejpam-6135	153	56	ifg	ifg	VERB
ejpam-6135	153	57	=	=	PUNCT
ejpam-6135	153	58	g2	g2	PROPN
ejpam-6135	153	59	⊓	⊓	PROPN
ejpam-6135	153	60	g3	g3	PROPN
ejpam-6135	153	61	(	(	PUNCT
ejpam-6135	153	62	5/7	5/7	NUM
ejpam-6135	153	63	,	,	PUNCT
ejpam-6135	153	64	5/9	5/9	NUM
ejpam-6135	153	65	)	)	PUNCT
ejpam-6135	153	66	,	,	PUNCT
ejpam-6135	153	67	ifg	ifg	VERB
ejpam-6135	153	68	=	=	PUNCT
ejpam-6135	153	69	g2	g2	PROPN
ejpam-6135	153	70	⊓	⊓	NOUN
ejpam-6135	153	71	g4	g4	NOUN
ejpam-6135	153	72	(	(	PUNCT
ejpam-6135	153	73	6/7	6/7	NUM
ejpam-6135	153	74	,	,	PUNCT
ejpam-6135	153	75	6/9	6/9	NUM
ejpam-6135	153	76	)	)	PUNCT
ejpam-6135	153	77	,	,	PUNCT
ejpam-6135	153	78	ifg	ifg	VERB
ejpam-6135	153	79	=	=	PUNCT
ejpam-6135	153	80	g2	g2	PROPN
ejpam-6135	153	81	⊓	⊓	PROPN
ejpam-6135	153	82	g5	g5	NOUN
ejpam-6135	153	83	(	(	PUNCT
ejpam-6135	153	84	3/7	3/7	NUM
ejpam-6135	153	85	,	,	PUNCT
ejpam-6135	153	86	8/9	8/9	NUM
ejpam-6135	153	87	)	)	PUNCT
ejpam-6135	153	88	,	,	PUNCT
ejpam-6135	153	89	ifg	ifg	PROPN
ejpam-6135	153	90	=	=	SYM
ejpam-6135	153	91	g3	g3	ADJ
ejpam-6135	153	92	⊓	⊓	NOUN
ejpam-6135	153	93	g4	g4	NOUN
ejpam-6135	153	94	(	(	PUNCT
ejpam-6135	153	95	4/9	4/9	NUM
ejpam-6135	153	96	,	,	PUNCT
ejpam-6135	153	97	1/10	1/10	NUM
ejpam-6135	153	98	)	)	PUNCT
ejpam-6135	153	99	,	,	PUNCT
ejpam-6135	153	100	ifg	ifg	PROPN
ejpam-6135	153	101	=	=	SYM
ejpam-6135	153	102	g3	g3	NOUN
ejpam-6135	153	103	⊓	⊓	PROPN
ejpam-6135	153	104	g5	g5	NOUN
ejpam-6135	153	105	(	(	PUNCT
ejpam-6135	153	106	1/6	1/6	NUM
ejpam-6135	153	107	,	,	PUNCT
ejpam-6135	153	108	4/7	4/7	NUM
ejpam-6135	153	109	)	)	PUNCT
ejpam-6135	153	110	,	,	PUNCT
ejpam-6135	153	111	ifg	ifg	VERB
ejpam-6135	153	112	=	=	SYM
ejpam-6135	153	113	g4	g4	NOUN
ejpam-6135	153	114	⊓	⊓	PROPN
ejpam-6135	153	115	g5	g5	NOUN
ejpam-6135	153	116	(	(	PUNCT
ejpam-6135	153	117	0	0	NUM
ejpam-6135	153	118	,	,	PUNCT
ejpam-6135	153	119	1	1	NUM
ejpam-6135	153	120	)	)	PUNCT
ejpam-6135	153	121	,	,	PUNCT
ejpam-6135	153	122	otherwise	otherwise	ADV
ejpam-6135	153	123	clearly	clearly	ADV
ejpam-6135	153	124	,	,	PUNCT
ejpam-6135	153	125	(	(	PUNCT
ejpam-6135	153	126	x	x	NOUN
ejpam-6135	153	127	,	,	PUNCT
ejpam-6135	153	128	υ	υ	NOUN
ejpam-6135	153	129	)	)	PUNCT
ejpam-6135	153	130	is	be	AUX
ejpam-6135	153	131	an	an	DET
ejpam-6135	153	132	if	if	SCONJ
ejpam-6135	153	133	−q	−q	ADJ
ejpam-6135	153	134	uniform	uniform	ADJ
ejpam-6135	153	135	space	space	NOUN
ejpam-6135	153	136	,	,	PUNCT
ejpam-6135	153	137	for	for	ADP
ejpam-6135	153	138	c=0.08	c=0.08	NOUN
ejpam-6135	153	139	and	and	CCONJ
ejpam-6135	153	140	d=0.03	d=0.03	NOUN
ejpam-6135	153	141	.	.	PUNCT
ejpam-6135	154	1	define	define	VERB
ejpam-6135	154	2	an	an	DET
ejpam-6135	154	3	if	if	SCONJ
ejpam-6135	154	4	mapping	mapping	NOUN
ejpam-6135	154	5	,	,	PUNCT
ejpam-6135	154	6	τυ	τυ	ADP
ejpam-6135	154	7	:	:	PUNCT
ejpam-6135	154	8	if	if	SCONJ
ejpam-6135	154	9	(	(	PUNCT
ejpam-6135	154	10	x	x	X
ejpam-6135	154	11	)	)	PUNCT
ejpam-6135	154	12	→	→	PUNCT
ejpam-6135	155	1	i	i	PRON
ejpam-6135	155	2	×	×	VERB
ejpam-6135	155	3	i	i	PRON
ejpam-6135	155	4	as	as	ADP
ejpam-6135	155	5	τυ(e	τυ(e	NUM
ejpam-6135	155	6	)	)	PUNCT
ejpam-6135	156	1	=	=	SYM
ejpam-6135	156	2			NOUN
ejpam-6135	156	3	(	(	PUNCT
ejpam-6135	156	4	0	0	NUM
ejpam-6135	156	5	,	,	PUNCT
ejpam-6135	156	6	1	1	NUM
ejpam-6135	156	7	)	)	PUNCT
ejpam-6135	156	8	,	,	PUNCT
ejpam-6135	156	9	ife	ife	PROPN
ejpam-6135	156	10	=	=	PUNCT
ejpam-6135	156	11	0∼	0∼	NUM
ejpam-6135	156	12	(	(	PUNCT
ejpam-6135	156	13	2/5	2/5	NUM
ejpam-6135	156	14	,	,	PUNCT
ejpam-6135	156	15	3/7	3/7	NUM
ejpam-6135	156	16	)	)	PUNCT
ejpam-6135	156	17	,	,	PUNCT
ejpam-6135	156	18	ife	ife	PROPN
ejpam-6135	156	19	=	=	PUNCT
ejpam-6135	156	20	a	a	DET
ejpam-6135	156	21	(	(	PUNCT
ejpam-6135	156	22	1/8	1/8	NUM
ejpam-6135	156	23	,	,	PUNCT
ejpam-6135	156	24	2/7	2/7	NUM
ejpam-6135	156	25	)	)	PUNCT
ejpam-6135	156	26	,	,	PUNCT
ejpam-6135	156	27	ife	ife	PROPN
ejpam-6135	156	28	=	=	SYM
ejpam-6135	156	29	b	b	PROPN
ejpam-6135	156	30	(	(	PUNCT
ejpam-6135	156	31	1/3	1/3	NUM
ejpam-6135	156	32	,	,	PUNCT
ejpam-6135	156	33	3/8	3/8	NUM
ejpam-6135	156	34	)	)	PUNCT
ejpam-6135	156	35	,	,	PUNCT
ejpam-6135	156	36	ife	ife	PROPN
ejpam-6135	156	37	=	=	SYM
ejpam-6135	156	38	c	c	PROPN
ejpam-6135	156	39	(	(	PUNCT
ejpam-6135	156	40	2/5	2/5	NUM
ejpam-6135	156	41	,	,	PUNCT
ejpam-6135	156	42	3/5	3/5	NUM
ejpam-6135	156	43	)	)	PUNCT
ejpam-6135	156	44	,	,	PUNCT
ejpam-6135	156	45	ife	ife	PROPN
ejpam-6135	157	1	=	=	SYM
ejpam-6135	157	2	d	d	PROPN
ejpam-6135	157	3	(	(	PUNCT
ejpam-6135	157	4	1	1	NUM
ejpam-6135	157	5	,	,	PUNCT
ejpam-6135	157	6	0	0	NUM
ejpam-6135	157	7	)	)	PUNCT
ejpam-6135	157	8	,	,	PUNCT
ejpam-6135	157	9	otherwise	otherwise	ADV
ejpam-6135	157	10	then	then	ADV
ejpam-6135	157	11	τυ={a	τυ={a	ADP
ejpam-6135	157	12	,	,	PUNCT
ejpam-6135	157	13	b	b	NOUN
ejpam-6135	157	14	,	,	PUNCT
ejpam-6135	157	15	c	c	X
ejpam-6135	157	16	,	,	PUNCT
ejpam-6135	157	17	d	d	NOUN
ejpam-6135	157	18	,	,	PUNCT
ejpam-6135	157	19	0∼	0∼	NUM
ejpam-6135	157	20	,	,	PUNCT
ejpam-6135	157	21	1∼	1∼	NUM
ejpam-6135	157	22	}	}	PUNCT
ejpam-6135	157	23	be	be	AUX
ejpam-6135	157	24	an	an	DET
ejpam-6135	157	25	if	if	SCONJ
ejpam-6135	157	26	−q	−q	ADJ
ejpam-6135	157	27	uniform	uniform	ADJ
ejpam-6135	157	28	topological	topological	ADJ
ejpam-6135	157	29	space	space	NOUN
ejpam-6135	157	30	.	.	PUNCT
ejpam-6135	158	1	the	the	DET
ejpam-6135	158	2	elements	element	NOUN
ejpam-6135	158	3	of	of	ADP
ejpam-6135	158	4	τυ	τυ	PROPN
ejpam-6135	158	5	are	be	AUX
ejpam-6135	158	6	called	call	VERB
ejpam-6135	158	7	(	(	PUNCT
ejpam-6135	158	8	c	c	X
ejpam-6135	158	9	,	,	PUNCT
ejpam-6135	158	10	d	d	NOUN
ejpam-6135	158	11	)	)	PUNCT
ejpam-6135	158	12	if	if	SCONJ
ejpam-6135	158	13	−q	−q	ADJ
ejpam-6135	158	14	uniform	uniform	ADJ
ejpam-6135	158	15	open	open	ADJ
ejpam-6135	158	16	sets	set	NOUN
ejpam-6135	158	17	and	and	CCONJ
ejpam-6135	158	18	the	the	DET
ejpam-6135	158	19	complements	complement	NOUN
ejpam-6135	158	20	are	be	AUX
ejpam-6135	158	21	(	(	PUNCT
ejpam-6135	158	22	c	c	X
ejpam-6135	158	23	,	,	PUNCT
ejpam-6135	158	24	d	d	NOUN
ejpam-6135	158	25	)	)	PUNCT
ejpam-6135	158	26	if	if	SCONJ
ejpam-6135	158	27	−q	−q	ADJ
ejpam-6135	158	28	uniform	uniform	NOUN
ejpam-6135	158	29	closed	close	VERB
ejpam-6135	158	30	sets	set	NOUN
ejpam-6135	158	31	.	.	PUNCT
ejpam-6135	159	1	clearly	clearly	ADV
ejpam-6135	159	2	(	(	PUNCT
ejpam-6135	159	3	x	x	X
ejpam-6135	159	4	,	,	PUNCT
ejpam-6135	159	5	τυ	τυ	NUM
ejpam-6135	159	6	)	)	PUNCT
ejpam-6135	159	7	is	be	AUX
ejpam-6135	159	8	an	an	DET
ejpam-6135	159	9	if	if	SCONJ
ejpam-6135	159	10	−q	−q	ADJ
ejpam-6135	159	11	uniform	uniform	ADJ
ejpam-6135	159	12	topological	topological	ADJ
ejpam-6135	159	13	space	space	NOUN
ejpam-6135	159	14	.	.	PUNCT
ejpam-6135	160	1	let	let	VERB
ejpam-6135	160	2	a	a	DET
ejpam-6135	160	3	,	,	PUNCT
ejpam-6135	160	4	b	b	NOUN
ejpam-6135	160	5	and	and	CCONJ
ejpam-6135	160	6	c	c	PROPN
ejpam-6135	160	7	are	be	AUX
ejpam-6135	160	8	(	(	PUNCT
ejpam-6135	160	9	c	c	X
ejpam-6135	160	10	,	,	PUNCT
ejpam-6135	160	11	d	d	NOUN
ejpam-6135	160	12	)	)	PUNCT
ejpam-6135	160	13	if	if	SCONJ
ejpam-6135	160	14	−q	−q	ADJ
ejpam-6135	160	15	uniform	uniform	NOUN
ejpam-6135	160	16	irreducible	irreducible	ADJ
ejpam-6135	160	17	open	open	ADJ
ejpam-6135	160	18	sets	set	NOUN
ejpam-6135	160	19	.	.	PUNCT
ejpam-6135	161	1	from	from	ADP
ejpam-6135	161	2	the	the	DET
ejpam-6135	161	3	definition	definition	NOUN
ejpam-6135	161	4	6.2	6.2	NUM
ejpam-6135	161	5	,	,	PUNCT
ejpam-6135	161	6	the	the	DET
ejpam-6135	161	7	collection	collection	NOUN
ejpam-6135	161	8	ir=	ir=	PROPN
ejpam-6135	161	9	{	{	PUNCT
ejpam-6135	161	10	a	a	PROPN
ejpam-6135	161	11	,	,	PUNCT
ejpam-6135	161	12	b	b	NOUN
ejpam-6135	161	13	,	,	PUNCT
ejpam-6135	161	14	c	c	NOUN
ejpam-6135	161	15	,	,	PUNCT
ejpam-6135	161	16	0∼	0∼	NUM
ejpam-6135	161	17	}	}	PUNCT
ejpam-6135	161	18	are	be	AUX
ejpam-6135	161	19	(	(	PUNCT
ejpam-6135	161	20	c	c	X
ejpam-6135	161	21	,	,	PUNCT
ejpam-6135	161	22	d	d	NOUN
ejpam-6135	161	23	)	)	PUNCT
ejpam-6135	161	24	if	if	SCONJ
ejpam-6135	161	25	−q	−q	ADJ
ejpam-6135	161	26	uniform	uniform	NOUN
ejpam-6135	161	27	irreducible	irreducible	ADJ
ejpam-6135	161	28	open	open	ADJ
ejpam-6135	161	29	sets	set	NOUN
ejpam-6135	161	30	.	.	PUNCT
ejpam-6135	162	1	remark	remark	NOUN
ejpam-6135	162	2	1	1	NUM
ejpam-6135	162	3	.	.	PUNCT
ejpam-6135	163	1	from	from	ADP
ejpam-6135	163	2	the	the	DET
ejpam-6135	163	3	above	above	ADJ
ejpam-6135	163	4	example	example	NOUN
ejpam-6135	163	5	6.3	6.3	NUM
ejpam-6135	163	6	,	,	PUNCT
ejpam-6135	163	7	clearly	clearly	ADV
ejpam-6135	163	8	ir∗=	ir∗=	NOUN
ejpam-6135	163	9	ir∪{1∼	ir∪{1∼	PROPN
ejpam-6135	163	10	}	}	PUNCT
ejpam-6135	163	11	.	.	PUNCT
ejpam-6135	164	1	then	then	ADV
ejpam-6135	164	2	ir∗=	ir∗=	PROPN
ejpam-6135	164	3	{	{	PUNCT
ejpam-6135	164	4	a	a	DET
ejpam-6135	164	5	,	,	PUNCT
ejpam-6135	164	6	b	b	NOUN
ejpam-6135	164	7	,	,	PUNCT
ejpam-6135	164	8	c	c	NOUN
ejpam-6135	164	9	,	,	PUNCT
ejpam-6135	164	10	0∼}∪	0∼}∪	NOUN
ejpam-6135	164	11	1∼	1∼	NUM
ejpam-6135	164	12	is	be	AUX
ejpam-6135	164	13	said	say	VERB
ejpam-6135	164	14	to	to	PART
ejpam-6135	164	15	be	be	AUX
ejpam-6135	164	16	(	(	PUNCT
ejpam-6135	164	17	c	c	X
ejpam-6135	164	18	,	,	PUNCT
ejpam-6135	164	19	d	d	NOUN
ejpam-6135	164	20	)	)	PUNCT
ejpam-6135	164	21	if	if	SCONJ
ejpam-6135	164	22	−q	−q	ADJ
ejpam-6135	164	23	uniform	uniform	ADJ
ejpam-6135	164	24	ir∗	ir∗	PROPN
ejpam-6135	164	25	irreducible	irreducible	ADJ
ejpam-6135	164	26	open	open	ADJ
ejpam-6135	164	27	sets	set	NOUN
ejpam-6135	164	28	.	.	PUNCT
ejpam-6135	165	1	definition	definition	NOUN
ejpam-6135	165	2	11	11	NUM
ejpam-6135	165	3	.	.	PUNCT
ejpam-6135	166	1	let	let	AUX
ejpam-6135	166	2	(	(	PUNCT
ejpam-6135	166	3	x	x	X
ejpam-6135	166	4	,	,	PUNCT
ejpam-6135	166	5	τυ	τυ	NUM
ejpam-6135	166	6	)	)	PUNCT
ejpam-6135	166	7	be	be	AUX
ejpam-6135	166	8	an	an	DET
ejpam-6135	166	9	if	if	SCONJ
ejpam-6135	166	10	−q	−q	ADJ
ejpam-6135	166	11	uniform	uniform	ADJ
ejpam-6135	166	12	topological	topological	ADJ
ejpam-6135	166	13	space	space	NOUN
ejpam-6135	166	14	on	on	ADP
ejpam-6135	166	15	x.	x.	NOUN
ejpam-6135	166	16	then	then	ADV
ejpam-6135	166	17	(	(	PUNCT
ejpam-6135	166	18	x	x	X
ejpam-6135	166	19	,	,	PUNCT
ejpam-6135	166	20	τυ	τυ	NUM
ejpam-6135	166	21	)	)	PUNCT
ejpam-6135	166	22	is	be	AUX
ejpam-6135	166	23	said	say	VERB
ejpam-6135	166	24	to	to	PART
ejpam-6135	166	25	be	be	AUX
ejpam-6135	166	26	(	(	PUNCT
ejpam-6135	166	27	c	c	X
ejpam-6135	166	28	,	,	PUNCT
ejpam-6135	166	29	d	d	NOUN
ejpam-6135	166	30	)	)	PUNCT
ejpam-6135	166	31	if	if	SCONJ
ejpam-6135	166	32	−q	−q	ADJ
ejpam-6135	166	33	uniform	uniform	ADJ
ejpam-6135	166	34	ir∗	ir∗	NOUN
ejpam-6135	166	35	structure	structure	NOUN
ejpam-6135	166	36	space	space	NOUN
ejpam-6135	166	37	,	,	PUNCT
ejpam-6135	166	38	then	then	ADV
ejpam-6135	166	39	the	the	DET
ejpam-6135	166	40	corresponding	corresponding	ADJ
ejpam-6135	166	41	requirements	requirement	NOUN
ejpam-6135	166	42	are	be	AUX
ejpam-6135	166	43	to	to	PART
ejpam-6135	166	44	be	be	AUX
ejpam-6135	166	45	fulfilled	fulfil	VERB
ejpam-6135	166	46	:	:	PUNCT
ejpam-6135	166	47	(	(	PUNCT
ejpam-6135	166	48	i	i	NOUN
ejpam-6135	166	49	)	)	PUNCT
ejpam-6135	166	50	0∼	0∼	ADP
ejpam-6135	166	51	,	,	PUNCT
ejpam-6135	166	52	1∼	1∼	NUM
ejpam-6135	166	53	∈	∈	NOUN
ejpam-6135	166	54	ir∗.	ir∗.	PROPN
ejpam-6135	166	55	s.	s.	PROPN
ejpam-6135	166	56	thirukumaran	thirukumaran	PROPN
ejpam-6135	166	57	,	,	PUNCT
ejpam-6135	166	58	g.	g.	PROPN
ejpam-6135	166	59	k.	k.	PROPN
ejpam-6135	166	60	revathi	revathi	PROPN
ejpam-6135	166	61	/	/	SYM
ejpam-6135	166	62	eur	eur	PROPN
ejpam-6135	166	63	.	.	PUNCT
ejpam-6135	167	1	j.	j.	PROPN
ejpam-6135	167	2	pure	pure	PROPN
ejpam-6135	167	3	appl	appl	PROPN
ejpam-6135	167	4	.	.	PROPN
ejpam-6135	167	5	math	math	PROPN
ejpam-6135	167	6	,	,	PUNCT
ejpam-6135	167	7	18	18	NUM
ejpam-6135	167	8	(	(	PUNCT
ejpam-6135	167	9	2	2	NUM
ejpam-6135	167	10	)	)	PUNCT
ejpam-6135	167	11	(	(	PUNCT
ejpam-6135	167	12	2025	2025	NUM
ejpam-6135	167	13	)	)	PUNCT
ejpam-6135	167	14	,	,	PUNCT
ejpam-6135	167	15	6135	6135	NUM
ejpam-6135	167	16	9	9	NUM
ejpam-6135	167	17	of	of	ADP
ejpam-6135	167	18	17	17	NUM
ejpam-6135	167	19	(	(	PUNCT
ejpam-6135	167	20	ii	ii	NOUN
ejpam-6135	167	21	)	)	PUNCT
ejpam-6135	167	22	if	if	SCONJ
ejpam-6135	167	23	{	{	PUNCT
ejpam-6135	167	24	ai	ai	VERB
ejpam-6135	167	25	:	:	PUNCT
ejpam-6135	167	26	i	i	PRON
ejpam-6135	167	27	∈	∈	PROPN
ejpam-6135	168	1	i	i	PRON
ejpam-6135	168	2	,	,	PUNCT
ejpam-6135	168	3	∀ai	∀ai	PROPN
ejpam-6135	168	4	∈	∈	PROPN
ejpam-6135	168	5	ir∗	ir∗	PROPN
ejpam-6135	168	6	}	}	PUNCT
ejpam-6135	168	7	where	where	SCONJ
ejpam-6135	168	8	∪i∈i	∪i∈i	NUM
ejpam-6135	168	9	ai	ai	VERB
ejpam-6135	168	10	∈	∈	PROPN
ejpam-6135	168	11	ir∗.	ir∗.	PROPN
ejpam-6135	168	12	(	(	PUNCT
ejpam-6135	168	13	iii	iii	NOUN
ejpam-6135	168	14	)	)	PUNCT
ejpam-6135	168	15	if	if	SCONJ
ejpam-6135	168	16	a	a	DET
ejpam-6135	168	17	,	,	PUNCT
ejpam-6135	168	18	b	b	PROPN
ejpam-6135	168	19	∈	∈	PROPN
ejpam-6135	168	20	ir∗	ir∗	NOUN
ejpam-6135	168	21	,	,	PUNCT
ejpam-6135	168	22	then	then	ADV
ejpam-6135	168	23	a	a	DET
ejpam-6135	168	24	∩	∩	ADJ
ejpam-6135	168	25	b	b	X
ejpam-6135	168	26	∈	∈	NOUN
ejpam-6135	168	27	ir∗.	ir∗.	VERB
ejpam-6135	168	28	every	every	DET
ejpam-6135	168	29	member	member	NOUN
ejpam-6135	168	30	of	of	ADP
ejpam-6135	168	31	(	(	PUNCT
ejpam-6135	168	32	x	x	NOUN
ejpam-6135	168	33	,	,	PUNCT
ejpam-6135	168	34	τυ	τυ	NUM
ejpam-6135	168	35	)	)	PUNCT
ejpam-6135	168	36	is	be	AUX
ejpam-6135	168	37	said	say	VERB
ejpam-6135	168	38	to	to	PART
ejpam-6135	168	39	be	be	AUX
ejpam-6135	168	40	(	(	PUNCT
ejpam-6135	168	41	c	c	X
ejpam-6135	168	42	,	,	PUNCT
ejpam-6135	168	43	d	d	NOUN
ejpam-6135	168	44	)	)	PUNCT
ejpam-6135	168	45	if	if	SCONJ
ejpam-6135	168	46	−q	−q	ADJ
ejpam-6135	168	47	uniform	uniform	ADJ
ejpam-6135	168	48	ir∗	ir∗	NOUN
ejpam-6135	168	49	structure	structure	NOUN
ejpam-6135	168	50	space	space	NOUN
ejpam-6135	168	51	.	.	PUNCT
ejpam-6135	169	1	the	the	DET
ejpam-6135	169	2	elements	element	NOUN
ejpam-6135	169	3	of	of	ADP
ejpam-6135	169	4	(	(	PUNCT
ejpam-6135	169	5	c	c	X
ejpam-6135	169	6	,	,	PUNCT
ejpam-6135	169	7	d	d	NOUN
ejpam-6135	169	8	)	)	PUNCT
ejpam-6135	169	9	if	if	SCONJ
ejpam-6135	169	10	−q	−q	ADJ
ejpam-6135	169	11	uniform	uniform	ADJ
ejpam-6135	169	12	ir∗	ir∗	NOUN
ejpam-6135	169	13	structure	structure	NOUN
ejpam-6135	169	14	space	space	NOUN
ejpam-6135	169	15	is	be	AUX
ejpam-6135	169	16	(	(	PUNCT
ejpam-6135	169	17	c	c	X
ejpam-6135	169	18	,	,	PUNCT
ejpam-6135	169	19	d	d	NOUN
ejpam-6135	169	20	)	)	PUNCT
ejpam-6135	169	21	if	if	SCONJ
ejpam-6135	169	22	−q	−q	ADJ
ejpam-6135	169	23	uniform	uniform	ADJ
ejpam-6135	169	24	ir∗	ir∗	NOUN
ejpam-6135	169	25	structure	structure	NOUN
ejpam-6135	169	26	open	open	ADJ
ejpam-6135	169	27	sets	set	NOUN
ejpam-6135	169	28	.	.	PUNCT
ejpam-6135	170	1	the	the	DET
ejpam-6135	170	2	complements	complement	NOUN
ejpam-6135	170	3	of	of	ADP
ejpam-6135	170	4	(	(	PUNCT
ejpam-6135	170	5	c	c	X
ejpam-6135	170	6	,	,	PUNCT
ejpam-6135	170	7	d	d	NOUN
ejpam-6135	170	8	)	)	PUNCT
ejpam-6135	170	9	if	if	SCONJ
ejpam-6135	170	10	−q	−q	ADJ
ejpam-6135	170	11	uniform	uniform	ADJ
ejpam-6135	170	12	ir∗	ir∗	NOUN
ejpam-6135	170	13	structure	structure	NOUN
ejpam-6135	170	14	open	open	ADJ
ejpam-6135	170	15	set	set	NOUN
ejpam-6135	170	16	is	be	AUX
ejpam-6135	170	17	(	(	PUNCT
ejpam-6135	170	18	c	c	X
ejpam-6135	170	19	,	,	PUNCT
ejpam-6135	170	20	d	d	NOUN
ejpam-6135	170	21	)	)	PUNCT
ejpam-6135	170	22	if	if	SCONJ
ejpam-6135	170	23	−q	−q	ADJ
ejpam-6135	170	24	uniform	uniform	ADJ
ejpam-6135	170	25	ir∗	ir∗	PROPN
ejpam-6135	170	26	structure	structure	NOUN
ejpam-6135	170	27	closed	close	VERB
ejpam-6135	170	28	sets	set	NOUN
ejpam-6135	170	29	.	.	PUNCT
ejpam-6135	171	1	definition	definition	NOUN
ejpam-6135	171	2	12	12	NUM
ejpam-6135	171	3	.	.	PUNCT
ejpam-6135	172	1	let	let	AUX
ejpam-6135	172	2	(	(	PUNCT
ejpam-6135	172	3	x	x	X
ejpam-6135	172	4	,	,	PUNCT
ejpam-6135	172	5	τυ	τυ	NUM
ejpam-6135	172	6	)	)	PUNCT
ejpam-6135	172	7	be	be	AUX
ejpam-6135	172	8	if	if	SCONJ
ejpam-6135	172	9	−q	−q	ADJ
ejpam-6135	172	10	uniform	uniform	ADJ
ejpam-6135	172	11	topological	topological	ADJ
ejpam-6135	172	12	space	space	NOUN
ejpam-6135	172	13	.	.	PUNCT
ejpam-6135	173	1	then	then	ADV
ejpam-6135	173	2	(	(	PUNCT
ejpam-6135	173	3	x	x	X
ejpam-6135	173	4	,	,	PUNCT
ejpam-6135	173	5	τυ	τυ	NUM
ejpam-6135	173	6	)	)	PUNCT
ejpam-6135	173	7	is	be	AUX
ejpam-6135	173	8	said	say	VERB
ejpam-6135	173	9	to	to	PART
ejpam-6135	173	10	be	be	AUX
ejpam-6135	173	11	(	(	PUNCT
ejpam-6135	173	12	c	c	X
ejpam-6135	173	13	,	,	PUNCT
ejpam-6135	173	14	d	d	NOUN
ejpam-6135	173	15	)	)	PUNCT
ejpam-6135	173	16	if	if	SCONJ
ejpam-6135	173	17	−q	−q	ADJ
ejpam-6135	173	18	uniform	uniform	ADJ
ejpam-6135	173	19	ir∗	ir∗	NOUN
ejpam-6135	173	20	structure	structure	NOUN
ejpam-6135	173	21	hausdorff	hausdorff	NOUN
ejpam-6135	173	22	space	space	PROPN
ejpam-6135	173	23	,	,	PUNCT
ejpam-6135	173	24	iff	iff	VERB
ejpam-6135	173	25	for	for	ADP
ejpam-6135	173	26	every	every	DET
ejpam-6135	173	27	x1	x1	PROPN
ejpam-6135	173	28	,	,	PUNCT
ejpam-6135	173	29	x2	x2	PROPN
ejpam-6135	173	30	∈	∈	PROPN
ejpam-6135	173	31	x	x	X
ejpam-6135	173	32	and	and	CCONJ
ejpam-6135	173	33	x1	x1	PROPN
ejpam-6135	173	34	̸=	̸=	PROPN
ejpam-6135	173	35	x2	x2	PROPN
ejpam-6135	173	36	implies	imply	VERB
ejpam-6135	173	37	that	that	SCONJ
ejpam-6135	173	38	there	there	PRON
ejpam-6135	173	39	exists	exist	VERB
ejpam-6135	173	40	g1=	g1=	NOUN
ejpam-6135	173	41	⟨x	⟨x	VERB
ejpam-6135	173	42	,	,	PUNCT
ejpam-6135	173	43	µg1	µg1	NOUN
ejpam-6135	173	44	,	,	PUNCT
ejpam-6135	173	45	νg1⟩	νg1⟩	PROPN
ejpam-6135	173	46	,	,	PUNCT
ejpam-6135	173	47	g2=	g2=	NOUN
ejpam-6135	173	48	⟨x	⟨x	VERB
ejpam-6135	173	49	,	,	PUNCT
ejpam-6135	173	50	µg2	µg2	INTJ
ejpam-6135	173	51	,	,	PUNCT
ejpam-6135	173	52	νg2⟩	νg2⟩	PROPN
ejpam-6135	173	53	∈	∈	PROPN
ejpam-6135	173	54	τυ	τυ	ADP
ejpam-6135	173	55	with	with	ADP
ejpam-6135	173	56	µg1(x1)=	µg1(x1)=	NOUN
ejpam-6135	173	57	1∼	1∼	NUM
ejpam-6135	173	58	,	,	PUNCT
ejpam-6135	173	59	νg1(x1)=	νg1(x1)=	VERB
ejpam-6135	173	60	0∼	0∼	NUM
ejpam-6135	173	61	,	,	PUNCT
ejpam-6135	173	62	µg2(x2)=	µg2(x2)=	NOUN
ejpam-6135	173	63	1∼	1∼	NUM
ejpam-6135	173	64	,	,	PUNCT
ejpam-6135	173	65	νg2(x2)=	νg2(x2)=	VERB
ejpam-6135	173	66	0∼	0∼	NOUN
ejpam-6135	173	67	and	and	CCONJ
ejpam-6135	173	68	g1	g1	VERB
ejpam-6135	173	69	∩g2=	∩g2=	NOUN
ejpam-6135	173	70	0∼	0∼	NUM
ejpam-6135	173	71	definition	definition	NOUN
ejpam-6135	173	72	13	13	NUM
ejpam-6135	173	73	.	.	PUNCT
ejpam-6135	174	1	let	let	VERB
ejpam-6135	174	2	(	(	PUNCT
ejpam-6135	174	3	x	x	X
ejpam-6135	174	4	,	,	PUNCT
ejpam-6135	174	5	τυ	τυ	NUM
ejpam-6135	174	6	)	)	PUNCT
ejpam-6135	174	7	is	be	AUX
ejpam-6135	174	8	said	say	VERB
ejpam-6135	174	9	to	to	PART
ejpam-6135	174	10	be	be	AUX
ejpam-6135	174	11	(	(	PUNCT
ejpam-6135	174	12	c	c	X
ejpam-6135	174	13	,	,	PUNCT
ejpam-6135	174	14	d	d	NOUN
ejpam-6135	174	15	)	)	PUNCT
ejpam-6135	174	16	if	if	SCONJ
ejpam-6135	174	17	−q	−q	ADJ
ejpam-6135	174	18	uniform	uniform	ADJ
ejpam-6135	174	19	ir∗	ir∗	NOUN
ejpam-6135	174	20	structure	structure	NOUN
ejpam-6135	174	21	hausdorff	hausdorff	NOUN
ejpam-6135	174	22	space	space	NOUN
ejpam-6135	174	23	.	.	PUNCT
ejpam-6135	175	1	the	the	DET
ejpam-6135	175	2	collection	collection	NOUN
ejpam-6135	175	3	p	p	X
ejpam-6135	175	4	=	=	X
ejpam-6135	175	5	{	{	PUNCT
ejpam-6135	175	6	ai}i∈δ	ai}i∈δ	NOUN
ejpam-6135	175	7	of	of	ADP
ejpam-6135	175	8	all	all	PRON
ejpam-6135	175	9	(	(	PUNCT
ejpam-6135	175	10	c	c	X
ejpam-6135	175	11	,	,	PUNCT
ejpam-6135	175	12	d	d	NOUN
ejpam-6135	175	13	)	)	PUNCT
ejpam-6135	175	14	if	if	SCONJ
ejpam-6135	175	15	−q	−q	ADJ
ejpam-6135	175	16	uniform	uniform	ADJ
ejpam-6135	175	17	ir∗	ir∗	NOUN
ejpam-6135	175	18	structure	structure	NOUN
ejpam-6135	175	19	open	open	ADJ
ejpam-6135	175	20	sets	set	NOUN
ejpam-6135	175	21	of	of	ADP
ejpam-6135	175	22	(	(	PUNCT
ejpam-6135	175	23	x	x	NOUN
ejpam-6135	175	24	,	,	PUNCT
ejpam-6135	175	25	τυ	τυ	NUM
ejpam-6135	175	26	)	)	PUNCT
ejpam-6135	175	27	referred	refer	VERB
ejpam-6135	175	28	to	to	ADP
ejpam-6135	175	29	as	as	ADP
ejpam-6135	175	30	(	(	PUNCT
ejpam-6135	175	31	c	c	NOUN
ejpam-6135	175	32	,	,	PUNCT
ejpam-6135	175	33	d	d	NOUN
ejpam-6135	175	34	)	)	PUNCT
ejpam-6135	176	1	if	if	SCONJ
ejpam-6135	176	2	−q	−q	ADJ
ejpam-6135	176	3	uniform	uniform	ADJ
ejpam-6135	176	4	ir∗	ir∗	NOUN
ejpam-6135	176	5	centred	centre	VERB
ejpam-6135	176	6	structure	structure	NOUN
ejpam-6135	176	7	system	system	NOUN
ejpam-6135	176	8	,	,	PUNCT
ejpam-6135	176	9	if	if	SCONJ
ejpam-6135	176	10	for	for	ADP
ejpam-6135	176	11	any	any	DET
ejpam-6135	176	12	finite	finite	ADJ
ejpam-6135	176	13	collection	collection	NOUN
ejpam-6135	176	14	of	of	ADP
ejpam-6135	176	15	elements	element	NOUN
ejpam-6135	176	16	in	in	ADP
ejpam-6135	176	17	if	if	SCONJ
ejpam-6135	176	18	−q	−q	ADJ
ejpam-6135	176	19	uniform	uniform	ADJ
ejpam-6135	176	20	ir∗	ir∗	NOUN
ejpam-6135	176	21	structure	structure	NOUN
ejpam-6135	176	22	space	space	NOUN
ejpam-6135	176	23	such	such	ADJ
ejpam-6135	176	24	that	that	SCONJ
ejpam-6135	176	25	∩n	∩n	NOUN
ejpam-6135	176	26	i=1ai	i=1ai	ADV
ejpam-6135	176	27	̸=	̸=	PROPN
ejpam-6135	176	28	0∼.	0∼.	VERB
ejpam-6135	176	29	definition	definition	NOUN
ejpam-6135	176	30	14	14	NUM
ejpam-6135	176	31	.	.	PUNCT
ejpam-6135	177	1	consider	consider	VERB
ejpam-6135	177	2	,	,	PUNCT
ejpam-6135	177	3	the	the	DET
ejpam-6135	177	4	sets	set	NOUN
ejpam-6135	177	5	px=	px=	VERB
ejpam-6135	177	6	{	{	PUNCT
ejpam-6135	177	7	pi	pi	NOUN
ejpam-6135	177	8	:	:	PUNCT
ejpam-6135	178	1	i	i	PROPN
ejpam-6135	178	2	∈	∈	PROPN
ejpam-6135	178	3	δ	δ	PROPN
ejpam-6135	178	4	}	}	PUNCT
ejpam-6135	178	5	where	where	SCONJ
ejpam-6135	178	6	p	p	NOUN
ejpam-6135	178	7	,	,	PUNCT
ejpam-6135	178	8	is	be	AUX
ejpam-6135	178	9	are	be	AUX
ejpam-6135	178	10	(	(	PUNCT
ejpam-6135	178	11	c	c	X
ejpam-6135	178	12	,	,	PUNCT
ejpam-6135	178	13	d	d	NOUN
ejpam-6135	178	14	)	)	PUNCT
ejpam-6135	178	15	if	if	SCONJ
ejpam-6135	178	16	−q	−q	ADJ
ejpam-6135	178	17	uniform	uniform	ADJ
ejpam-6135	178	18	ir∗	ir∗	NOUN
ejpam-6135	178	19	centred	centre	VERB
ejpam-6135	178	20	structure	structure	NOUN
ejpam-6135	178	21	systems	system	NOUN
ejpam-6135	178	22	in	in	ADP
ejpam-6135	178	23	(	(	PUNCT
ejpam-6135	178	24	x	x	NOUN
ejpam-6135	178	25	,	,	PUNCT
ejpam-6135	178	26	τυ	τυ	NOUN
ejpam-6135	178	27	)	)	PUNCT
ejpam-6135	178	28	which	which	PRON
ejpam-6135	178	29	are	be	AUX
ejpam-6135	178	30	also	also	ADV
ejpam-6135	178	31	called	call	VERB
ejpam-6135	178	32	as	as	ADP
ejpam-6135	178	33	(	(	PUNCT
ejpam-6135	178	34	c	c	X
ejpam-6135	178	35	,	,	PUNCT
ejpam-6135	178	36	d	d	NOUN
ejpam-6135	178	37	)	)	PUNCT
ejpam-6135	178	38	if	if	SCONJ
ejpam-6135	178	39	−q	−q	ADJ
ejpam-6135	178	40	uniform	uniform	ADJ
ejpam-6135	178	41	ir∗	ir∗	NOUN
ejpam-6135	178	42	centred	centre	VERB
ejpam-6135	178	43	structure	structure	NOUN
ejpam-6135	178	44	points	point	NOUN
ejpam-6135	178	45	.	.	PUNCT
ejpam-6135	179	1	then	then	ADV
ejpam-6135	179	2	the	the	DET
ejpam-6135	179	3	family	family	NOUN
ejpam-6135	179	4	τp	τp	NOUN
ejpam-6135	179	5	is	be	AUX
ejpam-6135	179	6	said	say	VERB
ejpam-6135	179	7	to	to	PART
ejpam-6135	179	8	be	be	AUX
ejpam-6135	179	9	an	an	DET
ejpam-6135	179	10	(	(	PUNCT
ejpam-6135	179	11	c	c	NOUN
ejpam-6135	179	12	,	,	PUNCT
ejpam-6135	179	13	d	d	NOUN
ejpam-6135	179	14	)	)	PUNCT
ejpam-6135	179	15	if	if	SCONJ
ejpam-6135	179	16	−q	−q	ADJ
ejpam-6135	179	17	uniform	uniform	ADJ
ejpam-6135	179	18	ir∗	ir∗	NOUN
ejpam-6135	179	19	centred	centre	VERB
ejpam-6135	179	20	structure	structure	NOUN
ejpam-6135	179	21	,	,	PUNCT
ejpam-6135	179	22	if	if	SCONJ
ejpam-6135	179	23	it	it	PRON
ejpam-6135	179	24	satisfies	satisfy	VERB
ejpam-6135	179	25	the	the	DET
ejpam-6135	179	26	following	follow	VERB
ejpam-6135	179	27	conditions	condition	NOUN
ejpam-6135	179	28	:	:	PUNCT
ejpam-6135	179	29	(	(	PUNCT
ejpam-6135	179	30	i	i	NOUN
ejpam-6135	179	31	)	)	PUNCT
ejpam-6135	179	32	∅	∅	NOUN
ejpam-6135	179	33	,	,	PUNCT
ejpam-6135	179	34	px	px	PROPN
ejpam-6135	179	35	∈	∈	PROPN
ejpam-6135	179	36	τp	τp	PROPN
ejpam-6135	179	37	(	(	PUNCT
ejpam-6135	179	38	ii	ii	NOUN
ejpam-6135	179	39	)	)	PUNCT
ejpam-6135	179	40	∪i∈j	∪i∈j	NOUN
ejpam-6135	179	41	τp	τp	NOUN
ejpam-6135	179	42	is	be	AUX
ejpam-6135	179	43	in	in	ADP
ejpam-6135	179	44	τp	τp	DET
ejpam-6135	179	45	.(arbitrary	.(arbitrary	PROPN
ejpam-6135	179	46	union	union	PROPN
ejpam-6135	179	47	)	)	PUNCT
ejpam-6135	179	48	(	(	PUNCT
ejpam-6135	179	49	iii	iii	X
ejpam-6135	179	50	)	)	PUNCT
ejpam-6135	179	51	∩n	∩n	NOUN
ejpam-6135	179	52	i=1	i=1	PROPN
ejpam-6135	180	1	τp	τp	PROPN
ejpam-6135	180	2	is	be	AUX
ejpam-6135	180	3	in	in	ADP
ejpam-6135	180	4	τp	τp	DET
ejpam-6135	180	5	.(finite	.(finite	NOUN
ejpam-6135	180	6	intersection	intersection	PROPN
ejpam-6135	180	7	)	)	PUNCT
ejpam-6135	180	8	the	the	DET
ejpam-6135	180	9	pair	pair	NOUN
ejpam-6135	180	10	(	(	PUNCT
ejpam-6135	180	11	px	px	INTJ
ejpam-6135	180	12	,	,	PUNCT
ejpam-6135	180	13	τp	τp	PROPN
ejpam-6135	180	14	)	)	PUNCT
ejpam-6135	180	15	is	be	AUX
ejpam-6135	180	16	called	call	VERB
ejpam-6135	180	17	(	(	PUNCT
ejpam-6135	180	18	c	c	X
ejpam-6135	180	19	,	,	PUNCT
ejpam-6135	180	20	d	d	NOUN
ejpam-6135	180	21	)	)	PUNCT
ejpam-6135	180	22	if	if	SCONJ
ejpam-6135	180	23	−q	−q	ADJ
ejpam-6135	180	24	uniform	uniform	ADJ
ejpam-6135	180	25	ir∗	ir∗	NOUN
ejpam-6135	180	26	centred	centre	VERB
ejpam-6135	180	27	structure	structure	NOUN
ejpam-6135	180	28	space	space	NOUN
ejpam-6135	180	29	.	.	PUNCT
ejpam-6135	181	1	each	each	DET
ejpam-6135	181	2	members	member	NOUN
ejpam-6135	181	3	of	of	ADP
ejpam-6135	181	4	(	(	PUNCT
ejpam-6135	181	5	px	px	PROPN
ejpam-6135	181	6	,	,	PUNCT
ejpam-6135	181	7	τp	τp	PROPN
ejpam-6135	181	8	)	)	PUNCT
ejpam-6135	181	9	are	be	AUX
ejpam-6135	181	10	called	call	VERB
ejpam-6135	181	11	(	(	PUNCT
ejpam-6135	181	12	c	c	X
ejpam-6135	181	13	,	,	PUNCT
ejpam-6135	181	14	d	d	NOUN
ejpam-6135	181	15	)	)	PUNCT
ejpam-6135	181	16	if	if	SCONJ
ejpam-6135	181	17	−q	−q	ADJ
ejpam-6135	181	18	uniform	uniform	ADJ
ejpam-6135	181	19	ir∗	ir∗	NOUN
ejpam-6135	181	20	centred	centre	VERB
ejpam-6135	181	21	structure	structure	NOUN
ejpam-6135	181	22	open	open	ADJ
ejpam-6135	181	23	set	set	NOUN
ejpam-6135	181	24	.	.	PUNCT
ejpam-6135	182	1	the	the	DET
ejpam-6135	182	2	complement	complement	NOUN
ejpam-6135	182	3	of	of	ADP
ejpam-6135	182	4	an	an	DET
ejpam-6135	182	5	(	(	PUNCT
ejpam-6135	182	6	c	c	NOUN
ejpam-6135	182	7	,	,	PUNCT
ejpam-6135	182	8	d	d	NOUN
ejpam-6135	182	9	)	)	PUNCT
ejpam-6135	182	10	if	if	SCONJ
ejpam-6135	182	11	−q	−q	ADJ
ejpam-6135	182	12	ir∗	ir∗	NOUN
ejpam-6135	182	13	centred	centre	VERB
ejpam-6135	182	14	structure	structure	NOUN
ejpam-6135	182	15	uniform	uniform	NOUN
ejpam-6135	182	16	open	open	ADJ
ejpam-6135	182	17	set	set	NOUN
ejpam-6135	182	18	is	be	AUX
ejpam-6135	182	19	(	(	PUNCT
ejpam-6135	182	20	c	c	X
ejpam-6135	182	21	,	,	PUNCT
ejpam-6135	182	22	d	d	NOUN
ejpam-6135	182	23	)	)	PUNCT
ejpam-6135	182	24	if	if	SCONJ
ejpam-6135	182	25	−q	−q	ADJ
ejpam-6135	182	26	uniform	uniform	ADJ
ejpam-6135	182	27	ir∗	ir∗	NOUN
ejpam-6135	182	28	centred	centre	VERB
ejpam-6135	182	29	structure	structure	NOUN
ejpam-6135	182	30	closed	close	VERB
ejpam-6135	182	31	set	set	NOUN
ejpam-6135	182	32	.	.	PUNCT
ejpam-6135	183	1	definition	definition	NOUN
ejpam-6135	183	2	15	15	NUM
ejpam-6135	183	3	.	.	PUNCT
ejpam-6135	184	1	let	let	VERB
ejpam-6135	184	2	(	(	PUNCT
ejpam-6135	184	3	px	px	INTJ
ejpam-6135	184	4	,	,	PUNCT
ejpam-6135	184	5	τp	τp	PROPN
ejpam-6135	184	6	)	)	PUNCT
ejpam-6135	184	7	be	be	AUX
ejpam-6135	184	8	(	(	PUNCT
ejpam-6135	184	9	c	c	X
ejpam-6135	184	10	,	,	PUNCT
ejpam-6135	184	11	d	d	NOUN
ejpam-6135	184	12	)	)	PUNCT
ejpam-6135	184	13	if	if	SCONJ
ejpam-6135	184	14	−q	−q	ADJ
ejpam-6135	184	15	uniform	uniform	ADJ
ejpam-6135	184	16	ir∗	ir∗	NOUN
ejpam-6135	184	17	centred	centre	VERB
ejpam-6135	184	18	structure	structure	NOUN
ejpam-6135	184	19	space	space	NOUN
ejpam-6135	184	20	and	and	CCONJ
ejpam-6135	184	21	a	a	DET
ejpam-6135	184	22	⊆	⊆	NUM
ejpam-6135	184	23	px	px	NOUN
ejpam-6135	184	24	.	.	PUNCT
ejpam-6135	185	1	then	then	ADV
ejpam-6135	185	2	(	(	PUNCT
ejpam-6135	185	3	c	c	X
ejpam-6135	185	4	,	,	PUNCT
ejpam-6135	185	5	d	d	NOUN
ejpam-6135	185	6	)	)	PUNCT
ejpam-6135	185	7	if	if	SCONJ
ejpam-6135	185	8	−q	−q	ADJ
ejpam-6135	185	9	uniform	uniform	ADJ
ejpam-6135	185	10	ir∗	ir∗	NOUN
ejpam-6135	185	11	centred	centre	VERB
ejpam-6135	185	12	structure	structure	NOUN
ejpam-6135	185	13	closure	closure	NOUN
ejpam-6135	185	14	and	and	CCONJ
ejpam-6135	185	15	(	(	PUNCT
ejpam-6135	185	16	c	c	X
ejpam-6135	185	17	,	,	PUNCT
ejpam-6135	185	18	d	d	NOUN
ejpam-6135	185	19	)	)	PUNCT
ejpam-6135	185	20	if	if	SCONJ
ejpam-6135	185	21	−q	−q	ADJ
ejpam-6135	185	22	uniform	uniform	ADJ
ejpam-6135	185	23	ir∗	ir∗	NOUN
ejpam-6135	185	24	centred	centre	VERB
ejpam-6135	185	25	structure	structure	NOUN
ejpam-6135	185	26	interior	interior	NOUN
ejpam-6135	185	27	of	of	ADP
ejpam-6135	185	28	a	a	PRON
ejpam-6135	185	29	is	be	AUX
ejpam-6135	185	30	defined	define	VERB
ejpam-6135	185	31	as	as	ADP
ejpam-6135	185	32	ir∗	ir∗	PROPN
ejpam-6135	185	33	cp	cp	PROPN
ejpam-6135	185	34	cl(a)=∩{b	cl(a)=∩{b	VERB
ejpam-6135	185	35	:	:	PUNCT
ejpam-6135	185	36	b	b	X
ejpam-6135	185	37	is	be	AUX
ejpam-6135	185	38	an	an	DET
ejpam-6135	185	39	(	(	PUNCT
ejpam-6135	185	40	c	c	NOUN
ejpam-6135	185	41	,	,	PUNCT
ejpam-6135	185	42	d	d	NOUN
ejpam-6135	185	43	)	)	PUNCT
ejpam-6135	185	44	if	if	SCONJ
ejpam-6135	185	45	−q	−q	ADJ
ejpam-6135	185	46	uniform	uniform	ADJ
ejpam-6135	185	47	ir∗	ir∗	NOUN
ejpam-6135	185	48	centred	centre	VERB
ejpam-6135	185	49	structure	structure	NOUN
ejpam-6135	185	50	closed	close	VERB
ejpam-6135	185	51	set	set	VERB
ejpam-6135	185	52	and	and	CCONJ
ejpam-6135	185	53	a	a	DET
ejpam-6135	185	54	⊆	⊆	NUM
ejpam-6135	185	55	b	b	NOUN
ejpam-6135	185	56	}	}	PUNCT
ejpam-6135	185	57	ir∗	ir∗	NOUN
ejpam-6135	185	58	cp	cp	PROPN
ejpam-6135	185	59	int(a)=∩{b	int(a)=∩{b	PROPN
ejpam-6135	185	60	:	:	PUNCT
ejpam-6135	185	61	b	b	NOUN
ejpam-6135	185	62	is	be	AUX
ejpam-6135	185	63	an	an	DET
ejpam-6135	185	64	(	(	PUNCT
ejpam-6135	185	65	c	c	NOUN
ejpam-6135	185	66	,	,	PUNCT
ejpam-6135	185	67	d	d	NOUN
ejpam-6135	185	68	)	)	PUNCT
ejpam-6135	185	69	if	if	SCONJ
ejpam-6135	185	70	−q	−q	ADJ
ejpam-6135	185	71	uniform	uniform	ADJ
ejpam-6135	185	72	ir∗	ir∗	NOUN
ejpam-6135	185	73	centred	centre	VERB
ejpam-6135	185	74	structure	structure	NOUN
ejpam-6135	185	75	closed	close	VERB
ejpam-6135	185	76	set	set	VERB
ejpam-6135	185	77	and	and	CCONJ
ejpam-6135	185	78	a	a	DET
ejpam-6135	185	79	⊇	⊇	ADJ
ejpam-6135	185	80	b	b	PROPN
ejpam-6135	185	81	}	}	PUNCT
ejpam-6135	185	82	definition	definition	NOUN
ejpam-6135	185	83	16	16	NUM
ejpam-6135	185	84	.	.	PUNCT
ejpam-6135	186	1	let	let	AUX
ejpam-6135	186	2	(	(	PUNCT
ejpam-6135	186	3	px	px	INTJ
ejpam-6135	186	4	,	,	PUNCT
ejpam-6135	186	5	τp	τp	PROPN
ejpam-6135	186	6	)	)	PUNCT
ejpam-6135	186	7	be	be	AUX
ejpam-6135	186	8	the	the	DET
ejpam-6135	186	9	(	(	PUNCT
ejpam-6135	186	10	c	c	NOUN
ejpam-6135	186	11	,	,	PUNCT
ejpam-6135	186	12	d	d	NOUN
ejpam-6135	186	13	)	)	PUNCT
ejpam-6135	186	14	if	if	SCONJ
ejpam-6135	186	15	−q	−q	ADJ
ejpam-6135	186	16	uniform	uniform	ADJ
ejpam-6135	186	17	ir∗	ir∗	NOUN
ejpam-6135	186	18	centred	centre	VERB
ejpam-6135	186	19	structure	structure	NOUN
ejpam-6135	186	20	space	space	NOUN
ejpam-6135	186	21	.	.	PUNCT
ejpam-6135	187	1	a	a	DET
ejpam-6135	187	2	collection	collection	NOUN
ejpam-6135	187	3	{	{	PUNCT
ejpam-6135	187	4	ai	ai	NOUN
ejpam-6135	187	5	:	:	PUNCT
ejpam-6135	187	6	i	i	PROPN
ejpam-6135	187	7	∈	∈	PROPN
ejpam-6135	187	8	δ	δ	PROPN
ejpam-6135	187	9	}	}	PUNCT
ejpam-6135	187	10	of	of	ADP
ejpam-6135	187	11	(	(	PUNCT
ejpam-6135	187	12	c	c	X
ejpam-6135	187	13	,	,	PUNCT
ejpam-6135	187	14	d	d	NOUN
ejpam-6135	187	15	)	)	PUNCT
ejpam-6135	187	16	if	if	SCONJ
ejpam-6135	187	17	−q	−q	ADJ
ejpam-6135	187	18	uniform	uniform	ADJ
ejpam-6135	187	19	ir∗	ir∗	NOUN
ejpam-6135	187	20	centred	centre	VERB
ejpam-6135	187	21	structure	structure	NOUN
ejpam-6135	187	22	open	open	ADJ
ejpam-6135	187	23	sets	set	NOUN
ejpam-6135	187	24	in	in	ADP
ejpam-6135	187	25	a	a	DET
ejpam-6135	187	26	(	(	PUNCT
ejpam-6135	187	27	c	c	NOUN
ejpam-6135	187	28	,	,	PUNCT
ejpam-6135	187	29	d	d	NOUN
ejpam-6135	187	30	)	)	PUNCT
ejpam-6135	187	31	if	if	SCONJ
ejpam-6135	187	32	−q	−q	ADJ
ejpam-6135	187	33	uniform	uniform	ADJ
ejpam-6135	187	34	ir∗	ir∗	NOUN
ejpam-6135	187	35	centred	centre	VERB
ejpam-6135	187	36	structure	structure	NOUN
ejpam-6135	187	37	space	space	NOUN
ejpam-6135	187	38	(	(	PUNCT
ejpam-6135	187	39	px	px	NOUN
ejpam-6135	187	40	,	,	PUNCT
ejpam-6135	187	41	τp	τp	PROPN
ejpam-6135	187	42	)	)	PUNCT
ejpam-6135	187	43	is	be	AUX
ejpam-6135	187	44	called	call	VERB
ejpam-6135	187	45	a	a	DET
ejpam-6135	187	46	(	(	PUNCT
ejpam-6135	187	47	c	c	NOUN
ejpam-6135	187	48	,	,	PUNCT
ejpam-6135	187	49	d	d	NOUN
ejpam-6135	187	50	)	)	PUNCT
ejpam-6135	187	51	if	if	SCONJ
ejpam-6135	187	52	−q	−q	ADJ
ejpam-6135	187	53	uniform	uniform	ADJ
ejpam-6135	187	54	ir∗	ir∗	NOUN
ejpam-6135	187	55	centred	centre	VERB
ejpam-6135	187	56	structure	structure	NOUN
ejpam-6135	187	57	open	open	ADJ
ejpam-6135	187	58	cover	cover	NOUN
ejpam-6135	187	59	of	of	ADP
ejpam-6135	187	60	(	(	PUNCT
ejpam-6135	187	61	c	c	X
ejpam-6135	187	62	,	,	PUNCT
ejpam-6135	187	63	d	d	NOUN
ejpam-6135	187	64	)	)	PUNCT
ejpam-6135	187	65	if	if	SCONJ
ejpam-6135	187	66	−q	−q	ADJ
ejpam-6135	187	67	uniform	uniform	ADJ
ejpam-6135	187	68	ir∗	ir∗	NOUN
ejpam-6135	187	69	centred	centre	VERB
ejpam-6135	187	70	subset	subset	PROPN
ejpam-6135	187	71	b	b	PROPN
ejpam-6135	187	72	of	of	ADP
ejpam-6135	187	73	px	px	PROPN
ejpam-6135	187	74	,	,	PUNCT
ejpam-6135	187	75	if	if	SCONJ
ejpam-6135	187	76	b	b	PROPN
ejpam-6135	187	77	⊆	⊆	X
ejpam-6135	187	78	∪	∪	X
ejpam-6135	187	79	{	{	PUNCT
ejpam-6135	187	80	ai	ai	NOUN
ejpam-6135	187	81	:	:	PUNCT
ejpam-6135	187	82	i	i	PROPN
ejpam-6135	187	83	∈	∈	PROPN
ejpam-6135	187	84	δ	δ	PROPN
ejpam-6135	187	85	}	}	PUNCT
ejpam-6135	187	86	.	.	PUNCT
ejpam-6135	188	1	s.	s.	PROPN
ejpam-6135	188	2	thirukumaran	thirukumaran	PROPN
ejpam-6135	188	3	,	,	PUNCT
ejpam-6135	188	4	g.	g.	PROPN
ejpam-6135	188	5	k.	k.	PROPN
ejpam-6135	188	6	revathi	revathi	PROPN
ejpam-6135	188	7	/	/	SYM
ejpam-6135	188	8	eur	eur	PROPN
ejpam-6135	188	9	.	.	PUNCT
ejpam-6135	189	1	j.	j.	PROPN
ejpam-6135	189	2	pure	pure	PROPN
ejpam-6135	189	3	appl	appl	PROPN
ejpam-6135	189	4	.	.	PROPN
ejpam-6135	189	5	math	math	PROPN
ejpam-6135	189	6	,	,	PUNCT
ejpam-6135	189	7	18	18	NUM
ejpam-6135	189	8	(	(	PUNCT
ejpam-6135	189	9	2	2	NUM
ejpam-6135	189	10	)	)	PUNCT
ejpam-6135	189	11	(	(	PUNCT
ejpam-6135	189	12	2025	2025	NUM
ejpam-6135	189	13	)	)	PUNCT
ejpam-6135	189	14	,	,	PUNCT
ejpam-6135	189	15	6135	6135	NUM
ejpam-6135	189	16	10	10	NUM
ejpam-6135	189	17	of	of	ADP
ejpam-6135	189	18	17	17	NUM
ejpam-6135	189	19	definition	definition	NOUN
ejpam-6135	189	20	17	17	NUM
ejpam-6135	189	21	.	.	PUNCT
ejpam-6135	190	1	let	let	AUX
ejpam-6135	190	2	(	(	PUNCT
ejpam-6135	190	3	px	px	INTJ
ejpam-6135	190	4	,	,	PUNCT
ejpam-6135	190	5	τp	τp	PROPN
ejpam-6135	190	6	)	)	PUNCT
ejpam-6135	190	7	be	be	AUX
ejpam-6135	190	8	the	the	DET
ejpam-6135	190	9	(	(	PUNCT
ejpam-6135	190	10	c	c	NOUN
ejpam-6135	190	11	,	,	PUNCT
ejpam-6135	190	12	d	d	NOUN
ejpam-6135	190	13	)	)	PUNCT
ejpam-6135	190	14	if	if	SCONJ
ejpam-6135	190	15	−q	−q	ADJ
ejpam-6135	190	16	uniform	uniform	ADJ
ejpam-6135	190	17	ir∗	ir∗	NOUN
ejpam-6135	190	18	centred	centre	VERB
ejpam-6135	190	19	structure	structure	NOUN
ejpam-6135	190	20	space	space	NOUN
ejpam-6135	190	21	is	be	AUX
ejpam-6135	190	22	said	say	VERB
ejpam-6135	190	23	to	to	PART
ejpam-6135	190	24	be	be	AUX
ejpam-6135	190	25	a	a	DET
ejpam-6135	190	26	(	(	PUNCT
ejpam-6135	190	27	c	c	NOUN
ejpam-6135	190	28	,	,	PUNCT
ejpam-6135	190	29	d	d	NOUN
ejpam-6135	190	30	)	)	PUNCT
ejpam-6135	190	31	if	if	SCONJ
ejpam-6135	190	32	−q	−q	ADJ
ejpam-6135	190	33	uniform	uniform	ADJ
ejpam-6135	190	34	ir∗	ir∗	NOUN
ejpam-6135	190	35	centred	centre	VERB
ejpam-6135	190	36	structure	structure	NOUN
ejpam-6135	190	37	compact	compact	ADJ
ejpam-6135	190	38	,	,	PUNCT
ejpam-6135	190	39	if	if	SCONJ
ejpam-6135	190	40	for	for	ADP
ejpam-6135	190	41	every	every	DET
ejpam-6135	190	42	(	(	PUNCT
ejpam-6135	190	43	c	c	NOUN
ejpam-6135	190	44	,	,	PUNCT
ejpam-6135	190	45	d	d	NOUN
ejpam-6135	190	46	)	)	PUNCT
ejpam-6135	190	47	if	if	SCONJ
ejpam-6135	190	48	−q	−q	ADJ
ejpam-6135	190	49	uniform	uniform	ADJ
ejpam-6135	190	50	ir∗	ir∗	NOUN
ejpam-6135	190	51	open	open	ADJ
ejpam-6135	190	52	cover	cover	NOUN
ejpam-6135	190	53	of	of	ADP
ejpam-6135	190	54	px	px	PROPN
ejpam-6135	190	55	possess	possess	VERB
ejpam-6135	190	56	a	a	DET
ejpam-6135	190	57	finite	finite	ADJ
ejpam-6135	190	58	subcover	subcover	PROPN
ejpam-6135	190	59	.	.	PUNCT
ejpam-6135	191	1	definition	definition	NOUN
ejpam-6135	191	2	18	18	NUM
ejpam-6135	191	3	.	.	PUNCT
ejpam-6135	192	1	a	a	DET
ejpam-6135	192	2	pairs	pair	NOUN
ejpam-6135	192	3	(	(	PUNCT
ejpam-6135	192	4	px	px	NOUN
ejpam-6135	192	5	,	,	PUNCT
ejpam-6135	192	6	τp	τp	PROPN
ejpam-6135	192	7	)	)	PUNCT
ejpam-6135	192	8	and	and	CCONJ
ejpam-6135	192	9	(	(	PUNCT
ejpam-6135	192	10	py	py	INTJ
ejpam-6135	192	11	,	,	PUNCT
ejpam-6135	192	12	τ	τ	PROPN
ejpam-6135	192	13	∗	∗	PROPN
ejpam-6135	192	14	p	p	NOUN
ejpam-6135	192	15	)	)	PUNCT
ejpam-6135	192	16	be	be	AUX
ejpam-6135	192	17	any	any	DET
ejpam-6135	192	18	two	two	NUM
ejpam-6135	192	19	(	(	PUNCT
ejpam-6135	192	20	c	c	NOUN
ejpam-6135	192	21	,	,	PUNCT
ejpam-6135	192	22	d	d	NOUN
ejpam-6135	192	23	)	)	PUNCT
ejpam-6135	192	24	if	if	SCONJ
ejpam-6135	192	25	−q	−q	ADJ
ejpam-6135	192	26	uniform	uniform	ADJ
ejpam-6135	192	27	ir∗	ir∗	NOUN
ejpam-6135	192	28	centred	centre	VERB
ejpam-6135	192	29	structure	structure	NOUN
ejpam-6135	192	30	space	space	NOUN
ejpam-6135	192	31	.	.	PUNCT
ejpam-6135	193	1	then	then	ADV
ejpam-6135	193	2	f	f	X
ejpam-6135	193	3	:	:	PUNCT
ejpam-6135	193	4	(	(	PUNCT
ejpam-6135	193	5	px	px	INTJ
ejpam-6135	193	6	,	,	PUNCT
ejpam-6135	193	7	τp	τp	PROPN
ejpam-6135	193	8	)	)	PUNCT
ejpam-6135	193	9	→	→	SYM
ejpam-6135	193	10	(	(	PUNCT
ejpam-6135	193	11	py	py	INTJ
ejpam-6135	193	12	,	,	PUNCT
ejpam-6135	193	13	τ	τ	PROPN
ejpam-6135	193	14	∗	∗	PROPN
ejpam-6135	193	15	p	p	NOUN
ejpam-6135	193	16	)	)	PUNCT
ejpam-6135	193	17	is	be	AUX
ejpam-6135	193	18	an	an	DET
ejpam-6135	193	19	(	(	PUNCT
ejpam-6135	193	20	c	c	NOUN
ejpam-6135	193	21	,	,	PUNCT
ejpam-6135	193	22	d	d	NOUN
ejpam-6135	193	23	)	)	PUNCT
ejpam-6135	193	24	if	if	SCONJ
ejpam-6135	193	25	−q	−q	ADJ
ejpam-6135	193	26	uniform	uniform	ADJ
ejpam-6135	193	27	ir∗	ir∗	NOUN
ejpam-6135	193	28	centred	centre	VERB
ejpam-6135	193	29	structure	structure	NOUN
ejpam-6135	193	30	continuous	continuous	ADJ
ejpam-6135	193	31	function	function	NOUN
ejpam-6135	193	32	,	,	PUNCT
ejpam-6135	193	33	if	if	SCONJ
ejpam-6135	193	34	f−1(v	f−1(v	PROPN
ejpam-6135	193	35	)	)	PUNCT
ejpam-6135	193	36	is	be	AUX
ejpam-6135	193	37	an	an	DET
ejpam-6135	193	38	(	(	PUNCT
ejpam-6135	193	39	c	c	NOUN
ejpam-6135	193	40	,	,	PUNCT
ejpam-6135	193	41	d	d	NOUN
ejpam-6135	193	42	)	)	PUNCT
ejpam-6135	193	43	if	if	SCONJ
ejpam-6135	193	44	−q	−q	ADJ
ejpam-6135	193	45	uniform	uniform	ADJ
ejpam-6135	193	46	ir∗	ir∗	NOUN
ejpam-6135	193	47	centred	centre	VERB
ejpam-6135	193	48	structure	structure	NOUN
ejpam-6135	193	49	open	open	ADJ
ejpam-6135	193	50	set	set	VERB
ejpam-6135	193	51	in	in	ADP
ejpam-6135	193	52	(	(	PUNCT
ejpam-6135	193	53	px	px	INTJ
ejpam-6135	193	54	,	,	PUNCT
ejpam-6135	193	55	τp	τp	INTJ
ejpam-6135	193	56	)	)	PUNCT
ejpam-6135	193	57	for	for	ADP
ejpam-6135	193	58	each	each	DET
ejpam-6135	193	59	(	(	PUNCT
ejpam-6135	193	60	c	c	X
ejpam-6135	193	61	,	,	PUNCT
ejpam-6135	193	62	d	d	NOUN
ejpam-6135	193	63	)	)	PUNCT
ejpam-6135	193	64	if	if	SCONJ
ejpam-6135	193	65	−q	−q	ADJ
ejpam-6135	193	66	uniform	uniform	NOUN
ejpam-6135	193	67	ir∗centred	ir∗centre	VERB
ejpam-6135	193	68	open	open	ADJ
ejpam-6135	193	69	set	set	VERB
ejpam-6135	193	70	v	v	NOUN
ejpam-6135	193	71	in	in	ADP
ejpam-6135	193	72	(	(	PUNCT
ejpam-6135	193	73	py	py	INTJ
ejpam-6135	193	74	,	,	PUNCT
ejpam-6135	193	75	τ	τ	PROPN
ejpam-6135	193	76	∗	∗	NOUN
ejpam-6135	193	77	p	p	NOUN
ejpam-6135	193	78	)	)	PUNCT
ejpam-6135	193	79	.	.	PUNCT
ejpam-6135	194	1	definition	definition	NOUN
ejpam-6135	194	2	19	19	NUM
ejpam-6135	194	3	.	.	PUNCT
ejpam-6135	195	1	let	let	AUX
ejpam-6135	195	2	(	(	PUNCT
ejpam-6135	195	3	px	px	INTJ
ejpam-6135	195	4	,	,	PUNCT
ejpam-6135	195	5	τp	τp	PROPN
ejpam-6135	195	6	)	)	PUNCT
ejpam-6135	195	7	be	be	AUX
ejpam-6135	195	8	a	a	DET
ejpam-6135	195	9	(	(	PUNCT
ejpam-6135	195	10	c	c	NOUN
ejpam-6135	195	11	,	,	PUNCT
ejpam-6135	195	12	d	d	NOUN
ejpam-6135	195	13	)	)	PUNCT
ejpam-6135	195	14	if	if	SCONJ
ejpam-6135	195	15	−q	−q	ADJ
ejpam-6135	195	16	uniform	uniform	ADJ
ejpam-6135	195	17	ir∗	ir∗	NOUN
ejpam-6135	195	18	centred	centre	VERB
ejpam-6135	195	19	structure	structure	NOUN
ejpam-6135	195	20	space	space	NOUN
ejpam-6135	195	21	and	and	CCONJ
ejpam-6135	195	22	let	let	VERB
ejpam-6135	195	23	p	p	PROPN
ejpam-6135	195	24	∈	∈	PROPN
ejpam-6135	195	25	px	px	NOUN
ejpam-6135	195	26	.	.	PUNCT
ejpam-6135	196	1	then	then	ADV
ejpam-6135	196	2	a	a	DET
ejpam-6135	196	3	(	(	PUNCT
ejpam-6135	196	4	c	c	NOUN
ejpam-6135	196	5	,	,	PUNCT
ejpam-6135	196	6	d	d	NOUN
ejpam-6135	196	7	)	)	PUNCT
ejpam-6135	196	8	if	if	SCONJ
ejpam-6135	196	9	−q	−q	ADJ
ejpam-6135	196	10	uniform	uniform	ADJ
ejpam-6135	196	11	ir∗	ir∗	NOUN
ejpam-6135	196	12	centred	centre	VERB
ejpam-6135	196	13	structure	structure	NOUN
ejpam-6135	196	14	subset	subset	VERB
ejpam-6135	196	15	n	n	PRON
ejpam-6135	196	16	⊆	⊆	NUM
ejpam-6135	196	17	px	px	PROPN
ejpam-6135	196	18	is	be	AUX
ejpam-6135	196	19	said	say	VERB
ejpam-6135	196	20	to	to	PART
ejpam-6135	196	21	be	be	AUX
ejpam-6135	196	22	(	(	PUNCT
ejpam-6135	196	23	c	c	X
ejpam-6135	196	24	,	,	PUNCT
ejpam-6135	196	25	d	d	NOUN
ejpam-6135	196	26	)	)	PUNCT
ejpam-6135	196	27	if	if	SCONJ
ejpam-6135	196	28	−q	−q	ADJ
ejpam-6135	196	29	uniform	uniform	ADJ
ejpam-6135	196	30	ir∗	ir∗	PROPN
ejpam-6135	196	31	structure	structure	NOUN
ejpam-6135	196	32	neighborhood	neighborhood	NOUN
ejpam-6135	196	33	,	,	PUNCT
ejpam-6135	196	34	if	if	SCONJ
ejpam-6135	196	35	there	there	PRON
ejpam-6135	196	36	exists	exist	VERB
ejpam-6135	196	37	a	a	DET
ejpam-6135	196	38	(	(	PUNCT
ejpam-6135	196	39	c	c	NOUN
ejpam-6135	196	40	,	,	PUNCT
ejpam-6135	196	41	d	d	NOUN
ejpam-6135	196	42	)	)	PUNCT
ejpam-6135	196	43	if	if	SCONJ
ejpam-6135	196	44	−q	−q	ADJ
ejpam-6135	196	45	uniform	uniform	ADJ
ejpam-6135	196	46	ir∗	ir∗	NOUN
ejpam-6135	196	47	structure	structure	NOUN
ejpam-6135	196	48	open	open	ADJ
ejpam-6135	196	49	sets	set	VERB
ejpam-6135	196	50	g	g	ADP
ejpam-6135	196	51	such	such	ADJ
ejpam-6135	196	52	that	that	SCONJ
ejpam-6135	196	53	p	p	PROPN
ejpam-6135	196	54	∈	∈	PROPN
ejpam-6135	196	55	g	g	ADP
ejpam-6135	196	56	⊆	⊆	NUM
ejpam-6135	196	57	n	n	NOUN
ejpam-6135	196	58	.	.	PUNCT
ejpam-6135	197	1	definition	definition	NOUN
ejpam-6135	197	2	20	20	NUM
ejpam-6135	197	3	.	.	PUNCT
ejpam-6135	198	1	let	let	AUX
ejpam-6135	198	2	(	(	PUNCT
ejpam-6135	198	3	px	px	INTJ
ejpam-6135	198	4	,	,	PUNCT
ejpam-6135	198	5	τp	τp	PROPN
ejpam-6135	198	6	)	)	PUNCT
ejpam-6135	198	7	be	be	AUX
ejpam-6135	198	8	a	a	DET
ejpam-6135	198	9	(	(	PUNCT
ejpam-6135	198	10	c	c	NOUN
ejpam-6135	198	11	,	,	PUNCT
ejpam-6135	198	12	d	d	NOUN
ejpam-6135	198	13	)	)	PUNCT
ejpam-6135	198	14	if	if	SCONJ
ejpam-6135	198	15	−q	−q	ADJ
ejpam-6135	198	16	uniform	uniform	ADJ
ejpam-6135	198	17	ir∗	ir∗	NOUN
ejpam-6135	198	18	centred	centre	VERB
ejpam-6135	198	19	structure	structure	NOUN
ejpam-6135	198	20	space	space	NOUN
ejpam-6135	198	21	.	.	PUNCT
ejpam-6135	199	1	a	a	DET
ejpam-6135	199	2	subset	subset	NOUN
ejpam-6135	199	3	a	a	PRON
ejpam-6135	199	4	of	of	ADP
ejpam-6135	199	5	px	px	PROPN
ejpam-6135	199	6	is	be	AUX
ejpam-6135	199	7	said	say	VERB
ejpam-6135	199	8	to	to	PART
ejpam-6135	199	9	be	be	AUX
ejpam-6135	199	10	a	a	DET
ejpam-6135	199	11	(	(	PUNCT
ejpam-6135	199	12	c	c	NOUN
ejpam-6135	199	13	,	,	PUNCT
ejpam-6135	199	14	d	d	NOUN
ejpam-6135	199	15	)	)	PUNCT
ejpam-6135	199	16	if	if	SCONJ
ejpam-6135	199	17	−q	−q	ADJ
ejpam-6135	199	18	uniform	uniform	NOUN
ejpam-6135	199	19	ir∗centred	ir∗centre	VERB
ejpam-6135	199	20	structure	structure	NOUN
ejpam-6135	199	21	dense	dense	ADJ
ejpam-6135	199	22	,	,	PUNCT
ejpam-6135	199	23	if	if	SCONJ
ejpam-6135	199	24	ir∗cp	ir∗cp	PROPN
ejpam-6135	199	25	cl(a)=px	cl(a)=px	PROPN
ejpam-6135	199	26	.	.	PUNCT
ejpam-6135	200	1	definition	definition	NOUN
ejpam-6135	200	2	21	21	NUM
ejpam-6135	200	3	.	.	PUNCT
ejpam-6135	201	1	a	a	DET
ejpam-6135	201	2	pair	pair	NOUN
ejpam-6135	201	3	(	(	PUNCT
ejpam-6135	201	4	px	px	NOUN
ejpam-6135	201	5	,	,	PUNCT
ejpam-6135	201	6	τp	τp	PROPN
ejpam-6135	201	7	)	)	PUNCT
ejpam-6135	201	8	be	be	AUX
ejpam-6135	201	9	a	a	DET
ejpam-6135	201	10	(	(	PUNCT
ejpam-6135	201	11	c	c	NOUN
ejpam-6135	201	12	,	,	PUNCT
ejpam-6135	201	13	d	d	NOUN
ejpam-6135	201	14	)	)	PUNCT
ejpam-6135	201	15	if	if	SCONJ
ejpam-6135	201	16	−q	−q	ADJ
ejpam-6135	201	17	uniform	uniform	ADJ
ejpam-6135	201	18	ir∗	ir∗	NOUN
ejpam-6135	201	19	centred	centre	VERB
ejpam-6135	201	20	structure	structure	NOUN
ejpam-6135	201	21	space	space	NOUN
ejpam-6135	201	22	.	.	PUNCT
ejpam-6135	202	1	then	then	ADV
ejpam-6135	202	2	a	a	DET
ejpam-6135	202	3	non	non	ADJ
ejpam-6135	202	4	-	-	ADJ
ejpam-6135	202	5	empty	empty	ADJ
ejpam-6135	202	6	family	family	NOUN
ejpam-6135	202	7	f	f	PROPN
ejpam-6135	202	8	of	of	ADP
ejpam-6135	202	9	subsets	subset	NOUN
ejpam-6135	202	10	of	of	ADP
ejpam-6135	202	11	px	px	PROPN
ejpam-6135	202	12	is	be	AUX
ejpam-6135	202	13	called	call	VERB
ejpam-6135	202	14	(	(	PUNCT
ejpam-6135	202	15	c	c	X
ejpam-6135	202	16	,	,	PUNCT
ejpam-6135	202	17	d	d	NOUN
ejpam-6135	202	18	)	)	PUNCT
ejpam-6135	202	19	if	if	SCONJ
ejpam-6135	202	20	−q	−q	ADJ
ejpam-6135	202	21	uniform	uniform	ADJ
ejpam-6135	202	22	ir∗	ir∗	NOUN
ejpam-6135	202	23	centred	centre	VERB
ejpam-6135	202	24	structure	structure	NOUN
ejpam-6135	202	25	filter	filter	NOUN
ejpam-6135	202	26	on	on	ADP
ejpam-6135	202	27	px	px	PROPN
ejpam-6135	202	28	,	,	PUNCT
ejpam-6135	202	29	iff	iff	VERB
ejpam-6135	202	30	it	it	PRON
ejpam-6135	202	31	satisfies	satisfy	VERB
ejpam-6135	202	32	the	the	DET
ejpam-6135	202	33	following	follow	VERB
ejpam-6135	202	34	conditions	condition	NOUN
ejpam-6135	202	35	:	:	PUNCT
ejpam-6135	202	36	(	(	PUNCT
ejpam-6135	202	37	i	i	NOUN
ejpam-6135	202	38	)	)	PUNCT
ejpam-6135	202	39	∅	∅	NOUN
ejpam-6135	202	40	∈	∈	PROPN
ejpam-6135	202	41	f	f	PROPN
ejpam-6135	202	42	(	(	PUNCT
ejpam-6135	202	43	ii	ii	NOUN
ejpam-6135	202	44	)	)	PUNCT
ejpam-6135	202	45	assume	assume	AUX
ejpam-6135	203	1	f	f	PROPN
ejpam-6135	203	2	∈	∈	PROPN
ejpam-6135	203	3	f	f	PROPN
ejpam-6135	203	4	and	and	CCONJ
ejpam-6135	203	5	f	f	PROPN
ejpam-6135	203	6	⊆	⊆	NUM
ejpam-6135	203	7	h	h	NOUN
ejpam-6135	203	8	,	,	PUNCT
ejpam-6135	203	9	then	then	ADV
ejpam-6135	203	10	h	h	PROPN
ejpam-6135	203	11	∈	∈	PROPN
ejpam-6135	203	12	f.	f.	PROPN
ejpam-6135	203	13	(	(	PUNCT
ejpam-6135	203	14	iii	iii	NOUN
ejpam-6135	203	15	)	)	PUNCT
ejpam-6135	203	16	consider	consider	VERB
ejpam-6135	203	17	f1	f1	NOUN
ejpam-6135	203	18	,	,	PUNCT
ejpam-6135	203	19	f2	f2	PROPN
ejpam-6135	203	20	∈	∈	PROPN
ejpam-6135	203	21	f	f	NOUN
ejpam-6135	203	22	,	,	PUNCT
ejpam-6135	203	23	then	then	ADV
ejpam-6135	203	24	f1	f1	PROPN
ejpam-6135	203	25	∩	∩	NOUN
ejpam-6135	203	26	f2	f2	PROPN
ejpam-6135	203	27	∈	∈	PROPN
ejpam-6135	203	28	f	f	PROPN
ejpam-6135	203	29	definition	definition	NOUN
ejpam-6135	203	30	22	22	NUM
ejpam-6135	203	31	.	.	PUNCT
ejpam-6135	204	1	consider	consider	VERB
ejpam-6135	204	2	(	(	PUNCT
ejpam-6135	204	3	c	c	NOUN
ejpam-6135	204	4	,	,	PUNCT
ejpam-6135	204	5	d	d	NOUN
ejpam-6135	204	6	)	)	PUNCT
ejpam-6135	204	7	if	if	SCONJ
ejpam-6135	204	8	−q	−q	ADJ
ejpam-6135	204	9	uniform	uniform	ADJ
ejpam-6135	204	10	ir∗	ir∗	NOUN
ejpam-6135	204	11	centred	centre	VERB
ejpam-6135	204	12	structure	structure	NOUN
ejpam-6135	204	13	net	net	NOUN
ejpam-6135	204	14	in	in	ADP
ejpam-6135	204	15	an	an	DET
ejpam-6135	204	16	(	(	PUNCT
ejpam-6135	204	17	c	c	NOUN
ejpam-6135	204	18	,	,	PUNCT
ejpam-6135	204	19	d	d	NOUN
ejpam-6135	204	20	)	)	PUNCT
ejpam-6135	204	21	if	if	SCONJ
ejpam-6135	204	22	−q	−q	ADJ
ejpam-6135	204	23	uniform	uniform	ADJ
ejpam-6135	204	24	ir∗	ir∗	NOUN
ejpam-6135	204	25	centred	centre	VERB
ejpam-6135	204	26	structure	structure	NOUN
ejpam-6135	204	27	space	space	NOUN
ejpam-6135	204	28	(	(	PUNCT
ejpam-6135	204	29	px	px	NOUN
ejpam-6135	204	30	,	,	PUNCT
ejpam-6135	204	31	τp	τp	PROPN
ejpam-6135	204	32	)	)	PUNCT
ejpam-6135	204	33	is	be	AUX
ejpam-6135	204	34	a	a	DET
ejpam-6135	204	35	function	function	NOUN
ejpam-6135	204	36	from	from	ADP
ejpam-6135	204	37	a	a	DET
ejpam-6135	204	38	directed	direct	VERB
ejpam-6135	204	39	set	set	NOUN
ejpam-6135	204	40	∆	∆	PROPN
ejpam-6135	204	41	to	to	ADP
ejpam-6135	204	42	px	px	PROPN
ejpam-6135	204	43	.	.	PUNCT
ejpam-6135	205	1	it	it	PRON
ejpam-6135	205	2	is	be	AUX
ejpam-6135	205	3	denoted	denote	VERB
ejpam-6135	205	4	as	as	ADP
ejpam-6135	205	5	{	{	PUNCT
ejpam-6135	205	6	pζ}ζ∈ς	pζ}ζ∈ς	NOUN
ejpam-6135	205	7	6.2	6.2	NUM
ejpam-6135	205	8	.	.	PUNCT
ejpam-6135	206	1	nets	net	NOUN
ejpam-6135	206	2	,	,	PUNCT
ejpam-6135	206	3	filters	filter	NOUN
ejpam-6135	206	4	and	and	CCONJ
ejpam-6135	206	5	convergence	convergence	NOUN
ejpam-6135	206	6	in	in	ADP
ejpam-6135	206	7	(	(	PUNCT
ejpam-6135	206	8	c	c	X
ejpam-6135	206	9	,	,	PUNCT
ejpam-6135	206	10	d	d	NOUN
ejpam-6135	206	11	)	)	PUNCT
ejpam-6135	206	12	if	if	SCONJ
ejpam-6135	206	13	−q	−q	ADJ
ejpam-6135	206	14	uniform	uniform	ADJ
ejpam-6135	206	15	ir∗	ir∗	NOUN
ejpam-6135	206	16	centred	centre	VERB
ejpam-6135	206	17	structure	structure	NOUN
ejpam-6135	206	18	space	space	NOUN
ejpam-6135	206	19	notation	notation	NOUN
ejpam-6135	206	20	:	:	PUNCT
ejpam-6135	206	21	here	here	ADV
ejpam-6135	206	22	,	,	PUNCT
ejpam-6135	206	23	throughout	throughout	ADP
ejpam-6135	206	24	this	this	DET
ejpam-6135	206	25	article	article	NOUN
ejpam-6135	206	26	the	the	DET
ejpam-6135	206	27	notation	notation	NOUN
ejpam-6135	206	28	⊘	⊘	NUM
ejpam-6135	206	29	is	be	AUX
ejpam-6135	206	30	used	use	VERB
ejpam-6135	206	31	for	for	ADP
ejpam-6135	206	32	eventually	eventually	ADV
ejpam-6135	206	33	and	and	CCONJ
ejpam-6135	206	34	⊖	⊖	NOUN
ejpam-6135	206	35	is	be	AUX
ejpam-6135	206	36	used	use	VERB
ejpam-6135	206	37	for	for	ADP
ejpam-6135	206	38	frequently	frequently	ADV
ejpam-6135	206	39	definition	definition	NOUN
ejpam-6135	206	40	23	23	NUM
ejpam-6135	206	41	.	.	PUNCT
ejpam-6135	207	1	let	let	VERB
ejpam-6135	207	2	{	{	PUNCT
ejpam-6135	207	3	pζ	pζ	NOUN
ejpam-6135	207	4	}	}	PUNCT
ejpam-6135	207	5	ζ∈ς	ζ∈ς	NOUN
ejpam-6135	207	6	be	be	AUX
ejpam-6135	207	7	a	a	DET
ejpam-6135	207	8	(	(	PUNCT
ejpam-6135	207	9	c	c	NOUN
ejpam-6135	207	10	,	,	PUNCT
ejpam-6135	207	11	d	d	NOUN
ejpam-6135	207	12	)	)	PUNCT
ejpam-6135	207	13	if	if	SCONJ
ejpam-6135	207	14	−q	−q	ADJ
ejpam-6135	207	15	uniform	uniform	ADJ
ejpam-6135	207	16	ir∗	ir∗	NOUN
ejpam-6135	207	17	centred	centre	VERB
ejpam-6135	207	18	structure	structure	NOUN
ejpam-6135	207	19	net	net	NOUN
ejpam-6135	207	20	in	in	ADP
ejpam-6135	207	21	an	an	DET
ejpam-6135	207	22	(	(	PUNCT
ejpam-6135	207	23	c	c	NOUN
ejpam-6135	207	24	,	,	PUNCT
ejpam-6135	207	25	d	d	NOUN
ejpam-6135	207	26	)	)	PUNCT
ejpam-6135	207	27	if	if	SCONJ
ejpam-6135	207	28	−q	−q	ADJ
ejpam-6135	207	29	uniform	uniform	ADJ
ejpam-6135	207	30	ir∗	ir∗	NOUN
ejpam-6135	207	31	centred	centre	VERB
ejpam-6135	207	32	structure	structure	NOUN
ejpam-6135	207	33	space	space	NOUN
ejpam-6135	207	34	px	px	PROPN
ejpam-6135	207	35	and	and	CCONJ
ejpam-6135	207	36	let	let	VERB
ejpam-6135	207	37	g	g	PRON
ejpam-6135	207	38	be	be	AUX
ejpam-6135	207	39	a	a	DET
ejpam-6135	207	40	(	(	PUNCT
ejpam-6135	207	41	c	c	NOUN
ejpam-6135	207	42	,	,	PUNCT
ejpam-6135	207	43	d	d	NOUN
ejpam-6135	207	44	)	)	PUNCT
ejpam-6135	207	45	if	if	SCONJ
ejpam-6135	207	46	−q	−q	ADJ
ejpam-6135	207	47	uniform	uniform	ADJ
ejpam-6135	207	48	ir∗	ir∗	NOUN
ejpam-6135	207	49	centred	centre	VERB
ejpam-6135	207	50	structure	structure	NOUN
ejpam-6135	207	51	subset	subset	NOUN
ejpam-6135	207	52	of	of	ADP
ejpam-6135	207	53	px	px	PROPN
ejpam-6135	207	54	.	.	PUNCT
ejpam-6135	208	1	then	then	ADV
ejpam-6135	208	2	the	the	DET
ejpam-6135	208	3	(	(	PUNCT
ejpam-6135	208	4	c	c	NOUN
ejpam-6135	208	5	,	,	PUNCT
ejpam-6135	208	6	d	d	NOUN
ejpam-6135	208	7	)	)	PUNCT
ejpam-6135	208	8	if	if	SCONJ
ejpam-6135	208	9	−q	−q	ADJ
ejpam-6135	208	10	uniform	uniform	ADJ
ejpam-6135	208	11	ir∗	ir∗	NOUN
ejpam-6135	208	12	centred	centre	VERB
ejpam-6135	208	13	structure	structure	NOUN
ejpam-6135	208	14	net	net	NOUN
ejpam-6135	208	15	is	be	AUX
ejpam-6135	208	16	expressed	express	VERB
ejpam-6135	208	17	as	as	ADP
ejpam-6135	208	18	(	(	PUNCT
ejpam-6135	208	19	i	i	NOUN
ejpam-6135	208	20	)	)	PUNCT
ejpam-6135	208	21	in	in	ADP
ejpam-6135	208	22	g	g	PROPN
ejpam-6135	208	23	iff	iff	PROPN
ejpam-6135	208	24	{	{	PUNCT
ejpam-6135	208	25	pζ	pζ	PROPN
ejpam-6135	208	26	}	}	PUNCT
ejpam-6135	208	27	∈	∈	PROPN
ejpam-6135	208	28	g	g	NOUN
ejpam-6135	208	29	,	,	PUNCT
ejpam-6135	208	30	∀ζ	∀ζ	PROPN
ejpam-6135	208	31	∈	∈	PROPN
ejpam-6135	208	32	ς	ς	PROPN
ejpam-6135	208	33	.	.	PUNCT
ejpam-6135	208	34	(	(	PUNCT
ejpam-6135	208	35	ii	ii	NOUN
ejpam-6135	208	36	)	)	PUNCT
ejpam-6135	208	37	⊘	⊘	X
ejpam-6135	209	1	∈	∈	PROPN
ejpam-6135	209	2	g	g	PROPN
ejpam-6135	209	3	iff	iff	PROPN
ejpam-6135	209	4	there	there	PRON
ejpam-6135	209	5	is	be	VERB
ejpam-6135	209	6	an	an	DET
ejpam-6135	209	7	existence	existence	NOUN
ejpam-6135	209	8	of	of	ADP
ejpam-6135	209	9	ϑ	ϑ	X
ejpam-6135	209	10	∈	∈	NOUN
ejpam-6135	209	11	ς∀α	ς∀α	NUM
ejpam-6135	209	12	∈	∈	PROPN
ejpam-6135	210	1	ς	ς	PROPN
ejpam-6135	210	2	α	α	NOUN
ejpam-6135	210	3	≥	≥	NOUN
ejpam-6135	210	4	ϑ	ϑ	X
ejpam-6135	210	5	,	,	PUNCT
ejpam-6135	210	6	{	{	PUNCT
ejpam-6135	210	7	pζ	pζ	NOUN
ejpam-6135	210	8	}	}	PUNCT
ejpam-6135	210	9	∈	∈	PROPN
ejpam-6135	210	10	g	g	PROPN
ejpam-6135	210	11	s.	s.	PROPN
ejpam-6135	210	12	thirukumaran	thirukumaran	PROPN
ejpam-6135	210	13	,	,	PUNCT
ejpam-6135	210	14	g.	g.	PROPN
ejpam-6135	210	15	k.	k.	PROPN
ejpam-6135	210	16	revathi	revathi	PROPN
ejpam-6135	210	17	/	/	SYM
ejpam-6135	210	18	eur	eur	PROPN
ejpam-6135	210	19	.	.	PUNCT
ejpam-6135	211	1	j.	j.	PROPN
ejpam-6135	211	2	pure	pure	PROPN
ejpam-6135	211	3	appl	appl	PROPN
ejpam-6135	211	4	.	.	PROPN
ejpam-6135	211	5	math	math	PROPN
ejpam-6135	211	6	,	,	PUNCT
ejpam-6135	211	7	18	18	NUM
ejpam-6135	211	8	(	(	PUNCT
ejpam-6135	211	9	2	2	NUM
ejpam-6135	211	10	)	)	PUNCT
ejpam-6135	211	11	(	(	PUNCT
ejpam-6135	211	12	2025	2025	NUM
ejpam-6135	211	13	)	)	PUNCT
ejpam-6135	211	14	,	,	PUNCT
ejpam-6135	211	15	6135	6135	NUM
ejpam-6135	211	16	11	11	NUM
ejpam-6135	211	17	of	of	ADP
ejpam-6135	211	18	17	17	NUM
ejpam-6135	211	19	(	(	PUNCT
ejpam-6135	211	20	iii	iii	NOUN
ejpam-6135	211	21	)	)	PUNCT
ejpam-6135	211	22	⊖	⊖	NOUN
ejpam-6135	211	23	∈	∈	PROPN
ejpam-6135	211	24	g	g	PROPN
ejpam-6135	211	25	,	,	PUNCT
ejpam-6135	211	26	iff	iff	PROPN
ejpam-6135	211	27	for	for	ADP
ejpam-6135	211	28	all	all	PRON
ejpam-6135	211	29	ϑ	ϑ	PRON
ejpam-6135	211	30	∈	∈	PROPN
ejpam-6135	211	31	ς	ς	NOUN
ejpam-6135	211	32	,	,	PUNCT
ejpam-6135	211	33	there	there	PRON
ejpam-6135	211	34	is	be	VERB
ejpam-6135	211	35	an	an	DET
ejpam-6135	211	36	existence	existence	NOUN
ejpam-6135	211	37	of	of	ADP
ejpam-6135	211	38	ζ	ζ	NOUN
ejpam-6135	211	39	∈	∈	PROPN
ejpam-6135	211	40	ς	ς	NOUN
ejpam-6135	211	41	,	,	PUNCT
ejpam-6135	211	42	ζ	ζ	NOUN
ejpam-6135	211	43	≥	≥	X
ejpam-6135	211	44	ϑ	ϑ	X
ejpam-6135	211	45	and	and	CCONJ
ejpam-6135	211	46	{	{	PUNCT
ejpam-6135	211	47	pζ	pζ	PROPN
ejpam-6135	211	48	}	}	PUNCT
ejpam-6135	211	49	∈	∈	PROPN
ejpam-6135	211	50	g	g	NOUN
ejpam-6135	211	51	definition	definition	NOUN
ejpam-6135	211	52	24	24	NUM
ejpam-6135	211	53	.	.	PUNCT
ejpam-6135	212	1	let	let	VERB
ejpam-6135	212	2	{	{	PUNCT
ejpam-6135	212	3	pζ	pζ	PART
ejpam-6135	212	4	}	}	PUNCT
ejpam-6135	212	5	is	be	AUX
ejpam-6135	212	6	a	a	DET
ejpam-6135	212	7	(	(	PUNCT
ejpam-6135	212	8	c	c	NOUN
ejpam-6135	212	9	,	,	PUNCT
ejpam-6135	212	10	d	d	NOUN
ejpam-6135	212	11	)	)	PUNCT
ejpam-6135	212	12	if	if	SCONJ
ejpam-6135	212	13	−q	−q	ADJ
ejpam-6135	212	14	uniform	uniform	ADJ
ejpam-6135	212	15	ir∗	ir∗	NOUN
ejpam-6135	212	16	centred	centre	VERB
ejpam-6135	212	17	structure	structure	NOUN
ejpam-6135	212	18	net	net	NOUN
ejpam-6135	212	19	in	in	ADP
ejpam-6135	212	20	the	the	DET
ejpam-6135	212	21	(	(	PUNCT
ejpam-6135	212	22	c	c	NOUN
ejpam-6135	212	23	,	,	PUNCT
ejpam-6135	212	24	d	d	NOUN
ejpam-6135	212	25	)	)	PUNCT
ejpam-6135	212	26	if	if	SCONJ
ejpam-6135	212	27	−q	−q	ADJ
ejpam-6135	212	28	uniform	uniform	ADJ
ejpam-6135	212	29	ir∗	ir∗	NOUN
ejpam-6135	212	30	centred	centre	VERB
ejpam-6135	212	31	structure	structure	NOUN
ejpam-6135	212	32	px	px	NOUN
ejpam-6135	212	33	and	and	CCONJ
ejpam-6135	212	34	p	p	NOUN
ejpam-6135	212	35	is	be	AUX
ejpam-6135	212	36	a	a	DET
ejpam-6135	212	37	(	(	PUNCT
ejpam-6135	212	38	c	c	NOUN
ejpam-6135	212	39	,	,	PUNCT
ejpam-6135	212	40	d	d	NOUN
ejpam-6135	212	41	)	)	PUNCT
ejpam-6135	212	42	if	if	SCONJ
ejpam-6135	212	43	−q	−q	ADJ
ejpam-6135	212	44	uniform	uniform	ADJ
ejpam-6135	212	45	ir∗	ir∗	NOUN
ejpam-6135	212	46	centred	centre	VERB
ejpam-6135	212	47	structure	structure	NOUN
ejpam-6135	212	48	element	element	NOUN
ejpam-6135	212	49	of	of	ADP
ejpam-6135	212	50	px	px	PROPN
ejpam-6135	212	51	.	.	PUNCT
ejpam-6135	213	1	an	an	DET
ejpam-6135	213	2	(	(	PUNCT
ejpam-6135	213	3	c	c	NOUN
ejpam-6135	213	4	,	,	PUNCT
ejpam-6135	213	5	d	d	NOUN
ejpam-6135	213	6	)	)	PUNCT
ejpam-6135	213	7	if	if	SCONJ
ejpam-6135	213	8	−q	−q	ADJ
ejpam-6135	213	9	uniform	uniform	ADJ
ejpam-6135	213	10	ir∗	ir∗	NOUN
ejpam-6135	213	11	centred	centre	VERB
ejpam-6135	213	12	structure	structure	NOUN
ejpam-6135	213	13	net	net	NOUN
ejpam-6135	213	14	converges	converge	NOUN
ejpam-6135	213	15	towards	towards	ADP
ejpam-6135	213	16	p	p	PROPN
ejpam-6135	213	17	iff	iff	PROPN
ejpam-6135	213	18	for	for	ADP
ejpam-6135	213	19	every	every	PRON
ejpam-6135	213	20	(	(	PUNCT
ejpam-6135	213	21	c	c	NOUN
ejpam-6135	213	22	,	,	PUNCT
ejpam-6135	213	23	d	d	NOUN
ejpam-6135	213	24	)	)	PUNCT
ejpam-6135	213	25	if	if	SCONJ
ejpam-6135	213	26	−q	−q	ADJ
ejpam-6135	213	27	uniform	uniform	ADJ
ejpam-6135	213	28	ir∗	ir∗	NOUN
ejpam-6135	213	29	centred	centre	VERB
ejpam-6135	213	30	structure	structure	NOUN
ejpam-6135	213	31	neighborhood	neighborhood	NOUN
ejpam-6135	213	32	u	u	NOUN
ejpam-6135	213	33	of	of	ADP
ejpam-6135	213	34	p	p	NOUN
ejpam-6135	213	35	,	,	PUNCT
ejpam-6135	213	36	such	such	ADJ
ejpam-6135	213	37	that	that	SCONJ
ejpam-6135	213	38	{	{	PUNCT
ejpam-6135	213	39	pζ	pζ	NOUN
ejpam-6135	213	40	}	}	PUNCT
ejpam-6135	213	41	⊘	⊘	PROPN
ejpam-6135	213	42	in	in	ADP
ejpam-6135	213	43	u	u	PROPN
ejpam-6135	213	44	.	.	PUNCT
ejpam-6135	214	1	definition	definition	NOUN
ejpam-6135	214	2	25	25	NUM
ejpam-6135	214	3	.	.	PUNCT
ejpam-6135	215	1	a	a	DET
ejpam-6135	215	2	pair	pair	NOUN
ejpam-6135	215	3	(	(	PUNCT
ejpam-6135	215	4	c	c	X
ejpam-6135	215	5	,	,	PUNCT
ejpam-6135	215	6	d	d	NOUN
ejpam-6135	215	7	)	)	PUNCT
ejpam-6135	215	8	if	if	SCONJ
ejpam-6135	215	9	−q	−q	ADJ
ejpam-6135	215	10	uniform	uniform	ADJ
ejpam-6135	215	11	ir∗	ir∗	NOUN
ejpam-6135	215	12	centred	centre	VERB
ejpam-6135	215	13	structure	structure	NOUN
ejpam-6135	215	14	element	element	NOUN
ejpam-6135	215	15	p1	p1	NOUN
ejpam-6135	215	16	of	of	ADP
ejpam-6135	215	17	px	px	PROPN
ejpam-6135	215	18	is	be	AUX
ejpam-6135	215	19	said	say	VERB
ejpam-6135	215	20	to	to	PART
ejpam-6135	215	21	be	be	AUX
ejpam-6135	215	22	a	a	DET
ejpam-6135	215	23	(	(	PUNCT
ejpam-6135	215	24	c	c	NOUN
ejpam-6135	215	25	,	,	PUNCT
ejpam-6135	215	26	d	d	NOUN
ejpam-6135	215	27	)	)	PUNCT
ejpam-6135	215	28	if	if	SCONJ
ejpam-6135	215	29	−q	−q	ADJ
ejpam-6135	215	30	uniform	uniform	ADJ
ejpam-6135	215	31	ir∗	ir∗	NOUN
ejpam-6135	215	32	centred	centre	VERB
ejpam-6135	215	33	structure	structure	NOUN
ejpam-6135	215	34	accumulation	accumulation	NOUN
ejpam-6135	215	35	point	point	NOUN
ejpam-6135	215	36	or	or	CCONJ
ejpam-6135	215	37	cluster	cluster	NOUN
ejpam-6135	215	38	point	point	NOUN
ejpam-6135	215	39	of	of	ADP
ejpam-6135	215	40	a	a	DET
ejpam-6135	215	41	(	(	PUNCT
ejpam-6135	215	42	c	c	NOUN
ejpam-6135	215	43	,	,	PUNCT
ejpam-6135	215	44	d	d	NOUN
ejpam-6135	215	45	)	)	PUNCT
ejpam-6135	215	46	if	if	SCONJ
ejpam-6135	215	47	−q	−q	ADJ
ejpam-6135	215	48	uniform	uniform	ADJ
ejpam-6135	215	49	ir∗	ir∗	NOUN
ejpam-6135	215	50	centred	centre	VERB
ejpam-6135	215	51	structure	structure	NOUN
ejpam-6135	215	52	net	net	PROPN
ejpam-6135	215	53	iff	iff	PROPN
ejpam-6135	215	54	for	for	ADP
ejpam-6135	215	55	every	every	PRON
ejpam-6135	215	56	(	(	PUNCT
ejpam-6135	215	57	c	c	NOUN
ejpam-6135	215	58	,	,	PUNCT
ejpam-6135	215	59	d	d	NOUN
ejpam-6135	215	60	)	)	PUNCT
ejpam-6135	215	61	if	if	SCONJ
ejpam-6135	215	62	−q	−q	ADJ
ejpam-6135	215	63	uniform	uniform	ADJ
ejpam-6135	215	64	ir∗	ir∗	NOUN
ejpam-6135	215	65	centred	centre	VERB
ejpam-6135	215	66	structure	structure	NOUN
ejpam-6135	215	67	neighborhood	neighborhood	NOUN
ejpam-6135	215	68	u	u	NOUN
ejpam-6135	215	69	of	of	ADP
ejpam-6135	215	70	p1	p1	NOUN
ejpam-6135	215	71	,	,	PUNCT
ejpam-6135	215	72	so	so	SCONJ
ejpam-6135	215	73	that	that	SCONJ
ejpam-6135	215	74	(	(	PUNCT
ejpam-6135	215	75	c	c	X
ejpam-6135	215	76	,	,	PUNCT
ejpam-6135	215	77	d	d	NOUN
ejpam-6135	215	78	)	)	PUNCT
ejpam-6135	215	79	if	if	SCONJ
ejpam-6135	215	80	−q	−q	ADJ
ejpam-6135	215	81	uniform	uniform	ADJ
ejpam-6135	215	82	ir∗	ir∗	NOUN
ejpam-6135	215	83	centred	centre	VERB
ejpam-6135	215	84	structure	structure	NOUN
ejpam-6135	215	85	net	net	NOUN
ejpam-6135	215	86	is	be	AUX
ejpam-6135	215	87	⊖	⊖	NOUN
ejpam-6135	215	88	in	in	ADP
ejpam-6135	215	89	u	u	PROPN
ejpam-6135	215	90	.	.	PUNCT
ejpam-6135	216	1	definition	definition	NOUN
ejpam-6135	216	2	26	26	NUM
ejpam-6135	216	3	.	.	PUNCT
ejpam-6135	217	1	let	let	VERB
ejpam-6135	217	2	(	(	PUNCT
ejpam-6135	217	3	c	c	X
ejpam-6135	217	4	,	,	PUNCT
ejpam-6135	217	5	d	d	NOUN
ejpam-6135	217	6	)	)	PUNCT
ejpam-6135	217	7	if	if	SCONJ
ejpam-6135	217	8	−q	−q	ADJ
ejpam-6135	217	9	uniform	uniform	ADJ
ejpam-6135	217	10	ir∗	ir∗	NOUN
ejpam-6135	217	11	centred	centre	VERB
ejpam-6135	217	12	structure	structure	NOUN
ejpam-6135	217	13	net	net	NOUN
ejpam-6135	217	14	{	{	PUNCT
ejpam-6135	217	15	p	p	X
ejpam-6135	217	16	}	}	PUNCT
ejpam-6135	217	17	in	in	ADP
ejpam-6135	217	18	a	a	DET
ejpam-6135	217	19	set	set	NOUN
ejpam-6135	217	20	px	px	NOUN
ejpam-6135	217	21	is	be	AUX
ejpam-6135	217	22	said	say	VERB
ejpam-6135	217	23	to	to	PART
ejpam-6135	217	24	be	be	AUX
ejpam-6135	217	25	(	(	PUNCT
ejpam-6135	217	26	c	c	X
ejpam-6135	217	27	,	,	PUNCT
ejpam-6135	217	28	d	d	NOUN
ejpam-6135	217	29	)	)	PUNCT
ejpam-6135	217	30	if	if	SCONJ
ejpam-6135	217	31	−q	−q	ADJ
ejpam-6135	217	32	uniform	uniform	ADJ
ejpam-6135	217	33	ir∗	ir∗	NOUN
ejpam-6135	217	34	centred	centre	VERB
ejpam-6135	217	35	structure	structure	NOUN
ejpam-6135	217	36	universal	universal	ADJ
ejpam-6135	217	37	or	or	CCONJ
ejpam-6135	217	38	(	(	PUNCT
ejpam-6135	217	39	c	c	X
ejpam-6135	217	40	,	,	PUNCT
ejpam-6135	217	41	d	d	NOUN
ejpam-6135	217	42	)	)	PUNCT
ejpam-6135	218	1	if	if	SCONJ
ejpam-6135	218	2	−q	−q	ADJ
ejpam-6135	218	3	uniform	uniform	ADJ
ejpam-6135	218	4	ir∗	ir∗	NOUN
ejpam-6135	218	5	centred	centre	VERB
ejpam-6135	218	6	structure	structure	NOUN
ejpam-6135	218	7	ultranet	ultranet	NOUN
ejpam-6135	218	8	,	,	PUNCT
ejpam-6135	218	9	if	if	SCONJ
ejpam-6135	218	10	for	for	ADP
ejpam-6135	218	11	every	every	DET
ejpam-6135	218	12	(	(	PUNCT
ejpam-6135	218	13	c	c	NOUN
ejpam-6135	218	14	,	,	PUNCT
ejpam-6135	218	15	d	d	NOUN
ejpam-6135	218	16	)	)	PUNCT
ejpam-6135	218	17	if	if	SCONJ
ejpam-6135	218	18	−q	−q	ADJ
ejpam-6135	218	19	uniform	uniform	ADJ
ejpam-6135	218	20	ir∗	ir∗	NOUN
ejpam-6135	218	21	centred	centre	VERB
ejpam-6135	218	22	structure	structure	NOUN
ejpam-6135	218	23	subset	subset	VERB
ejpam-6135	218	24	a	a	PRON
ejpam-6135	218	25	of	of	ADP
ejpam-6135	218	26	px	px	PROPN
ejpam-6135	218	27	,	,	PUNCT
ejpam-6135	218	28	either	either	CCONJ
ejpam-6135	218	29	{	{	PUNCT
ejpam-6135	218	30	p	p	X
ejpam-6135	218	31	}	}	PUNCT
ejpam-6135	218	32	is	be	AUX
ejpam-6135	218	33	⊘	⊘	X
ejpam-6135	218	34	in	in	ADP
ejpam-6135	218	35	a	a	PRON
ejpam-6135	218	36	or	or	CCONJ
ejpam-6135	218	37	{	{	PUNCT
ejpam-6135	218	38	p	p	X
ejpam-6135	218	39	}	}	PUNCT
ejpam-6135	218	40	is	be	AUX
ejpam-6135	218	41	⊘	⊘	X
ejpam-6135	218	42	in	in	ADP
ejpam-6135	218	43	px	px	NOUN
ejpam-6135	218	44	−a	−a	NOUN
ejpam-6135	218	45	.	.	PUNCT
ejpam-6135	219	1	definition	definition	NOUN
ejpam-6135	219	2	27	27	NUM
ejpam-6135	219	3	.	.	PUNCT
ejpam-6135	220	1	a	a	DET
ejpam-6135	220	2	collection	collection	NOUN
ejpam-6135	220	3	ϕ	ϕ	NOUN
ejpam-6135	220	4	represents	represent	VERB
ejpam-6135	220	5	(	(	PUNCT
ejpam-6135	220	6	c	c	X
ejpam-6135	220	7	,	,	PUNCT
ejpam-6135	220	8	d	d	NOUN
ejpam-6135	220	9	)	)	PUNCT
ejpam-6135	220	10	if	if	SCONJ
ejpam-6135	220	11	−q	−q	ADJ
ejpam-6135	220	12	uniform	uniform	ADJ
ejpam-6135	220	13	ir∗	ir∗	NOUN
ejpam-6135	220	14	centred	centre	VERB
ejpam-6135	220	15	structure	structure	NOUN
ejpam-6135	220	16	continuous	continuous	ADJ
ejpam-6135	220	17	function	function	NOUN
ejpam-6135	220	18	on	on	ADP
ejpam-6135	220	19	an	an	DET
ejpam-6135	220	20	(	(	PUNCT
ejpam-6135	220	21	c	c	NOUN
ejpam-6135	220	22	,	,	PUNCT
ejpam-6135	220	23	d	d	NOUN
ejpam-6135	220	24	)	)	PUNCT
ejpam-6135	220	25	if	if	SCONJ
ejpam-6135	220	26	−q	−q	ADJ
ejpam-6135	220	27	uniform	uniform	ADJ
ejpam-6135	220	28	ir∗	ir∗	NOUN
ejpam-6135	220	29	centred	centre	VERB
ejpam-6135	220	30	structure	structure	NOUN
ejpam-6135	220	31	space	space	NOUN
ejpam-6135	220	32	px	px	NOUN
ejpam-6135	220	33	.	.	PUNCT
ejpam-6135	221	1	a	a	DET
ejpam-6135	221	2	(	(	PUNCT
ejpam-6135	221	3	c	c	NOUN
ejpam-6135	221	4	,	,	PUNCT
ejpam-6135	221	5	d	d	NOUN
ejpam-6135	221	6	)	)	PUNCT
ejpam-6135	221	7	if	if	SCONJ
ejpam-6135	221	8	−q	−q	ADJ
ejpam-6135	221	9	uniform	uniform	ADJ
ejpam-6135	221	10	ir∗	ir∗	NOUN
ejpam-6135	221	11	centred	centre	VERB
ejpam-6135	221	12	structure	structure	NOUN
ejpam-6135	221	13	net	net	NOUN
ejpam-6135	221	14	{	{	PUNCT
ejpam-6135	221	15	pi	pi	NOUN
ejpam-6135	221	16	}	}	PUNCT
ejpam-6135	221	17	in	in	ADP
ejpam-6135	221	18	px	px	PROPN
ejpam-6135	221	19	will	will	AUX
ejpam-6135	221	20	be	be	AUX
ejpam-6135	221	21	called	call	VERB
ejpam-6135	221	22	as	as	ADP
ejpam-6135	221	23	(	(	PUNCT
ejpam-6135	221	24	c	c	X
ejpam-6135	221	25	,	,	PUNCT
ejpam-6135	221	26	d	d	NOUN
ejpam-6135	221	27	)	)	PUNCT
ejpam-6135	221	28	if	if	SCONJ
ejpam-6135	221	29	−q	−q	ADJ
ejpam-6135	221	30	uniform	uniform	ADJ
ejpam-6135	221	31	ir∗	ir∗	NOUN
ejpam-6135	221	32	centred	centre	VERB
ejpam-6135	221	33	structure	structure	NOUN
ejpam-6135	221	34	ϕ	ϕ	PROPN
ejpam-6135	221	35	net	net	NOUN
ejpam-6135	221	36	,	,	PUNCT
ejpam-6135	221	37	converges	converge	VERB
ejpam-6135	221	38	to	to	ADP
ejpam-6135	221	39	each	each	DET
ejpam-6135	221	40	f	f	NOUN
ejpam-6135	221	41	in	in	ADP
ejpam-6135	221	42	the	the	DET
ejpam-6135	221	43	mapping	mapping	NOUN
ejpam-6135	221	44	ϕ.	ϕ.	ADJ
ejpam-6135	221	45	definition	definition	NOUN
ejpam-6135	221	46	28	28	NUM
ejpam-6135	221	47	.	.	PUNCT
ejpam-6135	222	1	a	a	DET
ejpam-6135	222	2	mapping	mapping	NOUN
ejpam-6135	222	3	ϕ	ϕ	NOUN
ejpam-6135	222	4	contains	contain	VERB
ejpam-6135	222	5	a	a	DET
ejpam-6135	222	6	collection	collection	NOUN
ejpam-6135	222	7	of	of	ADP
ejpam-6135	222	8	bdd	bdd	PROPN
ejpam-6135	222	9	real	real	ADV
ejpam-6135	222	10	valued	value	VERB
ejpam-6135	222	11	continuous	continuous	ADJ
ejpam-6135	222	12	function	function	NOUN
ejpam-6135	222	13	on	on	ADP
ejpam-6135	222	14	px	px	PROPN
ejpam-6135	222	15	.	.	PUNCT
ejpam-6135	223	1	here	here	ADV
ejpam-6135	223	2	,	,	PUNCT
ejpam-6135	223	3	px	px	PROPN
ejpam-6135	223	4	is	be	AUX
ejpam-6135	223	5	a	a	DET
ejpam-6135	223	6	(	(	PUNCT
ejpam-6135	223	7	c	c	NOUN
ejpam-6135	223	8	,	,	PUNCT
ejpam-6135	223	9	d	d	NOUN
ejpam-6135	223	10	)	)	PUNCT
ejpam-6135	223	11	if	if	SCONJ
ejpam-6135	223	12	−q	−q	ADJ
ejpam-6135	223	13	uniform	uniform	ADJ
ejpam-6135	223	14	ir∗	ir∗	NOUN
ejpam-6135	223	15	centred	centre	VERB
ejpam-6135	223	16	structure	structure	NOUN
ejpam-6135	223	17	compact	compact	ADJ
ejpam-6135	223	18	set	set	NOUN
ejpam-6135	223	19	,	,	PUNCT
ejpam-6135	223	20	for	for	SCONJ
ejpam-6135	223	21	every	every	DET
ejpam-6135	223	22	ϕ	ϕ	PROPN
ejpam-6135	223	23	net	net	NOUN
ejpam-6135	223	24	has	have	VERB
ejpam-6135	223	25	an	an	DET
ejpam-6135	223	26	(	(	PUNCT
ejpam-6135	223	27	c	c	NOUN
ejpam-6135	223	28	,	,	PUNCT
ejpam-6135	223	29	d	d	NOUN
ejpam-6135	223	30	)	)	PUNCT
ejpam-6135	223	31	if	if	SCONJ
ejpam-6135	223	32	−q	−q	ADJ
ejpam-6135	223	33	uniform	uniform	ADJ
ejpam-6135	223	34	ir∗	ir∗	NOUN
ejpam-6135	223	35	centred	centre	VERB
ejpam-6135	223	36	structure	structure	NOUN
ejpam-6135	223	37	cluster	cluster	NOUN
ejpam-6135	223	38	point	point	NOUN
ejpam-6135	223	39	in	in	ADP
ejpam-6135	223	40	px	px	PROPN
ejpam-6135	223	41	.	.	PUNCT
ejpam-6135	224	1	definition	definition	NOUN
ejpam-6135	224	2	29	29	NUM
ejpam-6135	224	3	.	.	PUNCT
ejpam-6135	225	1	let	let	VERB
ejpam-6135	225	2	px	px	PART
ejpam-6135	225	3	be	be	AUX
ejpam-6135	225	4	an	an	DET
ejpam-6135	225	5	(	(	PUNCT
ejpam-6135	225	6	c	c	NOUN
ejpam-6135	225	7	,	,	PUNCT
ejpam-6135	225	8	d	d	NOUN
ejpam-6135	225	9	)	)	PUNCT
ejpam-6135	225	10	if	if	SCONJ
ejpam-6135	225	11	−q	−q	ADJ
ejpam-6135	225	12	uniform	uniform	ADJ
ejpam-6135	225	13	ir∗	ir∗	NOUN
ejpam-6135	225	14	centred	centre	VERB
ejpam-6135	225	15	structure	structure	NOUN
ejpam-6135	225	16	space	space	NOUN
ejpam-6135	225	17	,	,	PUNCT
ejpam-6135	225	18	c∗(px)=	c∗(px)=	CCONJ
ejpam-6135	225	19	{	{	PUNCT
ejpam-6135	225	20	fζ	fζ	ADP
ejpam-6135	225	21	:	:	PUNCT
ejpam-6135	225	22	ζ	ζ	NOUN
ejpam-6135	225	23	∈	∈	PROPN
ejpam-6135	225	24	ς	ς	AUX
ejpam-6135	225	25	}	}	PUNCT
ejpam-6135	225	26	be	be	AUX
ejpam-6135	225	27	the	the	DET
ejpam-6135	225	28	collection	collection	NOUN
ejpam-6135	225	29	of	of	ADP
ejpam-6135	225	30	all	all	DET
ejpam-6135	225	31	bdd	bdd	PROPN
ejpam-6135	225	32	real	real	ADV
ejpam-6135	225	33	-	-	PUNCT
ejpam-6135	225	34	valued	value	VERB
ejpam-6135	225	35	continuous	continuous	ADJ
ejpam-6135	225	36	function	function	NOUN
ejpam-6135	225	37	on	on	ADP
ejpam-6135	225	38	px	px	PROPN
ejpam-6135	225	39	.	.	PUNCT
ejpam-6135	226	1	regarding	regard	VERB
ejpam-6135	226	2	a	a	DET
ejpam-6135	226	3	c∗(px	c∗(px	NOUN
ejpam-6135	226	4	)	)	PUNCT
ejpam-6135	226	5	net	net	NOUN
ejpam-6135	226	6	{	{	PUNCT
ejpam-6135	226	7	pi	pi	NOUN
ejpam-6135	226	8	}	}	PUNCT
ejpam-6135	226	9	and	and	CCONJ
ejpam-6135	226	10	f{pi}=	f{pi}=	NOUN
ejpam-6135	226	11	{	{	PUNCT
ejpam-6135	226	12	u	u	NOUN
ejpam-6135	226	13	:	:	PUNCT
ejpam-6135	226	14	u	u	NOUN
ejpam-6135	226	15	is	be	AUX
ejpam-6135	226	16	a	a	DET
ejpam-6135	226	17	(	(	PUNCT
ejpam-6135	226	18	c	c	NOUN
ejpam-6135	226	19	,	,	PUNCT
ejpam-6135	226	20	d	d	NOUN
ejpam-6135	226	21	)	)	PUNCT
ejpam-6135	226	22	if	if	SCONJ
ejpam-6135	226	23	−q	−q	ADJ
ejpam-6135	226	24	uniform	uniform	ADJ
ejpam-6135	226	25	ir∗	ir∗	NOUN
ejpam-6135	226	26	centred	centre	VERB
ejpam-6135	226	27	structure	structure	NOUN
ejpam-6135	226	28	open	open	ADJ
ejpam-6135	226	29	set	set	VERB
ejpam-6135	226	30	in	in	ADP
ejpam-6135	226	31	px	px	PROPN
ejpam-6135	226	32	and	and	CCONJ
ejpam-6135	226	33	{	{	PUNCT
ejpam-6135	226	34	pi	pi	NOUN
ejpam-6135	226	35	}	}	PUNCT
ejpam-6135	226	36	is	be	AUX
ejpam-6135	226	37	⊘	⊘	X
ejpam-6135	226	38	in	in	ADP
ejpam-6135	226	39	u	u	NOUN
ejpam-6135	226	40	}	}	PUNCT
ejpam-6135	226	41	.	.	PUNCT
ejpam-6135	227	1	by	by	ADP
ejpam-6135	227	2	knowing	know	VERB
ejpam-6135	227	3	that	that	SCONJ
ejpam-6135	227	4	,	,	PUNCT
ejpam-6135	227	5	f{pi	f{pi	PROPN
ejpam-6135	227	6	}	}	PUNCT
ejpam-6135	227	7	is	be	AUX
ejpam-6135	227	8	an	an	DET
ejpam-6135	227	9	(	(	PUNCT
ejpam-6135	227	10	c	c	NOUN
ejpam-6135	227	11	,	,	PUNCT
ejpam-6135	227	12	d	d	NOUN
ejpam-6135	227	13	)	)	PUNCT
ejpam-6135	227	14	if	if	SCONJ
ejpam-6135	227	15	−q	−q	ADJ
ejpam-6135	227	16	uniform	uniform	ADJ
ejpam-6135	227	17	ir∗	ir∗	NOUN
ejpam-6135	227	18	centred	centre	VERB
ejpam-6135	227	19	structure	structure	NOUN
ejpam-6135	227	20	open	open	ADJ
ejpam-6135	227	21	filter	filter	NOUN
ejpam-6135	227	22	and	and	CCONJ
ejpam-6135	227	23	some	some	PRON
ejpam-6135	227	24	fζ	fζ	ADP
ejpam-6135	227	25	∈	∈	PROPN
ejpam-6135	227	26	c∗(px	c∗(px	NOUN
ejpam-6135	227	27	)	)	PUNCT
ejpam-6135	227	28	,	,	PUNCT
ejpam-6135	227	29	any	any	PRON
ejpam-6135	227	30	ϵ	ϵ	X
ejpam-6135	227	31	>	>	X
ejpam-6135	227	32	0	0	NUM
ejpam-6135	227	33	,	,	PUNCT
ejpam-6135	227	34	(	(	PUNCT
ejpam-6135	227	35	fζ	fζ	ADJ
ejpam-6135	227	36	)	)	PUNCT
ejpam-6135	227	37	−1((rζ−ε	−1((rζ−ε	PROPN
ejpam-6135	227	38	,	,	PUNCT
ejpam-6135	227	39	rζ+ε	rζ+ε	NUM
ejpam-6135	227	40	)	)	PUNCT
ejpam-6135	227	41	)	)	PUNCT
ejpam-6135	227	42	∈	∈	PROPN
ejpam-6135	227	43	f{pi	f{pi	PROPN
ejpam-6135	227	44	}	}	PUNCT
ejpam-6135	228	1	where	where	SCONJ
ejpam-6135	228	2	rζ=	rζ=	VERB
ejpam-6135	228	3	lim	lim	PROPN
ejpam-6135	228	4	{	{	PUNCT
ejpam-6135	228	5	fζ(pi	fζ(pi	PROPN
ejpam-6135	228	6	)	)	PUNCT
ejpam-6135	228	7	}	}	PUNCT
ejpam-6135	228	8	f{pi	f{pi	PROPN
ejpam-6135	228	9	}	}	PUNCT
ejpam-6135	228	10	is	be	AUX
ejpam-6135	228	11	the	the	DET
ejpam-6135	228	12	(	(	PUNCT
ejpam-6135	228	13	c	c	NOUN
ejpam-6135	228	14	,	,	PUNCT
ejpam-6135	228	15	d	d	NOUN
ejpam-6135	228	16	)	)	PUNCT
ejpam-6135	228	17	if	if	SCONJ
ejpam-6135	228	18	−q	−q	ADJ
ejpam-6135	228	19	uniform	uniform	ADJ
ejpam-6135	228	20	ir∗	ir∗	NOUN
ejpam-6135	228	21	centred	centre	VERB
ejpam-6135	228	22	structure	structure	NOUN
ejpam-6135	228	23	open	open	ADJ
ejpam-6135	228	24	filter	filter	NOUN
ejpam-6135	228	25	in	in	ADP
ejpam-6135	228	26	px	px	NOUN
ejpam-6135	228	27	induced	induce	VERB
ejpam-6135	228	28	by	by	ADP
ejpam-6135	228	29	{	{	PUNCT
ejpam-6135	228	30	pi	pi	NOUN
ejpam-6135	228	31	}	}	PUNCT
ejpam-6135	228	32	.	.	PUNCT
ejpam-6135	229	1	definition	definition	NOUN
ejpam-6135	229	2	30	30	NUM
ejpam-6135	229	3	.	.	PUNCT
ejpam-6135	230	1	let	let	VERB
ejpam-6135	230	2	f	f	PROPN
ejpam-6135	230	3	is	be	AUX
ejpam-6135	230	4	a	a	DET
ejpam-6135	230	5	(	(	PUNCT
ejpam-6135	230	6	c	c	NOUN
ejpam-6135	230	7	,	,	PUNCT
ejpam-6135	230	8	d	d	NOUN
ejpam-6135	230	9	)	)	PUNCT
ejpam-6135	230	10	if	if	SCONJ
ejpam-6135	230	11	−q	−q	ADJ
ejpam-6135	230	12	uniform	uniform	ADJ
ejpam-6135	230	13	ir∗	ir∗	NOUN
ejpam-6135	230	14	centred	centre	VERB
ejpam-6135	230	15	strcture	strcture	NOUN
ejpam-6135	230	16	filter	filter	NOUN
ejpam-6135	230	17	on	on	ADP
ejpam-6135	230	18	px	px	PROPN
ejpam-6135	230	19	.	.	PUNCT
ejpam-6135	231	1	let	let	VERB
ejpam-6135	231	2	ςf=	ςf=	PROPN
ejpam-6135	231	3	{	{	PUNCT
ejpam-6135	231	4	(	(	PUNCT
ejpam-6135	231	5	p	p	X
ejpam-6135	231	6	,	,	PUNCT
ejpam-6135	231	7	f	f	PROPN
ejpam-6135	231	8	)	)	PUNCT
ejpam-6135	231	9	:	:	PUNCT
ejpam-6135	232	1	p	p	X
ejpam-6135	232	2	∈	∈	X
ejpam-6135	232	3	f	f	X
ejpam-6135	232	4	∈	∈	PROPN
ejpam-6135	232	5	f	f	PROPN
ejpam-6135	232	6	}	}	PUNCT
ejpam-6135	232	7	.	.	PUNCT
ejpam-6135	233	1	so	so	ADV
ejpam-6135	233	2	ςf	ςf	PROPN
ejpam-6135	233	3	is	be	AUX
ejpam-6135	233	4	expressed	express	VERB
ejpam-6135	233	5	as	as	ADP
ejpam-6135	233	6	the	the	DET
ejpam-6135	233	7	relation	relation	NOUN
ejpam-6135	233	8	(	(	PUNCT
ejpam-6135	233	9	p1	p1	NOUN
ejpam-6135	233	10	,	,	PUNCT
ejpam-6135	233	11	f1	f1	NOUN
ejpam-6135	233	12	)	)	PUNCT
ejpam-6135	233	13	≤	≤	NOUN
ejpam-6135	233	14	(	(	PUNCT
ejpam-6135	233	15	p2	p2	NOUN
ejpam-6135	233	16	,	,	PUNCT
ejpam-6135	233	17	f2	f2	PROPN
ejpam-6135	233	18	)	)	PUNCT
ejpam-6135	233	19	iff	iff	PROPN
ejpam-6135	233	20	f2	f2	PROPN
ejpam-6135	233	21	⊂	⊂	PROPN
ejpam-6135	233	22	f1	f1	PROPN
ejpam-6135	233	23	and	and	CCONJ
ejpam-6135	233	24	the	the	DET
ejpam-6135	233	25	function	function	NOUN
ejpam-6135	234	1	m	m	VERB
ejpam-6135	234	2	:	:	PUNCT
ejpam-6135	234	3	ςf	ςf	PROPN
ejpam-6135	234	4	→	→	SYM
ejpam-6135	234	5	px	px	NOUN
ejpam-6135	234	6	expressed	express	VERB
ejpam-6135	234	7	as	as	ADP
ejpam-6135	234	8	m(p	m(p	PROPN
ejpam-6135	234	9	,	,	PUNCT
ejpam-6135	234	10	f1	f1	NOUN
ejpam-6135	234	11	)	)	PUNCT
ejpam-6135	235	1	=	=	PUNCT
ejpam-6135	236	1	p	p	NOUN
ejpam-6135	236	2	is	be	AUX
ejpam-6135	236	3	an	an	DET
ejpam-6135	236	4	(	(	PUNCT
ejpam-6135	236	5	c	c	NOUN
ejpam-6135	236	6	,	,	PUNCT
ejpam-6135	236	7	d	d	NOUN
ejpam-6135	236	8	)	)	PUNCT
ejpam-6135	236	9	if	if	SCONJ
ejpam-6135	236	10	−q	−q	ADJ
ejpam-6135	236	11	uniform	uniform	ADJ
ejpam-6135	236	12	ir∗	ir∗	NOUN
ejpam-6135	236	13	centred	centre	VERB
ejpam-6135	236	14	structure	structure	NOUN
ejpam-6135	236	15	net	net	NOUN
ejpam-6135	236	16	in	in	ADP
ejpam-6135	236	17	px	px	PROPN
ejpam-6135	236	18	.	.	PUNCT
ejpam-6135	237	1	it	it	PRON
ejpam-6135	237	2	is	be	AUX
ejpam-6135	237	3	called	call	VERB
ejpam-6135	237	4	as	as	ADP
ejpam-6135	237	5	(	(	PUNCT
ejpam-6135	237	6	c	c	X
ejpam-6135	237	7	,	,	PUNCT
ejpam-6135	237	8	d	d	NOUN
ejpam-6135	237	9	)	)	PUNCT
ejpam-6135	237	10	if	if	SCONJ
ejpam-6135	237	11	−q	−q	ADJ
ejpam-6135	237	12	uniform	uniform	ADJ
ejpam-6135	237	13	ir∗	ir∗	NOUN
ejpam-6135	237	14	centred	centre	VERB
ejpam-6135	237	15	net	net	NOUN
ejpam-6135	237	16	based	base	VERB
ejpam-6135	237	17	on	on	ADP
ejpam-6135	237	18	f	f	PROPN
ejpam-6135	237	19	.	.	PUNCT
ejpam-6135	238	1	definition	definition	NOUN
ejpam-6135	238	2	31	31	NUM
ejpam-6135	238	3	.	.	PUNCT
ejpam-6135	239	1	the	the	DET
ejpam-6135	239	2	pair	pair	NOUN
ejpam-6135	239	3	(	(	PUNCT
ejpam-6135	239	4	c	c	X
ejpam-6135	239	5	,	,	PUNCT
ejpam-6135	239	6	d	d	NOUN
ejpam-6135	239	7	)	)	PUNCT
ejpam-6135	239	8	be	be	AUX
ejpam-6135	239	9	an	an	DET
ejpam-6135	239	10	if	if	SCONJ
ejpam-6135	239	11	−q	−q	ADJ
ejpam-6135	239	12	uniform	uniform	ADJ
ejpam-6135	239	13	ir∗	ir∗	NOUN
ejpam-6135	239	14	centred	centre	VERB
ejpam-6135	239	15	structure	structure	NOUN
ejpam-6135	239	16	filter	filter	NOUN
ejpam-6135	239	17	fp	fp	PROPN
ejpam-6135	239	18	converges	converge	NOUN
ejpam-6135	239	19	to	to	ADP
ejpam-6135	239	20	p	p	NOUN
ejpam-6135	239	21	in	in	ADP
ejpam-6135	239	22	px	px	PROPN
ejpam-6135	239	23	,	,	PUNCT
ejpam-6135	239	24	if	if	SCONJ
ejpam-6135	239	25	the	the	DET
ejpam-6135	239	26	(	(	PUNCT
ejpam-6135	239	27	c	c	NOUN
ejpam-6135	239	28	,	,	PUNCT
ejpam-6135	239	29	d	d	NOUN
ejpam-6135	239	30	)	)	PUNCT
ejpam-6135	239	31	if	if	SCONJ
ejpam-6135	239	32	−q	−q	ADJ
ejpam-6135	239	33	uniform	uniform	ADJ
ejpam-6135	239	34	ir∗	ir∗	NOUN
ejpam-6135	239	35	centred	centre	VERB
ejpam-6135	239	36	structure	structure	NOUN
ejpam-6135	239	37	net	net	NOUN
ejpam-6135	239	38	converges	converge	NOUN
ejpam-6135	239	39	to	to	ADP
ejpam-6135	239	40	p	p	NOUN
ejpam-6135	239	41	with	with	ADP
ejpam-6135	239	42	respect	respect	NOUN
ejpam-6135	239	43	to	to	ADP
ejpam-6135	239	44	fp	fp	PROPN
ejpam-6135	239	45	.	.	PUNCT
ejpam-6135	240	1	s.	s.	PROPN
ejpam-6135	240	2	thirukumaran	thirukumaran	PROPN
ejpam-6135	240	3	,	,	PUNCT
ejpam-6135	240	4	g.	g.	PROPN
ejpam-6135	240	5	k.	k.	PROPN
ejpam-6135	240	6	revathi	revathi	PROPN
ejpam-6135	240	7	/	/	SYM
ejpam-6135	240	8	eur	eur	PROPN
ejpam-6135	240	9	.	.	PUNCT
ejpam-6135	241	1	j.	j.	PROPN
ejpam-6135	241	2	pure	pure	PROPN
ejpam-6135	241	3	appl	appl	PROPN
ejpam-6135	241	4	.	.	PROPN
ejpam-6135	241	5	math	math	PROPN
ejpam-6135	241	6	,	,	PUNCT
ejpam-6135	241	7	18	18	NUM
ejpam-6135	241	8	(	(	PUNCT
ejpam-6135	241	9	2	2	NUM
ejpam-6135	241	10	)	)	PUNCT
ejpam-6135	241	11	(	(	PUNCT
ejpam-6135	241	12	2025	2025	NUM
ejpam-6135	241	13	)	)	PUNCT
ejpam-6135	241	14	,	,	PUNCT
ejpam-6135	241	15	6135	6135	NUM
ejpam-6135	241	16	12	12	NUM
ejpam-6135	241	17	of	of	ADP
ejpam-6135	241	18	17	17	NUM
ejpam-6135	241	19	definition	definition	NOUN
ejpam-6135	241	20	32	32	NUM
ejpam-6135	241	21	.	.	PUNCT
ejpam-6135	242	1	let	let	VERB
ejpam-6135	242	2	p	p	PRON
ejpam-6135	242	3	be	be	AUX
ejpam-6135	242	4	a	a	DET
ejpam-6135	242	5	(	(	PUNCT
ejpam-6135	242	6	c	c	NOUN
ejpam-6135	242	7	,	,	PUNCT
ejpam-6135	242	8	d	d	NOUN
ejpam-6135	242	9	)	)	PUNCT
ejpam-6135	242	10	if	if	SCONJ
ejpam-6135	242	11	−q	−q	ADJ
ejpam-6135	242	12	uniform	uniform	ADJ
ejpam-6135	242	13	ir∗	ir∗	NOUN
ejpam-6135	242	14	centred	centre	VERB
ejpam-6135	242	15	structure	structure	NOUN
ejpam-6135	242	16	open	open	ADJ
ejpam-6135	242	17	filter	filter	NOUN
ejpam-6135	242	18	on	on	ADP
ejpam-6135	242	19	px	px	PROPN
ejpam-6135	242	20	and	and	CCONJ
ejpam-6135	242	21	{	{	PUNCT
ejpam-6135	242	22	pi	pi	NOUN
ejpam-6135	242	23	}	}	PUNCT
ejpam-6135	242	24	be	be	AUX
ejpam-6135	242	25	an	an	DET
ejpam-6135	242	26	(	(	PUNCT
ejpam-6135	242	27	c	c	NOUN
ejpam-6135	242	28	,	,	PUNCT
ejpam-6135	242	29	d	d	NOUN
ejpam-6135	242	30	)	)	PUNCT
ejpam-6135	242	31	if	if	SCONJ
ejpam-6135	242	32	−q	−q	ADJ
ejpam-6135	242	33	uniform	uniform	ADJ
ejpam-6135	242	34	ir∗	ir∗	NOUN
ejpam-6135	242	35	centred	centre	VERB
ejpam-6135	242	36	net	net	NOUN
ejpam-6135	242	37	related	relate	VERB
ejpam-6135	242	38	to	to	ADP
ejpam-6135	242	39	p	p	NOUN
ejpam-6135	242	40	,	,	PUNCT
ejpam-6135	242	41	and	and	CCONJ
ejpam-6135	242	42	i=	i=	PROPN
ejpam-6135	242	43	{	{	PUNCT
ejpam-6135	242	44	u	u	NOUN
ejpam-6135	242	45	:	:	PUNCT
ejpam-6135	242	46	u	u	NOUN
ejpam-6135	242	47	is	be	AUX
ejpam-6135	242	48	a	a	DET
ejpam-6135	242	49	(	(	PUNCT
ejpam-6135	242	50	c	c	NOUN
ejpam-6135	242	51	,	,	PUNCT
ejpam-6135	242	52	d	d	NOUN
ejpam-6135	242	53	)	)	PUNCT
ejpam-6135	242	54	if	if	SCONJ
ejpam-6135	242	55	−q	−q	ADJ
ejpam-6135	242	56	uniform	uniform	ADJ
ejpam-6135	242	57	ir∗	ir∗	NOUN
ejpam-6135	242	58	centred	centre	VERB
ejpam-6135	242	59	structure	structure	NOUN
ejpam-6135	242	60	open	open	ADJ
ejpam-6135	242	61	in	in	ADP
ejpam-6135	242	62	px	px	PROPN
ejpam-6135	242	63	also	also	ADV
ejpam-6135	242	64	{	{	PUNCT
ejpam-6135	242	65	pi	pi	NOUN
ejpam-6135	242	66	}	}	PUNCT
ejpam-6135	242	67	is	be	AUX
ejpam-6135	242	68	⊘	⊘	X
ejpam-6135	242	69	in	in	ADP
ejpam-6135	242	70	u	u	NOUN
ejpam-6135	242	71	}	}	PUNCT
ejpam-6135	242	72	.	.	PUNCT
ejpam-6135	243	1	then	then	ADV
ejpam-6135	243	2	i	i	PRON
ejpam-6135	243	3	=	=	PUNCT
ejpam-6135	243	4	p	p	NOUN
ejpam-6135	243	5	remark	remark	NOUN
ejpam-6135	243	6	2	2	NUM
ejpam-6135	243	7	.	.	PUNCT
ejpam-6135	244	1	every	every	DET
ejpam-6135	244	2	c∗(px	c∗(px	NOUN
ejpam-6135	244	3	)	)	PUNCT
ejpam-6135	244	4	net	net	NOUN
ejpam-6135	244	5	{	{	PUNCT
ejpam-6135	244	6	pi	pi	NOUN
ejpam-6135	244	7	}	}	PUNCT
ejpam-6135	244	8	in	in	ADP
ejpam-6135	244	9	px	px	PROPN
ejpam-6135	244	10	and	and	CCONJ
ejpam-6135	244	11	also	also	ADV
ejpam-6135	244	12	{	{	PUNCT
ejpam-6135	244	13	wpi	wpi	PROPN
ejpam-6135	244	14	k	k	PROPN
ejpam-6135	244	15	}	}	PUNCT
ejpam-6135	244	16	be	be	AUX
ejpam-6135	244	17	the	the	DET
ejpam-6135	244	18	(	(	PUNCT
ejpam-6135	244	19	c	c	NOUN
ejpam-6135	244	20	,	,	PUNCT
ejpam-6135	244	21	d	d	NOUN
ejpam-6135	244	22	)	)	PUNCT
ejpam-6135	244	23	if	if	SCONJ
ejpam-6135	244	24	−q	−q	ADJ
ejpam-6135	244	25	uniform	uniform	ADJ
ejpam-6135	244	26	ir∗	ir∗	NOUN
ejpam-6135	244	27	centred	centre	VERB
ejpam-6135	244	28	net	net	NOUN
ejpam-6135	244	29	based	base	VERB
ejpam-6135	244	30	on	on	ADP
ejpam-6135	244	31	the	the	DET
ejpam-6135	244	32	(	(	PUNCT
ejpam-6135	244	33	c	c	NOUN
ejpam-6135	244	34	,	,	PUNCT
ejpam-6135	244	35	d	d	NOUN
ejpam-6135	244	36	)	)	PUNCT
ejpam-6135	244	37	if	if	SCONJ
ejpam-6135	244	38	−q	−q	ADJ
ejpam-6135	244	39	uniform	uniform	ADJ
ejpam-6135	244	40	ir∗	ir∗	NOUN
ejpam-6135	244	41	centred	centre	VERB
ejpam-6135	244	42	structure	structure	NOUN
ejpam-6135	244	43	open	open	ADJ
ejpam-6135	244	44	filter	filter	NOUN
ejpam-6135	244	45	f{pi	f{pi	PROPN
ejpam-6135	244	46	}	}	PUNCT
ejpam-6135	244	47	induced	induce	VERB
ejpam-6135	244	48	by	by	ADP
ejpam-6135	244	49	{	{	PUNCT
ejpam-6135	244	50	pi	pi	NOUN
ejpam-6135	244	51	}	}	PUNCT
ejpam-6135	244	52	.	.	PUNCT
ejpam-6135	245	1	(	(	PUNCT
ejpam-6135	245	2	i	i	NOUN
ejpam-6135	245	3	)	)	PUNCT
ejpam-6135	245	4	{	{	PUNCT
ejpam-6135	245	5	wpi	wpi	PROPN
ejpam-6135	245	6	k	k	PROPN
ejpam-6135	245	7	}	}	PUNCT
ejpam-6135	245	8	is	be	AUX
ejpam-6135	245	9	distinctly	distinctly	ADV
ejpam-6135	245	10	established	establish	VERB
ejpam-6135	245	11	as	as	ADP
ejpam-6135	245	12	f{pi	f{pi	PROPN
ejpam-6135	245	13	}	}	PUNCT
ejpam-6135	245	14	and	and	CCONJ
ejpam-6135	245	15	f{pi}=	f{pi}=	NOUN
ejpam-6135	245	16	f{pj	f{pj	PROPN
ejpam-6135	245	17	}	}	PUNCT
ejpam-6135	245	18	iff	iff	NOUN
ejpam-6135	245	19	{	{	PUNCT
ejpam-6135	245	20	wpi	wpi	PROPN
ejpam-6135	245	21	k	k	PROPN
ejpam-6135	245	22	}	}	PUNCT
ejpam-6135	245	23	=	=	SYM
ejpam-6135	246	1	{	{	PUNCT
ejpam-6135	246	2	wpj	wpj	NOUN
ejpam-6135	246	3	k	k	X
ejpam-6135	246	4	}	}	PUNCT
ejpam-6135	246	5	.	.	PUNCT
ejpam-6135	247	1	(	(	PUNCT
ejpam-6135	247	2	ii	ii	NOUN
ejpam-6135	247	3	)	)	PUNCT
ejpam-6135	247	4	f{pi}=f{wpi	f{pi}=f{wpi	X
ejpam-6135	248	1	k	k	NOUN
ejpam-6135	248	2	}	}	PUNCT
ejpam-6135	248	3	=	=	PUNCT
ejpam-6135	248	4	{	{	PUNCT
ejpam-6135	248	5	o	o	NOUN
ejpam-6135	248	6	:	:	PUNCT
ejpam-6135	248	7	o	o	NOUN
ejpam-6135	248	8	is	be	AUX
ejpam-6135	248	9	(	(	PUNCT
ejpam-6135	248	10	c	c	X
ejpam-6135	248	11	,	,	PUNCT
ejpam-6135	248	12	d	d	NOUN
ejpam-6135	248	13	)	)	PUNCT
ejpam-6135	248	14	if	if	SCONJ
ejpam-6135	248	15	−q	−q	ADJ
ejpam-6135	248	16	uniform	uniform	ADJ
ejpam-6135	248	17	ir∗	ir∗	NOUN
ejpam-6135	248	18	centred	centre	VERB
ejpam-6135	248	19	structure	structure	NOUN
ejpam-6135	248	20	open	open	ADJ
ejpam-6135	248	21	set	set	VERB
ejpam-6135	248	22	in	in	ADP
ejpam-6135	248	23	px	px	PROPN
ejpam-6135	248	24	and	and	CCONJ
ejpam-6135	248	25	{	{	PUNCT
ejpam-6135	248	26	wpi	wpi	PROPN
ejpam-6135	248	27	k	k	PROPN
ejpam-6135	248	28	}	}	PUNCT
ejpam-6135	248	29	is	be	AUX
ejpam-6135	248	30	eventually	eventually	ADV
ejpam-6135	248	31	in	in	ADP
ejpam-6135	248	32	o	o	PROPN
ejpam-6135	248	33	}	}	PUNCT
ejpam-6135	248	34	(	(	PUNCT
ejpam-6135	248	35	iii	iii	NOUN
ejpam-6135	248	36	)	)	PUNCT
ejpam-6135	248	37	{	{	PUNCT
ejpam-6135	248	38	wpi	wpi	PROPN
ejpam-6135	248	39	k	k	PROPN
ejpam-6135	248	40	}	}	PUNCT
ejpam-6135	248	41	is	be	AUX
ejpam-6135	248	42	a	a	DET
ejpam-6135	248	43	c∗(px	c∗(px	NOUN
ejpam-6135	248	44	)	)	PUNCT
ejpam-6135	248	45	net	net	NOUN
ejpam-6135	248	46	along	along	ADP
ejpam-6135	248	47	with	with	ADP
ejpam-6135	248	48	lim	lim	PROPN
ejpam-6135	248	49	{	{	PUNCT
ejpam-6135	248	50	fζ(wpi	fζ(wpi	PROPN
ejpam-6135	248	51	k	k	PROPN
ejpam-6135	248	52	)	)	PUNCT
ejpam-6135	248	53	}	}	PUNCT
ejpam-6135	249	1	=	=	SYM
ejpam-6135	249	2	lim	lim	PROPN
ejpam-6135	249	3	{	{	PUNCT
ejpam-6135	249	4	fζ(pi	fζ(pi	PROPN
ejpam-6135	249	5	)	)	PUNCT
ejpam-6135	249	6	}	}	PUNCT
ejpam-6135	249	7	∀	∀	X
ejpam-6135	249	8	fζ	fζ	ADP
ejpam-6135	249	9	in	in	ADP
ejpam-6135	249	10	c∗(px	c∗(px	NOUN
ejpam-6135	249	11	)	)	PUNCT
ejpam-6135	249	12	.	.	PUNCT
ejpam-6135	250	1	(	(	PUNCT
ejpam-6135	250	2	iv	iv	X
ejpam-6135	250	3	)	)	PUNCT
ejpam-6135	250	4	requirements	requirement	NOUN
ejpam-6135	250	5	are	be	AUX
ejpam-6135	250	6	to	to	PART
ejpam-6135	250	7	be	be	AUX
ejpam-6135	250	8	hold	hold	VERB
ejpam-6135	250	9	:	:	PUNCT
ejpam-6135	250	10	(	(	PUNCT
ejpam-6135	250	11	a	a	X
ejpam-6135	250	12	)	)	PUNCT
ejpam-6135	250	13	{	{	PUNCT
ejpam-6135	250	14	wpi	wpi	NOUN
ejpam-6135	250	15	k	k	X
ejpam-6135	250	16	}	}	PUNCT
ejpam-6135	250	17	convergent	convergent	NOUN
ejpam-6135	250	18	to	to	ADP
ejpam-6135	250	19	p	p	PROPN
ejpam-6135	250	20	(	(	PUNCT
ejpam-6135	250	21	b	b	NOUN
ejpam-6135	250	22	)	)	PUNCT
ejpam-6135	250	23	here	here	ADV
ejpam-6135	250	24	,	,	PUNCT
ejpam-6135	250	25	converged	converge	VERB
ejpam-6135	250	26	to	to	ADP
ejpam-6135	250	27	p	p	NOUN
ejpam-6135	250	28	with	with	ADP
ejpam-6135	250	29	respect	respect	NOUN
ejpam-6135	250	30	to	to	ADP
ejpam-6135	250	31	{	{	PUNCT
ejpam-6135	250	32	pi	pi	NOUN
ejpam-6135	250	33	}	}	PUNCT
ejpam-6135	250	34	.	.	PUNCT
ejpam-6135	251	1	(	(	PUNCT
ejpam-6135	251	2	c	c	X
ejpam-6135	251	3	)	)	PUNCT
ejpam-6135	251	4	f{pi	f{pi	PROPN
ejpam-6135	251	5	}	}	PUNCT
ejpam-6135	251	6	converges	converge	VERB
ejpam-6135	251	7	to	to	ADP
ejpam-6135	251	8	p	p	PROPN
ejpam-6135	251	9	.	.	PUNCT
ejpam-6135	252	1	let	let	VERB
ejpam-6135	252	2	yp=	yp=	PROPN
ejpam-6135	252	3	{	{	PUNCT
ejpam-6135	252	4	{	{	PUNCT
ejpam-6135	252	5	wpi	wpi	PROPN
ejpam-6135	252	6	k	k	PROPN
ejpam-6135	252	7	}	}	PUNCT
ejpam-6135	252	8	∗	∗	NOUN
ejpam-6135	252	9	:	:	PUNCT
ejpam-6135	252	10	{	{	PUNCT
ejpam-6135	252	11	pi	pi	NOUN
ejpam-6135	252	12	}	}	PUNCT
ejpam-6135	252	13	is	be	AUX
ejpam-6135	252	14	an	an	DET
ejpam-6135	252	15	c∗(px	c∗(px	NOUN
ejpam-6135	252	16	)	)	PUNCT
ejpam-6135	252	17	net	net	NOUN
ejpam-6135	252	18	does	do	AUX
ejpam-6135	252	19	not	not	PART
ejpam-6135	252	20	converge	converge	VERB
ejpam-6135	252	21	to	to	ADP
ejpam-6135	252	22	px	px	PROPN
ejpam-6135	252	23	,	,	PUNCT
ejpam-6135	252	24	{	{	PUNCT
ejpam-6135	252	25	wpi	wpi	PROPN
ejpam-6135	252	26	k	k	X
ejpam-6135	252	27	}	}	PUNCT
ejpam-6135	252	28	is	be	AUX
ejpam-6135	252	29	(	(	PUNCT
ejpam-6135	252	30	c	c	X
ejpam-6135	252	31	,	,	PUNCT
ejpam-6135	252	32	d	d	NOUN
ejpam-6135	252	33	)	)	PUNCT
ejpam-6135	252	34	if	if	SCONJ
ejpam-6135	252	35	−q	−q	ADJ
ejpam-6135	252	36	uniform	uniform	ADJ
ejpam-6135	252	37	ir∗	ir∗	NOUN
ejpam-6135	252	38	centred	centre	VERB
ejpam-6135	252	39	structure	structure	NOUN
ejpam-6135	252	40	net	net	NOUN
ejpam-6135	252	41	based	base	VERB
ejpam-6135	252	42	on	on	ADP
ejpam-6135	252	43	(	(	PUNCT
ejpam-6135	252	44	c	c	X
ejpam-6135	252	45	,	,	PUNCT
ejpam-6135	252	46	d	d	NOUN
ejpam-6135	252	47	)	)	PUNCT
ejpam-6135	252	48	if	if	SCONJ
ejpam-6135	252	49	−q	−q	ADJ
ejpam-6135	252	50	uniform	uniform	ADJ
ejpam-6135	252	51	ir∗	ir∗	NOUN
ejpam-6135	252	52	centred	centre	VERB
ejpam-6135	252	53	structure	structure	NOUN
ejpam-6135	252	54	filter	filter	NOUN
ejpam-6135	252	55	f{pi	f{pi	PROPN
ejpam-6135	252	56	}	}	PUNCT
ejpam-6135	252	57	}	}	PUNCT
ejpam-6135	252	58	,	,	PUNCT
ejpam-6135	252	59	p	p	NOUN
ejpam-6135	252	60	∗	∗	NOUN
ejpam-6135	252	61	x=	x=	PUNCT
ejpam-6135	253	1	px	px	PROPN
ejpam-6135	253	2	∪	∪	VERB
ejpam-6135	253	3	yp	yp	PROPN
ejpam-6135	253	4	,	,	PUNCT
ejpam-6135	253	5	the	the	DET
ejpam-6135	253	6	disjoint	disjoint	PROPN
ejpam-6135	253	7	union	union	NOUN
ejpam-6135	253	8	of	of	ADP
ejpam-6135	253	9	px	px	PROPN
ejpam-6135	253	10	and	and	CCONJ
ejpam-6135	253	11	yp	yp	PROPN
ejpam-6135	253	12	.	.	PUNCT
ejpam-6135	254	1	for	for	ADP
ejpam-6135	254	2	each	each	PRON
ejpam-6135	254	3	(	(	PUNCT
ejpam-6135	254	4	c	c	X
ejpam-6135	254	5	,	,	PUNCT
ejpam-6135	254	6	d	d	NOUN
ejpam-6135	254	7	)	)	PUNCT
ejpam-6135	254	8	if	if	SCONJ
ejpam-6135	254	9	−q	−q	ADJ
ejpam-6135	254	10	uniform	uniform	ADJ
ejpam-6135	254	11	ir∗	ir∗	NOUN
ejpam-6135	254	12	centred	centre	VERB
ejpam-6135	254	13	structure	structure	NOUN
ejpam-6135	254	14	open	open	ADJ
ejpam-6135	254	15	set	set	VERB
ejpam-6135	254	16	u	u	PROPN
ejpam-6135	254	17	⊂	⊂	PROPN
ejpam-6135	254	18	px	px	AUX
ejpam-6135	254	19	define	define	VERB
ejpam-6135	254	20	u∗	u∗	ADV
ejpam-6135	254	21	⊆	⊆	NUM
ejpam-6135	254	22	p	p	NOUN
ejpam-6135	254	23	∗	∗	NOUN
ejpam-6135	254	24	x	x	PUNCT
ejpam-6135	254	25	and	and	CCONJ
ejpam-6135	254	26	the	the	DET
ejpam-6135	254	27	set	set	ADJ
ejpam-6135	254	28	u∗=	u∗=	ADJ
ejpam-6135	254	29	u	u	NOUN
ejpam-6135	254	30	∪	∪	X
ejpam-6135	254	31	{	{	PUNCT
ejpam-6135	254	32	{	{	PUNCT
ejpam-6135	254	33	wpi	wpi	NOUN
ejpam-6135	254	34	k	k	PROPN
ejpam-6135	254	35	}	}	PUNCT
ejpam-6135	254	36	∗	∗	NOUN
ejpam-6135	254	37	:	:	PUNCT
ejpam-6135	254	38	{	{	PUNCT
ejpam-6135	254	39	wpi	wpi	NOUN
ejpam-6135	254	40	k	k	ADJ
ejpam-6135	254	41	}	}	PUNCT
ejpam-6135	254	42	∗	∗	NOUN
ejpam-6135	254	43	}	}	PUNCT
ejpam-6135	254	44	∈	∈	PROPN
ejpam-6135	254	45	yp	yp	PROPN
ejpam-6135	254	46	and	and	CCONJ
ejpam-6135	254	47	{	{	PUNCT
ejpam-6135	254	48	wpi	wpi	PROPN
ejpam-6135	254	49	k	k	PROPN
ejpam-6135	254	50	}	}	PUNCT
ejpam-6135	254	51	is	be	AUX
ejpam-6135	254	52	⊘	⊘	X
ejpam-6135	254	53	in	in	ADP
ejpam-6135	254	54	u	u	NOUN
ejpam-6135	254	55	}	}	PUNCT
ejpam-6135	254	56	.	.	PUNCT
ejpam-6135	255	1	it	it	PRON
ejpam-6135	255	2	is	be	AUX
ejpam-6135	255	3	apparent	apparent	ADJ
ejpam-6135	255	4	that	that	SCONJ
ejpam-6135	255	5	if	if	SCONJ
ejpam-6135	255	6	u	u	PROPN
ejpam-6135	255	7	⊂	⊂	X
ejpam-6135	255	8	v	v	X
ejpam-6135	255	9	,	,	PUNCT
ejpam-6135	255	10	then	then	ADV
ejpam-6135	255	11	u∗	u∗	PROPN
ejpam-6135	255	12	⊂	⊂	PROPN
ejpam-6135	255	13	v	v	X
ejpam-6135	255	14	∗.	∗.	PROPN
ejpam-6135	255	15	proposition	proposition	NOUN
ejpam-6135	255	16	1	1	NUM
ejpam-6135	255	17	.	.	PUNCT
ejpam-6135	256	1	let	let	VERB
ejpam-6135	256	2	u	u	PRON
ejpam-6135	256	3	and	and	CCONJ
ejpam-6135	256	4	v	v	NOUN
ejpam-6135	256	5	be	be	AUX
ejpam-6135	256	6	any	any	DET
ejpam-6135	256	7	two	two	NUM
ejpam-6135	256	8	(	(	PUNCT
ejpam-6135	256	9	c	c	NOUN
ejpam-6135	256	10	,	,	PUNCT
ejpam-6135	256	11	d	d	NOUN
ejpam-6135	256	12	)	)	PUNCT
ejpam-6135	256	13	if	if	SCONJ
ejpam-6135	256	14	−q	−q	ADJ
ejpam-6135	256	15	uniform	uniform	ADJ
ejpam-6135	256	16	ir∗	ir∗	NOUN
ejpam-6135	256	17	centred	centre	VERB
ejpam-6135	256	18	structure	structure	NOUN
ejpam-6135	256	19	open	open	ADJ
ejpam-6135	256	20	sets	set	NOUN
ejpam-6135	256	21	in	in	ADP
ejpam-6135	256	22	px	px	PROPN
ejpam-6135	256	23	,	,	PUNCT
ejpam-6135	256	24	then	then	ADV
ejpam-6135	256	25	(	(	PUNCT
ejpam-6135	256	26	u	u	NOUN
ejpam-6135	256	27	∩	∩	NOUN
ejpam-6135	256	28	v	v	NOUN
ejpam-6135	256	29	)	)	PUNCT
ejpam-6135	256	30	∗=	∗=	NOUN
ejpam-6135	256	31	u∗	u∗	VERB
ejpam-6135	256	32	∩v	∩v	PUNCT
ejpam-6135	257	1	∗.	∗.	PROPN
ejpam-6135	257	2	proof	proof	NOUN
ejpam-6135	257	3	.	.	PUNCT
ejpam-6135	258	1	let	let	VERB
ejpam-6135	258	2	p2	p2	PROPN
ejpam-6135	258	3	∈	∈	PROPN
ejpam-6135	258	4	(	(	PUNCT
ejpam-6135	258	5	u	u	NOUN
ejpam-6135	258	6	∩	∩	ADJ
ejpam-6135	258	7	v	v	NOUN
ejpam-6135	258	8	)	)	PUNCT
ejpam-6135	258	9	∗	∗	NOUN
ejpam-6135	258	10	∩yp	∩yp	NOUN
ejpam-6135	258	11	,	,	PUNCT
ejpam-6135	258	12	then	then	ADV
ejpam-6135	258	13	p2=	p2=	PROPN
ejpam-6135	258	14	{	{	PUNCT
ejpam-6135	258	15	wpi	wpi	PROPN
ejpam-6135	258	16	k	k	X
ejpam-6135	258	17	}	}	PUNCT
ejpam-6135	258	18	∗	∗	NOUN
ejpam-6135	258	19	and	and	CCONJ
ejpam-6135	258	20	{	{	PUNCT
ejpam-6135	258	21	wpi	wpi	NOUN
ejpam-6135	258	22	k	k	PROPN
ejpam-6135	258	23	}	}	PUNCT
ejpam-6135	258	24	is	be	AUX
ejpam-6135	258	25	⊘	⊘	X
ejpam-6135	258	26	in	in	ADP
ejpam-6135	258	27	u	u	NOUN
ejpam-6135	258	28	∩	∩	NOUN
ejpam-6135	258	29	v	v	NOUN
ejpam-6135	258	30	.	.	PUNCT
ejpam-6135	259	1	this	this	PRON
ejpam-6135	259	2	indicates	indicate	VERB
ejpam-6135	259	3	that	that	SCONJ
ejpam-6135	259	4	{	{	PUNCT
ejpam-6135	259	5	wpi	wpi	PROPN
ejpam-6135	259	6	k	k	X
ejpam-6135	259	7	}	}	PUNCT
ejpam-6135	259	8	is	be	AUX
ejpam-6135	259	9	⊘	⊘	X
ejpam-6135	259	10	∈	∈	PROPN
ejpam-6135	259	11	u	u	PROPN
ejpam-6135	259	12	,	,	PUNCT
ejpam-6135	259	13	v	v	NOUN
ejpam-6135	259	14	.	.	PUNCT
ejpam-6135	260	1	here	here	ADV
ejpam-6135	260	2	,	,	PUNCT
ejpam-6135	260	3	{	{	PUNCT
ejpam-6135	260	4	wpi	wpi	PROPN
ejpam-6135	260	5	k	k	PROPN
ejpam-6135	260	6	}	}	PUNCT
ejpam-6135	260	7	∗	∗	NOUN
ejpam-6135	260	8	∈	∈	PROPN
ejpam-6135	260	9	u∗	u∗	NOUN
ejpam-6135	260	10	∩	∩	NOUN
ejpam-6135	260	11	v	v	ADP
ejpam-6135	260	12	∗.	∗.	PROPN
ejpam-6135	260	13	if	if	SCONJ
ejpam-6135	260	14	p2	p2	PROPN
ejpam-6135	260	15	∈	∈	PROPN
ejpam-6135	260	16	(	(	PUNCT
ejpam-6135	260	17	u∗	u∗	PROPN
ejpam-6135	260	18	∩	∩	NOUN
ejpam-6135	260	19	v	v	ADP
ejpam-6135	260	20	∗	∗	NOUN
ejpam-6135	260	21	)	)	PUNCT
ejpam-6135	260	22	∩	∩	NOUN
ejpam-6135	260	23	yp	yp	PROPN
ejpam-6135	260	24	,	,	PUNCT
ejpam-6135	260	25	then	then	ADV
ejpam-6135	260	26	p2=	p2=	PROPN
ejpam-6135	260	27	{	{	PUNCT
ejpam-6135	260	28	wpi	wpi	PROPN
ejpam-6135	260	29	k	k	X
ejpam-6135	260	30	}	}	PUNCT
ejpam-6135	260	31	∗	∗	NOUN
ejpam-6135	260	32	and	and	CCONJ
ejpam-6135	260	33	{	{	PUNCT
ejpam-6135	260	34	wpi	wpi	NOUN
ejpam-6135	260	35	k	k	PROPN
ejpam-6135	260	36	}	}	PUNCT
ejpam-6135	260	37	is	be	AUX
ejpam-6135	260	38	⊘	⊘	PROPN
ejpam-6135	260	39	is	be	AUX
ejpam-6135	260	40	both	both	PRON
ejpam-6135	260	41	in	in	ADP
ejpam-6135	260	42	u	u	NOUN
ejpam-6135	260	43	and	and	CCONJ
ejpam-6135	260	44	v	v	NOUN
ejpam-6135	260	45	.	.	PUNCT
ejpam-6135	261	1	so	so	ADV
ejpam-6135	261	2	{	{	PUNCT
ejpam-6135	261	3	wpi	wpi	PROPN
ejpam-6135	261	4	k	k	X
ejpam-6135	261	5	}	}	PUNCT
ejpam-6135	261	6	is	be	AUX
ejpam-6135	261	7	⊘	⊘	X
ejpam-6135	261	8	∈	∈	PROPN
ejpam-6135	261	9	u	u	NOUN
ejpam-6135	261	10	∩	∩	NOUN
ejpam-6135	261	11	v	v	NOUN
ejpam-6135	261	12	.	.	PUNCT
ejpam-6135	262	1	then	then	ADV
ejpam-6135	262	2	p2	p2	PROPN
ejpam-6135	262	3	∈	∈	PROPN
ejpam-6135	262	4	(	(	PUNCT
ejpam-6135	262	5	u	u	NOUN
ejpam-6135	262	6	∩	∩	ADJ
ejpam-6135	262	7	v	v	NOUN
ejpam-6135	262	8	)	)	PUNCT
ejpam-6135	262	9	∗	∗	NOUN
ejpam-6135	262	10	proposition	proposition	NOUN
ejpam-6135	262	11	2	2	NUM
ejpam-6135	262	12	.	.	X
ejpam-6135	262	13	assume	assume	VERB
ejpam-6135	262	14	b=	b=	NOUN
ejpam-6135	262	15	{	{	PUNCT
ejpam-6135	262	16	u∗	u∗	ADV
ejpam-6135	262	17	:	:	PUNCT
ejpam-6135	262	18	u	u	NOUN
ejpam-6135	262	19	be	be	VERB
ejpam-6135	262	20	an	an	DET
ejpam-6135	262	21	(	(	PUNCT
ejpam-6135	262	22	c	c	NOUN
ejpam-6135	262	23	,	,	PUNCT
ejpam-6135	262	24	d	d	NOUN
ejpam-6135	262	25	)	)	PUNCT
ejpam-6135	262	26	if	if	SCONJ
ejpam-6135	262	27	−q	−q	ADJ
ejpam-6135	262	28	uniform	uniform	ADJ
ejpam-6135	262	29	ir∗	ir∗	NOUN
ejpam-6135	262	30	centred	centre	VERB
ejpam-6135	262	31	structure	structure	NOUN
ejpam-6135	262	32	open	open	ADJ
ejpam-6135	262	33	set	set	VERB
ejpam-6135	262	34	in	in	ADP
ejpam-6135	262	35	px	px	PROPN
ejpam-6135	262	36	}	}	PUNCT
ejpam-6135	262	37	.	.	PUNCT
ejpam-6135	263	1	then	then	ADV
ejpam-6135	263	2	b	b	X
ejpam-6135	263	3	is	be	AUX
ejpam-6135	263	4	an	an	DET
ejpam-6135	263	5	(	(	PUNCT
ejpam-6135	263	6	c	c	NOUN
ejpam-6135	263	7	,	,	PUNCT
ejpam-6135	263	8	d	d	NOUN
ejpam-6135	263	9	)	)	PUNCT
ejpam-6135	263	10	if	if	SCONJ
ejpam-6135	263	11	−q	−q	ADJ
ejpam-6135	263	12	uniform	uniform	ADJ
ejpam-6135	263	13	ir∗	ir∗	NOUN
ejpam-6135	263	14	centred	centre	VERB
ejpam-6135	263	15	structure	structure	NOUN
ejpam-6135	263	16	base	base	NOUN
ejpam-6135	263	17	for	for	ADP
ejpam-6135	263	18	an	an	DET
ejpam-6135	263	19	(	(	PUNCT
ejpam-6135	263	20	c	c	NOUN
ejpam-6135	263	21	,	,	PUNCT
ejpam-6135	263	22	d	d	NOUN
ejpam-6135	263	23	)	)	PUNCT
ejpam-6135	263	24	if	if	SCONJ
ejpam-6135	263	25	−q	−q	ADJ
ejpam-6135	263	26	uniform	uniform	ADJ
ejpam-6135	263	27	ir∗	ir∗	NOUN
ejpam-6135	263	28	centred	centre	VERB
ejpam-6135	263	29	structure	structure	NOUN
ejpam-6135	263	30	on	on	ADP
ejpam-6135	263	31	p	p	PROPN
ejpam-6135	263	32	∗	∗	NOUN
ejpam-6135	263	33	x	x	SYM
ejpam-6135	263	34	,	,	PUNCT
ejpam-6135	263	35	if	if	SCONJ
ejpam-6135	263	36	(	(	PUNCT
ejpam-6135	263	37	i	i	NOUN
ejpam-6135	263	38	)	)	PUNCT
ejpam-6135	263	39	p	p	NOUN
ejpam-6135	263	40	∗	∗	NOUN
ejpam-6135	263	41	x	x	X
ejpam-6135	263	42	=	=	X
ejpam-6135	263	43	{	{	PUNCT
ejpam-6135	263	44	u∗	u∗	INTJ
ejpam-6135	263	45	:	:	PUNCT
ejpam-6135	263	46	u∗	u∗	PROPN
ejpam-6135	263	47	∈	∈	PROPN
ejpam-6135	263	48	b	b	NOUN
ejpam-6135	263	49	}	}	PUNCT
ejpam-6135	263	50	(	(	PUNCT
ejpam-6135	263	51	ii	ii	NOUN
ejpam-6135	263	52	)	)	PUNCT
ejpam-6135	263	53	each	each	PRON
ejpam-6135	263	54	u∗	u∗	PROPN
ejpam-6135	263	55	,	,	PUNCT
ejpam-6135	263	56	v	v	ADP
ejpam-6135	263	57	∗	∗	NOUN
ejpam-6135	263	58	∈	∈	PROPN
ejpam-6135	263	59	b	b	PROPN
ejpam-6135	263	60	with	with	ADP
ejpam-6135	263	61	p2	p2	PROPN
ejpam-6135	263	62	∈	∈	PROPN
ejpam-6135	263	63	u∗	u∗	NOUN
ejpam-6135	263	64	∩	∩	NOUN
ejpam-6135	263	65	v	v	ADP
ejpam-6135	263	66	∗	∗	NOUN
ejpam-6135	263	67	some	some	PRON
ejpam-6135	263	68	of	of	ADP
ejpam-6135	263	69	the	the	DET
ejpam-6135	263	70	w	w	PROPN
ejpam-6135	263	71	∗=	∗=	NOUN
ejpam-6135	263	72	(	(	PUNCT
ejpam-6135	263	73	u∗	u∗	PROPN
ejpam-6135	263	74	∩	∩	NOUN
ejpam-6135	263	75	v	v	ADP
ejpam-6135	263	76	∗	∗	NOUN
ejpam-6135	263	77	)	)	PUNCT
ejpam-6135	263	78	∈	∈	PROPN
ejpam-6135	263	79	b	b	PROPN
ejpam-6135	263	80	,	,	PUNCT
ejpam-6135	263	81	p2	p2	PROPN
ejpam-6135	263	82	∈	∈	PROPN
ejpam-6135	263	83	w	w	NOUN
ejpam-6135	263	84	∗	∗	X
ejpam-6135	263	85	⊂	⊂	PROPN
ejpam-6135	264	1	u∗	u∗	PROPN
ejpam-6135	264	2	∩	∩	ADJ
ejpam-6135	264	3	v	v	ADP
ejpam-6135	264	4	∗	∗	NOUN
ejpam-6135	264	5	proof	proof	NOUN
ejpam-6135	264	6	.	.	PUNCT
ejpam-6135	265	1	s.	s.	PROPN
ejpam-6135	265	2	thirukumaran	thirukumaran	PROPN
ejpam-6135	265	3	,	,	PUNCT
ejpam-6135	265	4	g.	g.	PROPN
ejpam-6135	265	5	k.	k.	PROPN
ejpam-6135	265	6	revathi	revathi	PROPN
ejpam-6135	265	7	/	/	SYM
ejpam-6135	265	8	eur	eur	PROPN
ejpam-6135	265	9	.	.	PUNCT
ejpam-6135	266	1	j.	j.	PROPN
ejpam-6135	266	2	pure	pure	PROPN
ejpam-6135	266	3	appl	appl	PROPN
ejpam-6135	266	4	.	.	PROPN
ejpam-6135	266	5	math	math	PROPN
ejpam-6135	266	6	,	,	PUNCT
ejpam-6135	266	7	18	18	NUM
ejpam-6135	266	8	(	(	PUNCT
ejpam-6135	266	9	2	2	NUM
ejpam-6135	266	10	)	)	PUNCT
ejpam-6135	266	11	(	(	PUNCT
ejpam-6135	266	12	2025	2025	NUM
ejpam-6135	266	13	)	)	PUNCT
ejpam-6135	266	14	,	,	PUNCT
ejpam-6135	266	15	6135	6135	NUM
ejpam-6135	266	16	13	13	NUM
ejpam-6135	266	17	of	of	ADP
ejpam-6135	266	18	17	17	NUM
ejpam-6135	266	19	(	(	PUNCT
ejpam-6135	266	20	i	i	NOUN
ejpam-6135	266	21	)	)	PUNCT
ejpam-6135	266	22	p	p	NOUN
ejpam-6135	266	23	∗	∗	NOUN
ejpam-6135	266	24	x	x	X
ejpam-6135	266	25	=	=	X
ejpam-6135	266	26	{	{	PUNCT
ejpam-6135	266	27	u∗	u∗	INTJ
ejpam-6135	266	28	:	:	PUNCT
ejpam-6135	266	29	u∗	u∗	PROPN
ejpam-6135	266	30	∈	∈	PROPN
ejpam-6135	266	31	b	b	X
ejpam-6135	266	32	}	}	PUNCT
ejpam-6135	266	33	,	,	PUNCT
ejpam-6135	266	34	let	let	VERB
ejpam-6135	266	35	p2	p2	PROPN
ejpam-6135	266	36	∈	∈	PROPN
ejpam-6135	266	37	yp	yp	PROPN
ejpam-6135	266	38	,	,	PUNCT
ejpam-6135	266	39	then	then	ADV
ejpam-6135	266	40	p2=	p2=	PROPN
ejpam-6135	266	41	{	{	PUNCT
ejpam-6135	266	42	wpi	wpi	PROPN
ejpam-6135	266	43	k	k	PROPN
ejpam-6135	266	44	}	}	PUNCT
ejpam-6135	266	45	∗.	∗.	PROPN
ejpam-6135	266	46	for	for	ADP
ejpam-6135	266	47	any	any	DET
ejpam-6135	266	48	fζ	fζ	ADP
ejpam-6135	266	49	∈	∈	PROPN
ejpam-6135	266	50	c∗(px	c∗(px	NOUN
ejpam-6135	266	51	)	)	PUNCT
ejpam-6135	266	52	,	,	PUNCT
ejpam-6135	266	53	let	let	VERB
ejpam-6135	266	54	rζ=	rζ=	VERB
ejpam-6135	266	55	lim	lim	PROPN
ejpam-6135	266	56	{	{	PUNCT
ejpam-6135	266	57	fζ(wpi	fζ(wpi	PROPN
ejpam-6135	266	58	k	k	PROPN
ejpam-6135	266	59	)	)	PUNCT
ejpam-6135	266	60	,	,	PUNCT
ejpam-6135	266	61	then	then	ADV
ejpam-6135	266	62	{	{	PUNCT
ejpam-6135	266	63	wpi	wpi	PROPN
ejpam-6135	266	64	k	k	X
ejpam-6135	266	65	}	}	PUNCT
ejpam-6135	266	66	is	be	AUX
ejpam-6135	266	67	⊘	⊘	X
ejpam-6135	266	68	in	in	ADP
ejpam-6135	266	69	f−1	f−1	PROPN
ejpam-6135	266	70	α	α	NOUN
ejpam-6135	266	71	(	(	PUNCT
ejpam-6135	266	72	(	(	PUNCT
ejpam-6135	266	73	rζ	rζ	NOUN
ejpam-6135	266	74	−	−	PROPN
ejpam-6135	266	75	ε	ε	PROPN
ejpam-6135	266	76	,	,	PUNCT
ejpam-6135	266	77	rζ	rζ	X
ejpam-6135	266	78	+	+	CCONJ
ejpam-6135	266	79	ε	ε	PROPN
ejpam-6135	266	80	)	)	PUNCT
ejpam-6135	266	81	)	)	PUNCT
ejpam-6135	266	82	,	,	PUNCT
ejpam-6135	266	83	for	for	ADP
ejpam-6135	266	84	any	any	DET
ejpam-6135	266	85	ε	ε	PROPN
ejpam-6135	266	86	>	>	X
ejpam-6135	266	87	0	0	PROPN
ejpam-6135	266	88	,	,	PUNCT
ejpam-6135	266	89	that	that	PRON
ejpam-6135	266	90	is	be	AUX
ejpam-6135	266	91	{	{	PUNCT
ejpam-6135	266	92	wpi	wpi	PROPN
ejpam-6135	266	93	k	k	PROPN
ejpam-6135	266	94	}	}	PUNCT
ejpam-6135	266	95	∗	∗	NOUN
ejpam-6135	266	96	is	be	AUX
ejpam-6135	266	97	in	in	ADP
ejpam-6135	266	98	f−1	f−1	PROPN
ejpam-6135	266	99	ζ	ζ	NOUN
ejpam-6135	266	100	(	(	PUNCT
ejpam-6135	266	101	(	(	PUNCT
ejpam-6135	266	102	rζ	rζ	NOUN
ejpam-6135	266	103	−ε	−ε	NOUN
ejpam-6135	266	104	,	,	PUNCT
ejpam-6135	266	105	rζ	rζ	X
ejpam-6135	266	106	+	+	NOUN
ejpam-6135	266	107	ε	ε	PROPN
ejpam-6135	266	108	)	)	PUNCT
ejpam-6135	266	109	)	)	PUNCT
ejpam-6135	266	110	for	for	ADP
ejpam-6135	266	111	all	all	PRON
ejpam-6135	266	112	υ	υ	PROPN
ejpam-6135	266	113	>	>	X
ejpam-6135	266	114	0	0	NUM
ejpam-6135	266	115	,	,	PUNCT
ejpam-6135	266	116	accordingly	accordingly	ADV
ejpam-6135	266	117	yp	yp	PROPN
ejpam-6135	266	118	⊂	⊂	PROPN
ejpam-6135	266	119	∪{u∗	∪{u∗	PROPN
ejpam-6135	266	120	:	:	PUNCT
ejpam-6135	266	121	u∗	u∗	PROPN
ejpam-6135	266	122	∈	∈	PROPN
ejpam-6135	266	123	b	b	X
ejpam-6135	266	124	}	}	PUNCT
ejpam-6135	266	125	consequently	consequently	ADV
ejpam-6135	266	126	p	p	X
ejpam-6135	266	127	∗	∗	NOUN
ejpam-6135	266	128	x	x	PUNCT
ejpam-6135	267	1	⊂	⊂	PROPN
ejpam-6135	267	2	∪{u∗	∪{u∗	NOUN
ejpam-6135	267	3	:	:	PUNCT
ejpam-6135	267	4	u∗	u∗	PROPN
ejpam-6135	267	5	∈	∈	PROPN
ejpam-6135	267	6	b	b	NOUN
ejpam-6135	267	7	}	}	PUNCT
ejpam-6135	267	8	.	.	PUNCT
ejpam-6135	268	1	for	for	ADP
ejpam-6135	268	2	{	{	PUNCT
ejpam-6135	268	3	u∗	u∗	INTJ
ejpam-6135	268	4	:	:	PUNCT
ejpam-6135	268	5	u∗	u∗	PROPN
ejpam-6135	268	6	∈	∈	PROPN
ejpam-6135	268	7	b	b	X
ejpam-6135	268	8	}	}	PUNCT
ejpam-6135	268	9	⊂	⊂	PROPN
ejpam-6135	268	10	p	p	NOUN
ejpam-6135	268	11	∗	∗	NOUN
ejpam-6135	268	12	x	x	VERB
ejpam-6135	268	13	is	be	AUX
ejpam-6135	268	14	explained	explain	VERB
ejpam-6135	268	15	.	.	PUNCT
ejpam-6135	269	1	(	(	PUNCT
ejpam-6135	269	2	ii	ii	NOUN
ejpam-6135	269	3	)	)	PUNCT
ejpam-6135	269	4	if	if	SCONJ
ejpam-6135	269	5	p2	p2	PROPN
ejpam-6135	269	6	∈	∈	PROPN
ejpam-6135	269	7	u∗	u∗	ADJ
ejpam-6135	269	8	∩	∩	NOUN
ejpam-6135	269	9	v	v	ADP
ejpam-6135	269	10	∗	∗	NOUN
ejpam-6135	269	11	,	,	PUNCT
ejpam-6135	269	12	for	for	ADP
ejpam-6135	269	13	any	any	DET
ejpam-6135	269	14	u∗	u∗	NOUN
ejpam-6135	269	15	and	and	CCONJ
ejpam-6135	269	16	v	v	ADP
ejpam-6135	269	17	∗	∗	NOUN
ejpam-6135	269	18	in	in	ADP
ejpam-6135	269	19	b	b	NOUN
ejpam-6135	269	20	,	,	PUNCT
ejpam-6135	269	21	since	since	SCONJ
ejpam-6135	269	22	(	(	PUNCT
ejpam-6135	269	23	u	u	NOUN
ejpam-6135	269	24	∩	∩	NOUN
ejpam-6135	269	25	v	v	NOUN
ejpam-6135	269	26	)	)	PUNCT
ejpam-6135	269	27	∗	∗	NOUN
ejpam-6135	269	28	is	be	AUX
ejpam-6135	269	29	in	in	ADP
ejpam-6135	269	30	b	b	PROPN
ejpam-6135	269	31	and	and	CCONJ
ejpam-6135	269	32	(	(	PUNCT
ejpam-6135	269	33	u	u	PROPN
ejpam-6135	269	34	∩	∩	NOUN
ejpam-6135	269	35	v	v	NOUN
ejpam-6135	269	36	)	)	PUNCT
ejpam-6135	269	37	∗=	∗=	NOUN
ejpam-6135	269	38	u∗	u∗	PROPN
ejpam-6135	269	39	∩	∩	PROPN
ejpam-6135	269	40	v	v	ADP
ejpam-6135	269	41	∗	∗	NOUN
ejpam-6135	269	42	,	,	PUNCT
ejpam-6135	269	43	thus	thus	ADV
ejpam-6135	269	44	p2	p2	PROPN
ejpam-6135	269	45	∈	∈	PROPN
ejpam-6135	269	46	(	(	PUNCT
ejpam-6135	269	47	u	u	NOUN
ejpam-6135	269	48	∩	∩	ADJ
ejpam-6135	269	49	v	v	NOUN
ejpam-6135	269	50	)	)	PUNCT
ejpam-6135	269	51	∗	∗	NOUN
ejpam-6135	269	52	⊂	⊂	PROPN
ejpam-6135	269	53	u∗	u∗	PROPN
ejpam-6135	269	54	∩	∩	X
ejpam-6135	269	55	v	v	ADP
ejpam-6135	269	56	∗.	∗.	PROPN
ejpam-6135	269	57	remark	remark	NOUN
ejpam-6135	269	58	3	3	NUM
ejpam-6135	269	59	.	.	PUNCT
ejpam-6135	270	1	consider	consider	VERB
ejpam-6135	270	2	the	the	DET
ejpam-6135	270	3	p	p	NOUN
ejpam-6135	270	4	∗	∗	NOUN
ejpam-6135	270	5	x	x	PUNCT
ejpam-6135	270	6	with	with	ADP
ejpam-6135	270	7	(	(	PUNCT
ejpam-6135	270	8	c	c	NOUN
ejpam-6135	270	9	,	,	PUNCT
ejpam-6135	270	10	d	d	NOUN
ejpam-6135	270	11	)	)	PUNCT
ejpam-6135	270	12	if	if	SCONJ
ejpam-6135	270	13	−q	−q	ADJ
ejpam-6135	270	14	uniform	uniform	ADJ
ejpam-6135	270	15	ir∗	ir∗	NOUN
ejpam-6135	270	16	centred	centre	VERB
ejpam-6135	270	17	structure	structure	NOUN
ejpam-6135	270	18	induced	induce	VERB
ejpam-6135	270	19	by	by	ADP
ejpam-6135	270	20	the	the	DET
ejpam-6135	270	21	(	(	PUNCT
ejpam-6135	270	22	c	c	NOUN
ejpam-6135	270	23	,	,	PUNCT
ejpam-6135	270	24	d	d	NOUN
ejpam-6135	270	25	)	)	PUNCT
ejpam-6135	270	26	if	if	SCONJ
ejpam-6135	270	27	−q	−q	ADJ
ejpam-6135	270	28	uniform	uniform	ADJ
ejpam-6135	270	29	ir∗	ir∗	NOUN
ejpam-6135	270	30	centred	centre	VERB
ejpam-6135	270	31	structure	structure	NOUN
ejpam-6135	270	32	base	base	NOUN
ejpam-6135	270	33	b.	b.	PROPN
ejpam-6135	270	34	for	for	ADP
ejpam-6135	270	35	all	all	PRON
ejpam-6135	270	36	fζ	fζ	ADV
ejpam-6135	270	37	in	in	ADP
ejpam-6135	270	38	c∗(px	c∗(px	NOUN
ejpam-6135	270	39	)	)	PUNCT
ejpam-6135	270	40	,	,	PUNCT
ejpam-6135	270	41	defined	define	VERB
ejpam-6135	270	42	f∗ζ	f∗ζ	PROPN
ejpam-6135	270	43	:	:	PUNCT
ejpam-6135	270	44	p	p	X
ejpam-6135	270	45	∗	∗	NOUN
ejpam-6135	270	46	x	x	PUNCT
ejpam-6135	270	47	→	→	SYM
ejpam-6135	270	48	r	r	NOUN
ejpam-6135	270	49	define	define	NOUN
ejpam-6135	270	50	that	that	SCONJ
ejpam-6135	270	51	f∗ζ(p1)=	f∗ζ(p1)=	PROPN
ejpam-6135	270	52	fζ(p1	fζ(p1	NOUN
ejpam-6135	270	53	)	)	PUNCT
ejpam-6135	270	54	if	if	SCONJ
ejpam-6135	270	55	p1	p1	PROPN
ejpam-6135	270	56	∈	∈	PROPN
ejpam-6135	270	57	px	px	NOUN
ejpam-6135	270	58	,	,	PUNCT
ejpam-6135	271	1	f∗ζ({w	f∗ζ({w	PROPN
ejpam-6135	271	2	pi	pi	NOUN
ejpam-6135	271	3	k	k	PROPN
ejpam-6135	271	4	}	}	PUNCT
ejpam-6135	271	5	∗)=	∗)=	PROPN
ejpam-6135	271	6	lim	lim	PROPN
ejpam-6135	271	7	{	{	PUNCT
ejpam-6135	271	8	fζ(w	fζ(w	NUM
ejpam-6135	271	9	pi	pi	NOUN
ejpam-6135	271	10	k	k	PROPN
ejpam-6135	271	11	)	)	PUNCT
ejpam-6135	271	12	}	}	PUNCT
ejpam-6135	271	13	for	for	ADP
ejpam-6135	271	14	any	any	DET
ejpam-6135	271	15	{	{	PUNCT
ejpam-6135	271	16	wpi	wpi	NOUN
ejpam-6135	271	17	k	k	PROPN
ejpam-6135	271	18	}	}	PUNCT
ejpam-6135	271	19	∗	∗	NOUN
ejpam-6135	271	20	in	in	ADP
ejpam-6135	271	21	yp	yp	PROPN
ejpam-6135	272	1	and	and	CCONJ
ejpam-6135	272	2	it	it	PRON
ejpam-6135	272	3	is	be	AUX
ejpam-6135	272	4	stated	state	VERB
ejpam-6135	272	5	as	as	SCONJ
ejpam-6135	272	6	f∗ζ	f∗ζ	NUM
ejpam-6135	272	7	is	be	AUX
ejpam-6135	272	8	clearly	clearly	ADV
ejpam-6135	272	9	specified	specify	VERB
ejpam-6135	272	10	that	that	SCONJ
ejpam-6135	272	11	it	it	PRON
ejpam-6135	272	12	is	be	AUX
ejpam-6135	272	13	bdd	bdd	PROPN
ejpam-6135	272	14	real	real	ADV
ejpam-6135	272	15	valued	value	VERB
ejpam-6135	272	16	function	function	NOUN
ejpam-6135	272	17	on	on	ADP
ejpam-6135	272	18	p	p	NOUN
ejpam-6135	272	19	∗	∗	NOUN
ejpam-6135	272	20	x.	x.	NOUN
ejpam-6135	272	21	proposition	proposition	NOUN
ejpam-6135	272	22	3	3	NUM
ejpam-6135	272	23	.	.	PUNCT
ejpam-6135	273	1	for	for	ADP
ejpam-6135	273	2	any	any	DET
ejpam-6135	273	3	fζ	fζ	NOUN
ejpam-6135	273	4	in	in	ADP
ejpam-6135	273	5	c∗(px	c∗(px	NOUN
ejpam-6135	273	6	)	)	PUNCT
ejpam-6135	273	7	,	,	PUNCT
ejpam-6135	273	8	f∗ζ	f∗ζ	PROPN
ejpam-6135	273	9	is	be	AUX
ejpam-6135	273	10	a	a	DET
ejpam-6135	273	11	bounded	bounded	ADJ
ejpam-6135	273	12	real	real	ADV
ejpam-6135	273	13	valued	value	VERB
ejpam-6135	273	14	continuous	continuous	ADJ
ejpam-6135	273	15	function	function	NOUN
ejpam-6135	273	16	on	on	ADP
ejpam-6135	273	17	p	p	NOUN
ejpam-6135	273	18	∗	∗	NOUN
ejpam-6135	273	19	x	x	X
ejpam-6135	273	20	.	.	PUNCT
ejpam-6135	274	1	proof	proof	NOUN
ejpam-6135	274	2	.	.	PUNCT
ejpam-6135	275	1	it	it	PRON
ejpam-6135	275	2	is	be	AUX
ejpam-6135	275	3	enough	enough	ADJ
ejpam-6135	275	4	to	to	PART
ejpam-6135	275	5	proof	proof	VERB
ejpam-6135	275	6	the	the	DET
ejpam-6135	275	7	continuity	continuity	NOUN
ejpam-6135	275	8	,	,	PUNCT
ejpam-6135	275	9	f∗ζ	f∗ζ	PROPN
ejpam-6135	275	10	at	at	ADP
ejpam-6135	275	11	any	any	DET
ejpam-6135	275	12	p3	p3	NOUN
ejpam-6135	275	13	in	in	ADP
ejpam-6135	275	14	p	p	NOUN
ejpam-6135	275	15	∗	∗	NOUN
ejpam-6135	275	16	x	x	PUNCT
ejpam-6135	275	17	,	,	PUNCT
ejpam-6135	275	18	let	let	VERB
ejpam-6135	275	19	tζ	tζ	PART
ejpam-6135	275	20	=	=	NOUN
ejpam-6135	275	21	f∗	f∗	ADJ
ejpam-6135	275	22	ζ	ζ	X
ejpam-6135	275	23	(	(	PUNCT
ejpam-6135	275	24	p3	p3	PROPN
ejpam-6135	275	25	)	)	PUNCT
ejpam-6135	275	26	.	.	PUNCT
ejpam-6135	276	1	it	it	PRON
ejpam-6135	276	2	will	will	AUX
ejpam-6135	276	3	be	be	AUX
ejpam-6135	276	4	shown	show	VERB
ejpam-6135	276	5	that	that	SCONJ
ejpam-6135	276	6	for	for	ADP
ejpam-6135	276	7	any	any	DET
ejpam-6135	276	8	ε	ε	PROPN
ejpam-6135	276	9	>	>	X
ejpam-6135	276	10	0	0	PROPN
ejpam-6135	276	11	,	,	PUNCT
ejpam-6135	276	12	there	there	PRON
ejpam-6135	276	13	is	be	VERB
ejpam-6135	276	14	an	an	DET
ejpam-6135	276	15	(	(	PUNCT
ejpam-6135	276	16	c	c	NOUN
ejpam-6135	276	17	,	,	PUNCT
ejpam-6135	276	18	d	d	NOUN
ejpam-6135	276	19	)	)	PUNCT
ejpam-6135	276	20	if	if	SCONJ
ejpam-6135	276	21	−q	−q	ADJ
ejpam-6135	276	22	uniform	uniform	ADJ
ejpam-6135	276	23	ir∗	ir∗	NOUN
ejpam-6135	276	24	centred	centre	VERB
ejpam-6135	276	25	structure	structure	NOUN
ejpam-6135	276	26	open	open	ADJ
ejpam-6135	276	27	set	set	VERB
ejpam-6135	276	28	u∗	u∗	PROPN
ejpam-6135	276	29	∈	∈	PROPN
ejpam-6135	276	30	b	b	NOUN
ejpam-6135	276	31	such	such	ADJ
ejpam-6135	277	1	that	that	SCONJ
ejpam-6135	277	2	p3	p3	PROPN
ejpam-6135	277	3	∈	∈	PROPN
ejpam-6135	278	1	u∗	u∗	PROPN
ejpam-6135	279	1	⊂	⊂	PROPN
ejpam-6135	280	1	(	(	PUNCT
ejpam-6135	280	2	f∗	f∗	NOUN
ejpam-6135	280	3	ζ	ζ	NOUN
ejpam-6135	280	4	)	)	PUNCT
ejpam-6135	280	5	−1((tζ	−1((tζ	NUM
ejpam-6135	280	6	−	−	PROPN
ejpam-6135	280	7	ε	ε	PROPN
ejpam-6135	280	8	,	,	PUNCT
ejpam-6135	280	9	tζ	tζ	PROPN
ejpam-6135	280	10	+	+	NUM
ejpam-6135	280	11	ε	ε	PROPN
ejpam-6135	280	12	)	)	PUNCT
ejpam-6135	280	13	)	)	PUNCT
ejpam-6135	280	14	.	.	PUNCT
ejpam-6135	281	1	let	let	VERB
ejpam-6135	281	2	u	u	PRON
ejpam-6135	281	3	=	=	VERB
ejpam-6135	281	4	f−1	f−1	ADJ
ejpam-6135	281	5	ζ	ζ	NOUN
ejpam-6135	281	6	(	(	PUNCT
ejpam-6135	281	7	(	(	PUNCT
ejpam-6135	281	8	tζ	tζ	INTJ
ejpam-6135	281	9	−	−	PROPN
ejpam-6135	281	10	ε/2	ε/2	PROPN
ejpam-6135	281	11	,	,	PUNCT
ejpam-6135	281	12	tζ	tζ	X
ejpam-6135	281	13	+	+	NUM
ejpam-6135	281	14	ε/2	ε/2	NUM
ejpam-6135	281	15	)	)	PUNCT
ejpam-6135	281	16	)	)	PUNCT
ejpam-6135	281	17	.	.	PUNCT
ejpam-6135	282	1	if	if	SCONJ
ejpam-6135	282	2	p3	p3	PROPN
ejpam-6135	282	3	∈	∈	PROPN
ejpam-6135	282	4	px	px	NOUN
ejpam-6135	282	5	,	,	PUNCT
ejpam-6135	282	6	since	since	SCONJ
ejpam-6135	282	7	fζ(p3	fζ(p3	NOUN
ejpam-6135	282	8	)	)	PUNCT
ejpam-6135	282	9	=	=	PUNCT
ejpam-6135	282	10	f∗	f∗	NOUN
ejpam-6135	282	11	ζ	ζ	X
ejpam-6135	282	12	(	(	PUNCT
ejpam-6135	282	13	p3	p3	PROPN
ejpam-6135	282	14	)	)	PUNCT
ejpam-6135	282	15	=	=	SYM
ejpam-6135	282	16	tζ	tζ	PROPN
ejpam-6135	282	17	,	,	PUNCT
ejpam-6135	282	18	thus	thus	ADV
ejpam-6135	282	19	p3	p3	PROPN
ejpam-6135	282	20	∈	∈	PROPN
ejpam-6135	282	21	f−1	f−1	PROPN
ejpam-6135	282	22	ζ	ζ	NOUN
ejpam-6135	282	23	(	(	PUNCT
ejpam-6135	282	24	(	(	PUNCT
ejpam-6135	282	25	tζ	tζ	INTJ
ejpam-6135	282	26	−	−	PROPN
ejpam-6135	282	27	ε/2	ε/2	PROPN
ejpam-6135	282	28	,	,	PUNCT
ejpam-6135	282	29	tζ	tζ	X
ejpam-6135	282	30	+	+	NUM
ejpam-6135	282	31	ε/2	ε/2	NUM
ejpam-6135	282	32	)	)	PUNCT
ejpam-6135	282	33	)	)	PUNCT
ejpam-6135	283	1	⊂	⊂	PROPN
ejpam-6135	283	2	(	(	PUNCT
ejpam-6135	283	3	f−1	f−1	PROPN
ejpam-6135	283	4	ζ	ζ	PROPN
ejpam-6135	283	5	(	(	PUNCT
ejpam-6135	283	6	(	(	PUNCT
ejpam-6135	283	7	tζ	tζ	INTJ
ejpam-6135	283	8	−	−	PROPN
ejpam-6135	283	9	ε/2	ε/2	PROPN
ejpam-6135	283	10	,	,	PUNCT
ejpam-6135	283	11	tζ	tζ	PROPN
ejpam-6135	283	12	+	+	CCONJ
ejpam-6135	283	13	ε/2)))∗.	ε/2)))∗.	PROPN
ejpam-6135	284	1	if	if	SCONJ
ejpam-6135	284	2	p3	p3	PROPN
ejpam-6135	284	3	∈	∈	PROPN
ejpam-6135	284	4	yp	yp	PROPN
ejpam-6135	284	5	,	,	PUNCT
ejpam-6135	284	6	then	then	ADV
ejpam-6135	284	7	p3=	p3=	PROPN
ejpam-6135	284	8	{	{	PUNCT
ejpam-6135	284	9	wpi	wpi	PROPN
ejpam-6135	284	10	k	k	PROPN
ejpam-6135	284	11	}	}	PUNCT
ejpam-6135	284	12	∗.	∗.	PROPN
ejpam-6135	284	13	since	since	SCONJ
ejpam-6135	284	14	tζ	tζ	PROPN
ejpam-6135	284	15	=	=	SYM
ejpam-6135	284	16	f∗	f∗	PROPN
ejpam-6135	284	17	ζ	ζ	NOUN
ejpam-6135	284	18	(	(	PUNCT
ejpam-6135	284	19	p3)=	p3)=	PROPN
ejpam-6135	284	20	lim	lim	PROPN
ejpam-6135	284	21	{	{	PUNCT
ejpam-6135	284	22	fζ(wpi	fζ(wpi	PROPN
ejpam-6135	284	23	k	k	PROPN
ejpam-6135	284	24	)	)	PUNCT
ejpam-6135	284	25	,	,	PUNCT
ejpam-6135	284	26	so	so	CCONJ
ejpam-6135	284	27	{	{	PUNCT
ejpam-6135	284	28	wpi	wpi	PROPN
ejpam-6135	284	29	k	k	X
ejpam-6135	284	30	}	}	PUNCT
ejpam-6135	284	31	is	be	AUX
ejpam-6135	284	32	⊘	⊘	X
ejpam-6135	284	33	in	in	ADP
ejpam-6135	284	34	f−1	f−1	PROPN
ejpam-6135	284	35	ζ	ζ	NOUN
ejpam-6135	284	36	(	(	PUNCT
ejpam-6135	284	37	(	(	PUNCT
ejpam-6135	284	38	tζ	tζ	INTJ
ejpam-6135	284	39	−	−	PROPN
ejpam-6135	284	40	ε/2	ε/2	PROPN
ejpam-6135	284	41	,	,	PUNCT
ejpam-6135	284	42	tζ	tζ	X
ejpam-6135	284	43	+	+	NUM
ejpam-6135	284	44	ε/2	ε/2	NUM
ejpam-6135	284	45	)	)	PUNCT
ejpam-6135	284	46	)	)	PUNCT
ejpam-6135	284	47	.	.	PUNCT
ejpam-6135	285	1	that	that	PRON
ejpam-6135	285	2	is	be	AUX
ejpam-6135	285	3	p3	p3	PROPN
ejpam-6135	285	4	=	=	SYM
ejpam-6135	285	5	{	{	PUNCT
ejpam-6135	285	6	wpi	wpi	NOUN
ejpam-6135	285	7	k	k	PROPN
ejpam-6135	285	8	}	}	PUNCT
ejpam-6135	285	9	∗	∗	X
ejpam-6135	285	10	∈	∈	NOUN
ejpam-6135	285	11	(	(	PUNCT
ejpam-6135	285	12	f−1	f−1	PROPN
ejpam-6135	285	13	ζ	ζ	NOUN
ejpam-6135	285	14	(	(	PUNCT
ejpam-6135	285	15	(	(	PUNCT
ejpam-6135	285	16	tζ	tζ	INTJ
ejpam-6135	285	17	−	−	PROPN
ejpam-6135	285	18	ε/2	ε/2	PROPN
ejpam-6135	285	19	,	,	PUNCT
ejpam-6135	285	20	tζ	tζ	PROPN
ejpam-6135	285	21	+	+	CCONJ
ejpam-6135	285	22	ε/2)))∗.	ε/2)))∗.	PROPN
ejpam-6135	285	23	finally	finally	ADV
ejpam-6135	285	24	show	show	VERB
ejpam-6135	285	25	that	that	SCONJ
ejpam-6135	285	26	,	,	PUNCT
ejpam-6135	285	27	(	(	PUNCT
ejpam-6135	285	28	f−1	f−1	PROPN
ejpam-6135	285	29	ζ	ζ	NOUN
ejpam-6135	285	30	(	(	PUNCT
ejpam-6135	285	31	(	(	PUNCT
ejpam-6135	285	32	tζ	tζ	INTJ
ejpam-6135	285	33	−	−	PROPN
ejpam-6135	285	34	ε/2	ε/2	PROPN
ejpam-6135	285	35	,	,	PUNCT
ejpam-6135	285	36	tζ	tζ	X
ejpam-6135	285	37	+	+	CCONJ
ejpam-6135	285	38	ε/2)))∗	ε/2)))∗	PROPN
ejpam-6135	285	39	⊂	⊂	PROPN
ejpam-6135	285	40	(	(	PUNCT
ejpam-6135	285	41	f∗	f∗	NOUN
ejpam-6135	285	42	ζ	ζ	NOUN
ejpam-6135	285	43	)	)	PUNCT
ejpam-6135	285	44	−1((tζ	−1((tζ	NUM
ejpam-6135	285	45	−	−	PROPN
ejpam-6135	285	46	ε	ε	PROPN
ejpam-6135	285	47	,	,	PUNCT
ejpam-6135	285	48	tζ	tζ	PROPN
ejpam-6135	285	49	+	+	NUM
ejpam-6135	285	50	ε	ε	PROPN
ejpam-6135	285	51	)	)	PUNCT
ejpam-6135	285	52	)	)	PUNCT
ejpam-6135	285	53	.	.	PUNCT
ejpam-6135	286	1	if	if	SCONJ
ejpam-6135	286	2	p1	p1	PROPN
ejpam-6135	286	3	is	be	AUX
ejpam-6135	286	4	in	in	ADP
ejpam-6135	286	5	px∩	px∩	PROPN
ejpam-6135	286	6	(	(	PUNCT
ejpam-6135	286	7	f−1	f−1	PROPN
ejpam-6135	286	8	ζ	ζ	NOUN
ejpam-6135	286	9	(	(	PUNCT
ejpam-6135	286	10	(	(	PUNCT
ejpam-6135	286	11	tζ	tζ	INTJ
ejpam-6135	286	12	−	−	PROPN
ejpam-6135	286	13	ε/2	ε/2	PROPN
ejpam-6135	286	14	,	,	PUNCT
ejpam-6135	286	15	tζ	tζ	X
ejpam-6135	287	1	+	+	CCONJ
ejpam-6135	287	2	ε/2)))∗	ε/2)))∗	ADV
ejpam-6135	287	3	then	then	ADV
ejpam-6135	287	4	p1	p1	PROPN
ejpam-6135	287	5	∈	∈	PROPN
ejpam-6135	287	6	f−1	f−1	PROPN
ejpam-6135	287	7	ζ	ζ	NOUN
ejpam-6135	287	8	(	(	PUNCT
ejpam-6135	287	9	(	(	PUNCT
ejpam-6135	287	10	tζ	tζ	INTJ
ejpam-6135	287	11	−	−	PROPN
ejpam-6135	287	12	ε/2	ε/2	PROPN
ejpam-6135	287	13	,	,	PUNCT
ejpam-6135	287	14	tζ	tζ	X
ejpam-6135	287	15	+	+	NUM
ejpam-6135	287	16	ε/2	ε/2	NUM
ejpam-6135	287	17	)	)	PUNCT
ejpam-6135	287	18	)	)	PUNCT
ejpam-6135	287	19	that	that	PRON
ejpam-6135	287	20	is	be	AUX
ejpam-6135	287	21	f∗	f∗	ADJ
ejpam-6135	287	22	ζ	ζ	X
ejpam-6135	287	23	(	(	PUNCT
ejpam-6135	287	24	p1)=	p1)=	NOUN
ejpam-6135	287	25	fζ(p1	fζ(p1	NOUN
ejpam-6135	287	26	)	)	PUNCT
ejpam-6135	287	27	∈	∈	PROPN
ejpam-6135	287	28	(	(	PUNCT
ejpam-6135	287	29	tζ	tζ	NOUN
ejpam-6135	287	30	−	−	PROPN
ejpam-6135	287	31	ε	ε	PROPN
ejpam-6135	287	32	,	,	PUNCT
ejpam-6135	287	33	tζ	tζ	PROPN
ejpam-6135	287	34	+	+	NUM
ejpam-6135	287	35	ε	ε	PROPN
ejpam-6135	287	36	)	)	PUNCT
ejpam-6135	287	37	.	.	PUNCT
ejpam-6135	288	1	so	so	ADV
ejpam-6135	288	2	,	,	PUNCT
ejpam-6135	288	3	p1	p1	PROPN
ejpam-6135	288	4	∈	∈	PROPN
ejpam-6135	288	5	(	(	PUNCT
ejpam-6135	288	6	f∗	f∗	NOUN
ejpam-6135	288	7	ζ	ζ	NOUN
ejpam-6135	288	8	)	)	PUNCT
ejpam-6135	288	9	−1((tζ	−1((tζ	NUM
ejpam-6135	288	10	−	−	PROPN
ejpam-6135	288	11	ε	ε	PROPN
ejpam-6135	288	12	,	,	PUNCT
ejpam-6135	288	13	tζ	tζ	PROPN
ejpam-6135	288	14	+	+	NUM
ejpam-6135	288	15	ε	ε	PROPN
ejpam-6135	288	16	)	)	PUNCT
ejpam-6135	288	17	)	)	PUNCT
ejpam-6135	288	18	.	.	PUNCT
ejpam-6135	289	1	if	if	SCONJ
ejpam-6135	289	2	p2	p2	PROPN
ejpam-6135	289	3	∈	∈	PROPN
ejpam-6135	289	4	(	(	PUNCT
ejpam-6135	289	5	f−1	f−1	PROPN
ejpam-6135	289	6	ζ	ζ	NOUN
ejpam-6135	289	7	(	(	PUNCT
ejpam-6135	289	8	(	(	PUNCT
ejpam-6135	289	9	tζ	tζ	INTJ
ejpam-6135	289	10	−	−	PROPN
ejpam-6135	289	11	ε/2	ε/2	PROPN
ejpam-6135	289	12	,	,	PUNCT
ejpam-6135	289	13	tζ	tζ	X
ejpam-6135	289	14	+	+	CCONJ
ejpam-6135	289	15	ε/2)))∗	ε/2)))∗	NOUN
ejpam-6135	289	16	∩yp	∩yp	NOUN
ejpam-6135	289	17	,	,	PUNCT
ejpam-6135	289	18	then	then	ADV
ejpam-6135	289	19	p2=	p2=	PROPN
ejpam-6135	289	20	{	{	PUNCT
ejpam-6135	289	21	wpi	wpi	PROPN
ejpam-6135	289	22	k	k	X
ejpam-6135	289	23	}	}	PUNCT
ejpam-6135	289	24	∗	∗	NOUN
ejpam-6135	289	25	and	and	CCONJ
ejpam-6135	289	26	{	{	PUNCT
ejpam-6135	289	27	wpi	wpi	NOUN
ejpam-6135	289	28	k	k	PROPN
ejpam-6135	289	29	}	}	PUNCT
ejpam-6135	289	30	is	be	AUX
ejpam-6135	289	31	⊘	⊘	X
ejpam-6135	289	32	in	in	ADP
ejpam-6135	289	33	(	(	PUNCT
ejpam-6135	289	34	fζ	fζ	PROPN
ejpam-6135	289	35	)	)	PUNCT
ejpam-6135	289	36	−1((tζ	−1((tζ	PRON
ejpam-6135	289	37	−ε/2	−ε/2	PROPN
ejpam-6135	289	38	,	,	PUNCT
ejpam-6135	289	39	tζ	tζ	X
ejpam-6135	289	40	+	+	NOUN
ejpam-6135	289	41	ε/2	ε/2	NUM
ejpam-6135	289	42	)	)	PUNCT
ejpam-6135	289	43	)	)	PUNCT
ejpam-6135	289	44	thus	thus	ADV
ejpam-6135	289	45	f∗	f∗	NOUN
ejpam-6135	289	46	ζ	ζ	NOUN
ejpam-6135	289	47	(	(	PUNCT
ejpam-6135	289	48	p2)=	p2)=	PROPN
ejpam-6135	289	49	lim	lim	PROPN
ejpam-6135	289	50	{	{	PUNCT
ejpam-6135	289	51	fζ(wpi	fζ(wpi	PROPN
ejpam-6135	289	52	k	k	PROPN
ejpam-6135	289	53	)	)	PUNCT
ejpam-6135	289	54	}	}	PUNCT
ejpam-6135	289	55	∈	∈	PROPN
ejpam-6135	290	1	[	[	X
ejpam-6135	290	2	tζ	tζ	X
ejpam-6135	290	3	−	−	PROPN
ejpam-6135	290	4	ε/2	ε/2	PROPN
ejpam-6135	290	5	,	,	PUNCT
ejpam-6135	290	6	tζ	tζ	X
ejpam-6135	290	7	+	+	ADJ
ejpam-6135	290	8	ε/2	ε/2	PROPN
ejpam-6135	290	9	]	]	X
ejpam-6135	291	1	⊂	⊂	X
ejpam-6135	291	2	(	(	PUNCT
ejpam-6135	291	3	tζ	tζ	X
ejpam-6135	291	4	−	−	PROPN
ejpam-6135	291	5	ε	ε	PROPN
ejpam-6135	291	6	,	,	PUNCT
ejpam-6135	291	7	tζ	tζ	PROPN
ejpam-6135	291	8	+	+	CCONJ
ejpam-6135	291	9	ε	ε	PROPN
ejpam-6135	291	10	)	)	PUNCT
ejpam-6135	291	11	that	that	PRON
ejpam-6135	291	12	is	be	AUX
ejpam-6135	291	13	p2	p2	PROPN
ejpam-6135	291	14	∈	∈	PROPN
ejpam-6135	291	15	(	(	PUNCT
ejpam-6135	291	16	f∗	f∗	NOUN
ejpam-6135	291	17	ζ	ζ	NOUN
ejpam-6135	291	18	)	)	PUNCT
ejpam-6135	291	19	−1((tζ	−1((tζ	NUM
ejpam-6135	291	20	−	−	PROPN
ejpam-6135	291	21	ε	ε	PROPN
ejpam-6135	291	22	,	,	PUNCT
ejpam-6135	291	23	tζ	tζ	PROPN
ejpam-6135	291	24	+	+	NUM
ejpam-6135	291	25	ε	ε	PROPN
ejpam-6135	291	26	)	)	PUNCT
ejpam-6135	291	27	)	)	PUNCT
ejpam-6135	291	28	.	.	PUNCT
ejpam-6135	292	1	proposition	proposition	NOUN
ejpam-6135	292	2	4	4	NUM
ejpam-6135	292	3	.	.	PUNCT
ejpam-6135	293	1	let	let	VERB
ejpam-6135	293	2	k	k	NOUN
ejpam-6135	293	3	:	:	PUNCT
ejpam-6135	293	4	px	px	PROPN
ejpam-6135	293	5	→	→	SYM
ejpam-6135	293	6	p	p	X
ejpam-6135	293	7	∗	∗	NOUN
ejpam-6135	293	8	x	x	VERB
ejpam-6135	293	9	be	be	AUX
ejpam-6135	293	10	defined	define	VERB
ejpam-6135	293	11	by	by	ADP
ejpam-6135	293	12	k(p1	k(p1	NOUN
ejpam-6135	293	13	)	)	PUNCT
ejpam-6135	294	1	=	=	SYM
ejpam-6135	294	2	p1	p1	PROPN
ejpam-6135	294	3	,	,	PUNCT
ejpam-6135	294	4	then	then	ADV
ejpam-6135	294	5	k	k	PROPN
ejpam-6135	294	6	is	be	AUX
ejpam-6135	294	7	an	an	DET
ejpam-6135	294	8	(	(	PUNCT
ejpam-6135	294	9	c	c	NOUN
ejpam-6135	294	10	,	,	PUNCT
ejpam-6135	294	11	d	d	NOUN
ejpam-6135	294	12	)	)	PUNCT
ejpam-6135	294	13	if	if	SCONJ
ejpam-6135	294	14	−q	−q	ADJ
ejpam-6135	294	15	uniform	uniform	ADJ
ejpam-6135	294	16	ir∗	ir∗	NOUN
ejpam-6135	294	17	centred	centre	VERB
ejpam-6135	294	18	structure	structure	NOUN
ejpam-6135	294	19	continuous	continuous	ADJ
ejpam-6135	294	20	mapping	mapping	NOUN
ejpam-6135	294	21	from	from	ADP
ejpam-6135	294	22	px	px	PROPN
ejpam-6135	294	23	into	into	ADP
ejpam-6135	294	24	p	p	PROPN
ejpam-6135	294	25	∗	∗	NOUN
ejpam-6135	294	26	x	x	X
ejpam-6135	294	27	.	.	PUNCT
ejpam-6135	295	1	proof	proof	NOUN
ejpam-6135	295	2	.	.	PUNCT
ejpam-6135	296	1	for	for	ADP
ejpam-6135	296	2	any	any	DET
ejpam-6135	296	3	(	(	PUNCT
ejpam-6135	296	4	c	c	NOUN
ejpam-6135	296	5	,	,	PUNCT
ejpam-6135	296	6	d	d	NOUN
ejpam-6135	296	7	)	)	PUNCT
ejpam-6135	296	8	if	if	SCONJ
ejpam-6135	296	9	−q	−q	ADJ
ejpam-6135	296	10	uniform	uniform	ADJ
ejpam-6135	296	11	ir∗	ir∗	NOUN
ejpam-6135	296	12	centred	centre	VERB
ejpam-6135	296	13	structure	structure	NOUN
ejpam-6135	296	14	open	open	ADJ
ejpam-6135	296	15	set	set	VERB
ejpam-6135	296	16	u∗	u∗	PROPN
ejpam-6135	296	17	∈b	∈b	PROPN
ejpam-6135	296	18	,	,	PUNCT
ejpam-6135	296	19	k−1(u∗	k−1(u∗	PROPN
ejpam-6135	296	20	)	)	PUNCT
ejpam-6135	296	21	=	=	SYM
ejpam-6135	296	22	u	u	NOUN
ejpam-6135	296	23	is	be	AUX
ejpam-6135	296	24	a	a	DET
ejpam-6135	296	25	(	(	PUNCT
ejpam-6135	296	26	c	c	NOUN
ejpam-6135	296	27	,	,	PUNCT
ejpam-6135	296	28	d	d	NOUN
ejpam-6135	296	29	)	)	PUNCT
ejpam-6135	296	30	if	if	SCONJ
ejpam-6135	296	31	−q	−q	ADJ
ejpam-6135	296	32	uniform	uniform	ADJ
ejpam-6135	296	33	ir∗	ir∗	NOUN
ejpam-6135	296	34	centred	centre	VERB
ejpam-6135	296	35	structure	structure	NOUN
ejpam-6135	296	36	open	open	ADJ
ejpam-6135	296	37	set	set	VERB
ejpam-6135	296	38	in	in	ADP
ejpam-6135	296	39	px	px	PROPN
ejpam-6135	296	40	,	,	PUNCT
ejpam-6135	296	41	so	so	ADV
ejpam-6135	296	42	k	k	PROPN
ejpam-6135	296	43	is	be	AUX
ejpam-6135	296	44	an	an	DET
ejpam-6135	296	45	(	(	PUNCT
ejpam-6135	296	46	c	c	NOUN
ejpam-6135	296	47	,	,	PUNCT
ejpam-6135	296	48	d	d	NOUN
ejpam-6135	296	49	)	)	PUNCT
ejpam-6135	296	50	if	if	SCONJ
ejpam-6135	296	51	−q	−q	ADJ
ejpam-6135	296	52	uniform	uniform	ADJ
ejpam-6135	296	53	ir∗	ir∗	NOUN
ejpam-6135	296	54	centred	centre	VERB
ejpam-6135	296	55	structure	structure	NOUN
ejpam-6135	296	56	continuous	continuous	ADJ
ejpam-6135	296	57	mapping	mapping	NOUN
ejpam-6135	296	58	on	on	ADP
ejpam-6135	296	59	px	px	PROPN
ejpam-6135	296	60	.	.	PROPN
ejpam-6135	296	61	proposition	proposition	NOUN
ejpam-6135	296	62	5	5	NUM
ejpam-6135	296	63	.	.	PUNCT
ejpam-6135	296	64	for	for	ADP
ejpam-6135	296	65	any	any	DET
ejpam-6135	296	66	p2	p2	NOUN
ejpam-6135	296	67	in	in	ADP
ejpam-6135	296	68	p	p	NOUN
ejpam-6135	296	69	∗	∗	NOUN
ejpam-6135	296	70	x	x	PUNCT
ejpam-6135	296	71	−	−	NOUN
ejpam-6135	296	72	px	px	NOUN
ejpam-6135	296	73	with	with	ADP
ejpam-6135	296	74	p2	p2	PROPN
ejpam-6135	296	75	=	=	SYM
ejpam-6135	296	76	{	{	PUNCT
ejpam-6135	296	77	wpi	wpi	NOUN
ejpam-6135	296	78	k	k	X
ejpam-6135	296	79	}	}	PUNCT
ejpam-6135	296	80	∗	∗	NOUN
ejpam-6135	296	81	,	,	PUNCT
ejpam-6135	296	82	{	{	PUNCT
ejpam-6135	296	83	k(wpi	k(wpi	X
ejpam-6135	296	84	k	k	PROPN
ejpam-6135	296	85	)	)	PUNCT
ejpam-6135	296	86	}	}	PUNCT
ejpam-6135	296	87	converges	converge	VERB
ejpam-6135	296	88	to	to	ADP
ejpam-6135	296	89	p2=	p2=	PROPN
ejpam-6135	296	90	{	{	PUNCT
ejpam-6135	296	91	(	(	PUNCT
ejpam-6135	296	92	wpi	wpi	PROPN
ejpam-6135	296	93	k	k	PROPN
ejpam-6135	296	94	)	)	PUNCT
ejpam-6135	296	95	}	}	PUNCT
ejpam-6135	297	1	∗.	∗.	NOUN
ejpam-6135	297	2	proof	proof	NOUN
ejpam-6135	297	3	.	.	PUNCT
ejpam-6135	298	1	let	let	VERB
ejpam-6135	298	2	u∗	u∗	ADV
ejpam-6135	298	3	be	be	AUX
ejpam-6135	298	4	any	any	DET
ejpam-6135	298	5	(	(	PUNCT
ejpam-6135	298	6	c	c	NOUN
ejpam-6135	298	7	,	,	PUNCT
ejpam-6135	298	8	d	d	NOUN
ejpam-6135	298	9	)	)	PUNCT
ejpam-6135	298	10	if	if	SCONJ
ejpam-6135	298	11	−q	−q	ADJ
ejpam-6135	298	12	uniform	uniform	ADJ
ejpam-6135	298	13	ir∗	ir∗	NOUN
ejpam-6135	298	14	centred	centre	VERB
ejpam-6135	298	15	structure	structure	NOUN
ejpam-6135	298	16	open	open	NOUN
ejpam-6135	298	17	set	set	VERB
ejpam-6135	298	18	in	in	ADP
ejpam-6135	298	19	b	b	NOUN
ejpam-6135	298	20	containing	contain	VERB
ejpam-6135	298	21	p2	p2	NOUN
ejpam-6135	298	22	then	then	ADV
ejpam-6135	298	23	{	{	PUNCT
ejpam-6135	298	24	(	(	PUNCT
ejpam-6135	298	25	wpi	wpi	NOUN
ejpam-6135	298	26	k	k	X
ejpam-6135	298	27	}	}	PUNCT
ejpam-6135	298	28	and	and	CCONJ
ejpam-6135	298	29	⊘	⊘	NUM
ejpam-6135	298	30	∈	∈	PROPN
ejpam-6135	298	31	u	u	PROPN
ejpam-6135	298	32	in	in	ADP
ejpam-6135	298	33	px	px	PROPN
ejpam-6135	298	34	.	.	PUNCT
ejpam-6135	299	1	this	this	PRON
ejpam-6135	299	2	implies	imply	VERB
ejpam-6135	299	3	that	that	SCONJ
ejpam-6135	299	4	{	{	PUNCT
ejpam-6135	299	5	k(wpi	k(wpi	X
ejpam-6135	299	6	k	k	PROPN
ejpam-6135	299	7	)	)	PUNCT
ejpam-6135	299	8	}	}	PUNCT
ejpam-6135	299	9	is	be	AUX
ejpam-6135	299	10	⊘	⊘	X
ejpam-6135	299	11	in	in	ADP
ejpam-6135	299	12	u∗	u∗	PROPN
ejpam-6135	299	13	,	,	PUNCT
ejpam-6135	299	14	thus	thus	ADV
ejpam-6135	299	15	{	{	PUNCT
ejpam-6135	299	16	k(wpi	k(wpi	X
ejpam-6135	299	17	k	k	PROPN
ejpam-6135	299	18	)	)	PUNCT
ejpam-6135	299	19	}	}	PUNCT
ejpam-6135	299	20	it	it	PRON
ejpam-6135	299	21	is	be	AUX
ejpam-6135	299	22	converged	converge	VERB
ejpam-6135	299	23	to	to	ADP
ejpam-6135	299	24	p2={wpi	p2={wpi	PROPN
ejpam-6135	299	25	k	k	PROPN
ejpam-6135	299	26	}	}	PUNCT
ejpam-6135	299	27	∗.	∗.	PROPN
ejpam-6135	299	28	s.	s.	PROPN
ejpam-6135	299	29	thirukumaran	thirukumaran	PROPN
ejpam-6135	299	30	,	,	PUNCT
ejpam-6135	299	31	g.	g.	PROPN
ejpam-6135	299	32	k.	k.	PROPN
ejpam-6135	299	33	revathi	revathi	PROPN
ejpam-6135	299	34	/	/	SYM
ejpam-6135	299	35	eur	eur	PROPN
ejpam-6135	299	36	.	.	PUNCT
ejpam-6135	300	1	j.	j.	PROPN
ejpam-6135	300	2	pure	pure	PROPN
ejpam-6135	300	3	appl	appl	PROPN
ejpam-6135	300	4	.	.	PROPN
ejpam-6135	300	5	math	math	PROPN
ejpam-6135	300	6	,	,	PUNCT
ejpam-6135	300	7	18	18	NUM
ejpam-6135	300	8	(	(	PUNCT
ejpam-6135	300	9	2	2	NUM
ejpam-6135	300	10	)	)	PUNCT
ejpam-6135	300	11	(	(	PUNCT
ejpam-6135	300	12	2025	2025	NUM
ejpam-6135	300	13	)	)	PUNCT
ejpam-6135	300	14	,	,	PUNCT
ejpam-6135	300	15	6135	6135	NUM
ejpam-6135	300	16	14	14	NUM
ejpam-6135	300	17	of	of	ADP
ejpam-6135	300	18	17	17	NUM
ejpam-6135	300	19	proposition	proposition	NOUN
ejpam-6135	300	20	6	6	NUM
ejpam-6135	300	21	.	.	PUNCT
ejpam-6135	301	1	k(px	k(px	NOUN
ejpam-6135	301	2	)	)	PUNCT
ejpam-6135	301	3	is	be	AUX
ejpam-6135	301	4	an	an	DET
ejpam-6135	301	5	(	(	PUNCT
ejpam-6135	301	6	c	c	NOUN
ejpam-6135	301	7	,	,	PUNCT
ejpam-6135	301	8	d	d	NOUN
ejpam-6135	301	9	)	)	PUNCT
ejpam-6135	301	10	if	if	SCONJ
ejpam-6135	301	11	−q	−q	ADJ
ejpam-6135	301	12	uniform	uniform	ADJ
ejpam-6135	301	13	ir∗	ir∗	NOUN
ejpam-6135	301	14	centred	centre	VERB
ejpam-6135	301	15	structure	structure	NOUN
ejpam-6135	301	16	dense	dense	ADJ
ejpam-6135	301	17	in	in	ADP
ejpam-6135	301	18	p	p	NOUN
ejpam-6135	301	19	∗	∗	NOUN
ejpam-6135	301	20	x	x	PUNCT
ejpam-6135	301	21	proof	proof	NOUN
ejpam-6135	301	22	.	.	PUNCT
ejpam-6135	302	1	for	for	ADP
ejpam-6135	302	2	any	any	DET
ejpam-6135	302	3	p2	p2	NOUN
ejpam-6135	302	4	in	in	ADP
ejpam-6135	302	5	p	p	NOUN
ejpam-6135	302	6	∗	∗	NOUN
ejpam-6135	302	7	x	x	PUNCT
ejpam-6135	302	8	−px	−px	NOUN
ejpam-6135	302	9	.	.	PUNCT
ejpam-6135	302	10	p2	p2	PROPN
ejpam-6135	302	11	=	=	SYM
ejpam-6135	302	12	{	{	PUNCT
ejpam-6135	302	13	wpi	wpi	NOUN
ejpam-6135	302	14	k	k	PROPN
ejpam-6135	302	15	}	}	PUNCT
ejpam-6135	302	16	∗.	∗.	PROPN
ejpam-6135	302	17	by	by	ADP
ejpam-6135	302	18	the	the	DET
ejpam-6135	302	19	above	above	ADJ
ejpam-6135	302	20	proposition	proposition	NOUN
ejpam-6135	302	21	5	5	NUM
ejpam-6135	302	22	,	,	PUNCT
ejpam-6135	302	23	implies	imply	VERB
ejpam-6135	302	24	that	that	SCONJ
ejpam-6135	302	25	{	{	PUNCT
ejpam-6135	302	26	k(wpi	k(wpi	ADV
ejpam-6135	302	27	i	i	PRON
ejpam-6135	302	28	)	)	PUNCT
ejpam-6135	302	29	}	}	PUNCT
ejpam-6135	302	30	converges	converge	VERB
ejpam-6135	302	31	to	to	ADP
ejpam-6135	302	32	p2={wpi	p2={wpi	PROPN
ejpam-6135	302	33	k	k	X
ejpam-6135	302	34	}	}	PUNCT
ejpam-6135	302	35	∗.	∗.	PROPN
ejpam-6135	302	36	thus	thus	ADV
ejpam-6135	302	37	ir∗	ir∗	PROPN
ejpam-6135	302	38	cp	cp	PROPN
ejpam-6135	302	39	cl(k(px))=p	cl(k(px))=p	PROPN
ejpam-6135	302	40	∗	∗	NOUN
ejpam-6135	302	41	x.	x.	NOUN
ejpam-6135	302	42	remark	remark	PROPN
ejpam-6135	302	43	4	4	NUM
ejpam-6135	302	44	.	.	PUNCT
ejpam-6135	303	1	here	here	ADV
ejpam-6135	303	2	,	,	PUNCT
ejpam-6135	303	3	c={f∗	c={f∗	NOUN
ejpam-6135	303	4	ζ	ζ	NOUN
ejpam-6135	303	5	:	:	PUNCT
ejpam-6135	303	6	fζ	fζ	PROPN
ejpam-6135	303	7	∈	∈	PROPN
ejpam-6135	303	8	δ	δ	PROPN
ejpam-6135	303	9	}	}	PUNCT
ejpam-6135	303	10	represent	represent	VERB
ejpam-6135	303	11	{	{	PUNCT
ejpam-6135	303	12	f∗	f∗	NOUN
ejpam-6135	303	13	ζ	ζ	NOUN
ejpam-6135	303	14	:	:	PUNCT
ejpam-6135	303	15	fζ	fζ	PROPN
ejpam-6135	303	16	∈	∈	PROPN
ejpam-6135	303	17	c∗(px	c∗(px	NOUN
ejpam-6135	303	18	)	)	PUNCT
ejpam-6135	303	19	}	}	PUNCT
ejpam-6135	303	20	.	.	PUNCT
ejpam-6135	304	1	each	each	DET
ejpam-6135	304	2	c	c	PROPN
ejpam-6135	304	3	net	net	NOUN
ejpam-6135	304	4	pi	pi	NOUN
ejpam-6135	304	5	in	in	ADP
ejpam-6135	304	6	p	p	NOUN
ejpam-6135	304	7	∗	∗	NOUN
ejpam-6135	304	8	x	x	PUNCT
ejpam-6135	304	9	and	and	CCONJ
ejpam-6135	304	10	e	e	X
ejpam-6135	304	11	=	=	PUNCT
ejpam-6135	304	12	{	{	PUNCT
ejpam-6135	304	13	o	o	NOUN
ejpam-6135	304	14	:	:	PUNCT
ejpam-6135	304	15	o	o	NOUN
ejpam-6135	304	16	is	be	AUX
ejpam-6135	304	17	an	an	DET
ejpam-6135	304	18	(	(	PUNCT
ejpam-6135	304	19	c	c	NOUN
ejpam-6135	304	20	,	,	PUNCT
ejpam-6135	304	21	d	d	NOUN
ejpam-6135	304	22	)	)	PUNCT
ejpam-6135	304	23	if	if	SCONJ
ejpam-6135	304	24	−q	−q	ADJ
ejpam-6135	304	25	uniform	uniform	ADJ
ejpam-6135	304	26	ir∗	ir∗	NOUN
ejpam-6135	304	27	centred	centre	VERB
ejpam-6135	304	28	structure	structure	NOUN
ejpam-6135	304	29	open	open	ADJ
ejpam-6135	304	30	in	in	ADP
ejpam-6135	304	31	p	p	NOUN
ejpam-6135	304	32	∗	∗	NOUN
ejpam-6135	304	33	x	x	PUNCT
ejpam-6135	304	34	and	and	CCONJ
ejpam-6135	304	35	{	{	PUNCT
ejpam-6135	304	36	pi	pi	NOUN
ejpam-6135	304	37	}	}	PUNCT
ejpam-6135	304	38	is	be	AUX
ejpam-6135	304	39	⊘	⊘	X
ejpam-6135	304	40	in	in	ADP
ejpam-6135	304	41	o	o	NOUN
ejpam-6135	304	42	}	}	PUNCT
ejpam-6135	304	43	.	.	PUNCT
ejpam-6135	305	1	l	l	NOUN
ejpam-6135	305	2	=	=	PUNCT
ejpam-6135	305	3	{	{	PUNCT
ejpam-6135	305	4	u	u	NOUN
ejpam-6135	305	5	:	:	PUNCT
ejpam-6135	305	6	u	u	NOUN
ejpam-6135	305	7	is	be	AUX
ejpam-6135	305	8	an	an	DET
ejpam-6135	305	9	(	(	PUNCT
ejpam-6135	305	10	c	c	NOUN
ejpam-6135	305	11	,	,	PUNCT
ejpam-6135	305	12	d	d	NOUN
ejpam-6135	305	13	)	)	PUNCT
ejpam-6135	305	14	if	if	SCONJ
ejpam-6135	305	15	−q	−q	ADJ
ejpam-6135	305	16	uniform	uniform	ADJ
ejpam-6135	305	17	ir∗	ir∗	NOUN
ejpam-6135	305	18	centred	centre	VERB
ejpam-6135	305	19	structure	structure	NOUN
ejpam-6135	305	20	open	open	ADJ
ejpam-6135	305	21	in	in	ADP
ejpam-6135	305	22	px	px	NOUN
ejpam-6135	305	23	and	and	CCONJ
ejpam-6135	305	24	u∗	u∗	PROPN
ejpam-6135	305	25	∈	∈	PROPN
ejpam-6135	305	26	e	e	NOUN
ejpam-6135	305	27	}	}	PUNCT
ejpam-6135	305	28	.	.	PUNCT
ejpam-6135	306	1	proposition	proposition	NOUN
ejpam-6135	306	2	7	7	NUM
ejpam-6135	306	3	.	.	X
ejpam-6135	306	4	for	for	ADP
ejpam-6135	306	5	a	a	DET
ejpam-6135	306	6	c	c	PROPN
ejpam-6135	306	7	net	net	NOUN
ejpam-6135	306	8	{	{	PUNCT
ejpam-6135	306	9	pi	pi	NOUN
ejpam-6135	306	10	}	}	PUNCT
ejpam-6135	306	11	,	,	PUNCT
ejpam-6135	306	12	in	in	ADP
ejpam-6135	306	13	p	p	NOUN
ejpam-6135	306	14	∗	∗	NOUN
ejpam-6135	306	15	x.	x.	NOUN
ejpam-6135	306	16	let	let	AUX
ejpam-6135	306	17	rζ=	rζ=	VERB
ejpam-6135	306	18	lim	lim	PROPN
ejpam-6135	306	19	{	{	PUNCT
ejpam-6135	306	20	f∗	f∗	PROPN
ejpam-6135	306	21	ζ	ζ	PROPN
ejpam-6135	306	22	(	(	PUNCT
ejpam-6135	306	23	pi	pi	NOUN
ejpam-6135	306	24	)	)	PUNCT
ejpam-6135	306	25	}	}	PUNCT
ejpam-6135	306	26	.	.	PUNCT
ejpam-6135	307	1	all	all	PRON
ejpam-6135	307	2	f∗	f∗	NOUN
ejpam-6135	307	3	ζ	ζ	PROPN
ejpam-6135	307	4	∈	∈	PROPN
ejpam-6135	307	5	c.	c.	NOUN
ejpam-6135	307	6	then	then	ADV
ejpam-6135	307	7	for	for	ADP
ejpam-6135	307	8	arbitrary	arbitrary	ADJ
ejpam-6135	307	9	ε	ε	PROPN
ejpam-6135	307	10	>	>	X
ejpam-6135	307	11	0	0	PROPN
ejpam-6135	307	12	,	,	PUNCT
ejpam-6135	307	13	(	(	PUNCT
ejpam-6135	307	14	f∗	f∗	NOUN
ejpam-6135	307	15	ζ	ζ	NOUN
ejpam-6135	307	16	)	)	PUNCT
ejpam-6135	308	1	−1((rζ	−1((rζ	NUM
ejpam-6135	308	2	−	−	PROPN
ejpam-6135	308	3	ε	ε	PROPN
ejpam-6135	308	4	,	,	PUNCT
ejpam-6135	308	5	rζ	rζ	X
ejpam-6135	308	6	+	+	CCONJ
ejpam-6135	308	7	ε	ε	PROPN
ejpam-6135	308	8	)	)	PUNCT
ejpam-6135	308	9	)	)	PUNCT
ejpam-6135	309	1	⊂	⊂	PROPN
ejpam-6135	309	2	(	(	PUNCT
ejpam-6135	309	3	f−1	f−1	PROPN
ejpam-6135	309	4	ζ	ζ	PROPN
ejpam-6135	309	5	(	(	PUNCT
ejpam-6135	309	6	(	(	PUNCT
ejpam-6135	309	7	rζ	rζ	NOUN
ejpam-6135	309	8	−	−	PROPN
ejpam-6135	309	9	ε	ε	PROPN
ejpam-6135	309	10	,	,	PUNCT
ejpam-6135	309	11	rζ	rζ	X
ejpam-6135	309	12	+	+	CCONJ
ejpam-6135	309	13	ε)))∗.	ε)))∗.	NOUN
ejpam-6135	309	14	proof	proof	NOUN
ejpam-6135	309	15	.	.	PUNCT
ejpam-6135	310	1	consider	consider	VERB
ejpam-6135	310	2	,	,	PUNCT
ejpam-6135	310	3	p3	p3	PROPN
ejpam-6135	310	4	∈	∈	PROPN
ejpam-6135	310	5	(	(	PUNCT
ejpam-6135	310	6	f∗	f∗	NOUN
ejpam-6135	310	7	ζ	ζ	NOUN
ejpam-6135	310	8	)	)	PUNCT
ejpam-6135	311	1	−1((rζ	−1((rζ	NUM
ejpam-6135	311	2	−	−	PROPN
ejpam-6135	311	3	ε	ε	PROPN
ejpam-6135	311	4	,	,	PUNCT
ejpam-6135	311	5	rζ	rζ	X
ejpam-6135	311	6	+	+	CCONJ
ejpam-6135	311	7	ε	ε	PROPN
ejpam-6135	311	8	)	)	PUNCT
ejpam-6135	311	9	)	)	PUNCT
ejpam-6135	311	10	,	,	PUNCT
ejpam-6135	311	11	then	then	ADV
ejpam-6135	311	12	f∗	f∗	NOUN
ejpam-6135	311	13	ζ	ζ	PROPN
ejpam-6135	311	14	(	(	PUNCT
ejpam-6135	311	15	p3	p3	PROPN
ejpam-6135	311	16	)	)	PUNCT
ejpam-6135	311	17	∈	∈	PROPN
ejpam-6135	311	18	(	(	PUNCT
ejpam-6135	311	19	rζ	rζ	NOUN
ejpam-6135	311	20	−	−	PROPN
ejpam-6135	311	21	ε	ε	PROPN
ejpam-6135	311	22	,	,	PUNCT
ejpam-6135	311	23	rζ	rζ	X
ejpam-6135	311	24	+	+	CCONJ
ejpam-6135	311	25	ε	ε	PROPN
ejpam-6135	311	26	)	)	PUNCT
ejpam-6135	311	27	.	.	PUNCT
ejpam-6135	312	1	if	if	SCONJ
ejpam-6135	312	2	p3	p3	PROPN
ejpam-6135	312	3	=	=	NOUN
ejpam-6135	312	4	k(p1	k(p1	NOUN
ejpam-6135	312	5	)	)	PUNCT
ejpam-6135	312	6	=	=	SYM
ejpam-6135	313	1	p1,∀	p1,∀	NOUN
ejpam-6135	313	2	p	p	NOUN
ejpam-6135	313	3	∈	∈	PROPN
ejpam-6135	313	4	px	px	NOUN
ejpam-6135	313	5	.	.	PUNCT
ejpam-6135	314	1	given	give	VERB
ejpam-6135	314	2	that	that	PRON
ejpam-6135	314	3	,	,	PUNCT
ejpam-6135	314	4	fζ(p1)=	fζ(p1)=	NOUN
ejpam-6135	314	5	f∗	f∗	NOUN
ejpam-6135	314	6	ζ	ζ	X
ejpam-6135	314	7	(	(	PUNCT
ejpam-6135	314	8	p3	p3	PROPN
ejpam-6135	314	9	)	)	PUNCT
ejpam-6135	314	10	,	,	PUNCT
ejpam-6135	314	11	so	so	ADV
ejpam-6135	314	12	p1	p1	PROPN
ejpam-6135	314	13	is	be	AUX
ejpam-6135	314	14	in	in	ADP
ejpam-6135	314	15	(	(	PUNCT
ejpam-6135	314	16	fζ	fζ	ADP
ejpam-6135	314	17	)	)	PUNCT
ejpam-6135	314	18	−1((rζ	−1((rζ	PROPN
ejpam-6135	314	19	−	−	PROPN
ejpam-6135	314	20	ε	ε	PROPN
ejpam-6135	314	21	,	,	PUNCT
ejpam-6135	314	22	rζ	rζ	X
ejpam-6135	315	1	+	+	CCONJ
ejpam-6135	315	2	ε))∗.	ε))∗.	ADV
ejpam-6135	315	3	if	if	SCONJ
ejpam-6135	315	4	p3=	p3=	PROPN
ejpam-6135	315	5	{	{	PUNCT
ejpam-6135	315	6	wpi	wpi	PROPN
ejpam-6135	315	7	k	k	PROPN
ejpam-6135	315	8	}	}	PUNCT
ejpam-6135	315	9	∗	∗	NOUN
ejpam-6135	315	10	in	in	ADP
ejpam-6135	315	11	yp	yp	PROPN
ejpam-6135	315	12	,	,	PUNCT
ejpam-6135	315	13	then	then	ADV
ejpam-6135	315	14	lim	lim	PROPN
ejpam-6135	315	15	{	{	PUNCT
ejpam-6135	315	16	fζ(wpi	fζ(wpi	PROPN
ejpam-6135	315	17	k	k	PROPN
ejpam-6135	315	18	)	)	PUNCT
ejpam-6135	315	19	}	}	PUNCT
ejpam-6135	315	20	=	=	SYM
ejpam-6135	315	21	f∗	f∗	NOUN
ejpam-6135	315	22	ζ	ζ	X
ejpam-6135	315	23	(	(	PUNCT
ejpam-6135	315	24	p3	p3	PROPN
ejpam-6135	315	25	)	)	PUNCT
ejpam-6135	315	26	∈	∈	PROPN
ejpam-6135	315	27	(	(	PUNCT
ejpam-6135	315	28	rζ	rζ	NOUN
ejpam-6135	315	29	−	−	PROPN
ejpam-6135	315	30	ε	ε	PROPN
ejpam-6135	315	31	,	,	PUNCT
ejpam-6135	315	32	rζ	rζ	X
ejpam-6135	315	33	+	+	CCONJ
ejpam-6135	315	34	ε	ε	PROPN
ejpam-6135	315	35	)	)	PUNCT
ejpam-6135	315	36	.	.	PUNCT
ejpam-6135	316	1	this	this	PRON
ejpam-6135	316	2	implies	imply	VERB
ejpam-6135	316	3	that	that	SCONJ
ejpam-6135	316	4	{	{	PUNCT
ejpam-6135	316	5	wpi	wpi	PROPN
ejpam-6135	316	6	k	k	X
ejpam-6135	316	7	}	}	PUNCT
ejpam-6135	316	8	is	be	AUX
ejpam-6135	316	9	⊘	⊘	X
ejpam-6135	316	10	in	in	ADP
ejpam-6135	316	11	(	(	PUNCT
ejpam-6135	316	12	fζ	fζ	ADJ
ejpam-6135	316	13	)	)	PUNCT
ejpam-6135	316	14	−1	−1	NOUN
ejpam-6135	316	15	(	(	PUNCT
ejpam-6135	316	16	(	(	PUNCT
ejpam-6135	316	17	rζ	rζ	NOUN
ejpam-6135	316	18	−	−	PROPN
ejpam-6135	316	19	ε	ε	PROPN
ejpam-6135	316	20	,	,	PUNCT
ejpam-6135	316	21	rζ	rζ	X
ejpam-6135	316	22	+	+	CCONJ
ejpam-6135	316	23	ε	ε	PROPN
ejpam-6135	316	24	)	)	PUNCT
ejpam-6135	316	25	)	)	PUNCT
ejpam-6135	316	26	thus	thus	ADV
ejpam-6135	316	27	{	{	PUNCT
ejpam-6135	316	28	wpi	wpi	NOUN
ejpam-6135	316	29	k	k	PROPN
ejpam-6135	316	30	}	}	PUNCT
ejpam-6135	316	31	is	be	AUX
ejpam-6135	316	32	in	in	ADP
ejpam-6135	316	33	(	(	PUNCT
ejpam-6135	316	34	fζ	fζ	ADJ
ejpam-6135	316	35	)	)	PUNCT
ejpam-6135	316	36	−1(rζ	−1(rζ	NOUN
ejpam-6135	316	37	−	−	PROPN
ejpam-6135	316	38	ε	ε	PROPN
ejpam-6135	316	39	,	,	PUNCT
ejpam-6135	316	40	rζ	rζ	NOUN
ejpam-6135	317	1	+	+	CCONJ
ejpam-6135	317	2	ε)∗.	ε)∗.	PROPN
ejpam-6135	317	3	corollary	corollary	NOUN
ejpam-6135	317	4	1	1	NUM
ejpam-6135	317	5	.	.	PUNCT
ejpam-6135	318	1	for	for	ADP
ejpam-6135	318	2	a	a	DET
ejpam-6135	318	3	c	c	PROPN
ejpam-6135	318	4	net	net	NOUN
ejpam-6135	318	5	{	{	PUNCT
ejpam-6135	318	6	pi	pi	NOUN
ejpam-6135	318	7	}	}	PUNCT
ejpam-6135	318	8	in	in	ADP
ejpam-6135	318	9	p	p	NOUN
ejpam-6135	318	10	∗	∗	NOUN
ejpam-6135	318	11	x	x	X
ejpam-6135	318	12	.	.	PUNCT
ejpam-6135	319	1	let	let	VERB
ejpam-6135	319	2	rα	rα	VERB
ejpam-6135	319	3	=	=	VERB
ejpam-6135	319	4	lim	lim	NOUN
ejpam-6135	319	5	{	{	PUNCT
ejpam-6135	319	6	f∗	f∗	PROPN
ejpam-6135	319	7	ζ	ζ	PROPN
ejpam-6135	319	8	(	(	PUNCT
ejpam-6135	319	9	pi	pi	NOUN
ejpam-6135	319	10	)	)	PUNCT
ejpam-6135	319	11	}	}	PUNCT
ejpam-6135	319	12	for	for	ADP
ejpam-6135	319	13	every	every	DET
ejpam-6135	319	14	f∗	f∗	NOUN
ejpam-6135	319	15	ζ	ζ	PROPN
ejpam-6135	319	16	∈	∈	PROPN
ejpam-6135	319	17	c.	c.	NOUN
ejpam-6135	319	18	then	then	ADV
ejpam-6135	319	19	for	for	ADP
ejpam-6135	319	20	arbitrary	arbitrary	ADJ
ejpam-6135	319	21	ε	ε	PROPN
ejpam-6135	319	22	>	>	X
ejpam-6135	319	23	0	0	PROPN
ejpam-6135	319	24	,	,	PUNCT
ejpam-6135	319	25	(	(	PUNCT
ejpam-6135	319	26	f∗	f∗	NOUN
ejpam-6135	319	27	ζ	ζ	NOUN
ejpam-6135	319	28	)	)	PUNCT
ejpam-6135	320	1	−1((rζ	−1((rζ	NUM
ejpam-6135	320	2	−	−	PROPN
ejpam-6135	320	3	ε	ε	PROPN
ejpam-6135	320	4	,	,	PUNCT
ejpam-6135	320	5	rζ	rζ	X
ejpam-6135	320	6	+	+	CCONJ
ejpam-6135	320	7	ε	ε	PROPN
ejpam-6135	320	8	)	)	PUNCT
ejpam-6135	320	9	)	)	PUNCT
ejpam-6135	320	10	∈	∈	PROPN
ejpam-6135	320	11	e	e	X
ejpam-6135	320	12	and	and	CCONJ
ejpam-6135	320	13	(	(	PUNCT
ejpam-6135	320	14	fζ	fζ	ADP
ejpam-6135	320	15	)	)	PUNCT
ejpam-6135	320	16	−1((rζ	−1((rζ	PROPN
ejpam-6135	320	17	−	−	PROPN
ejpam-6135	320	18	ε	ε	PROPN
ejpam-6135	320	19	,	,	PUNCT
ejpam-6135	320	20	rζ	rζ	X
ejpam-6135	320	21	+	+	CCONJ
ejpam-6135	320	22	ε	ε	PROPN
ejpam-6135	320	23	)	)	PUNCT
ejpam-6135	320	24	)	)	PUNCT
ejpam-6135	320	25	∈	∈	PROPN
ejpam-6135	320	26	l.	l.	NOUN
ejpam-6135	320	27	proof	proof	NOUN
ejpam-6135	320	28	.	.	PUNCT
ejpam-6135	321	1	here	here	ADV
ejpam-6135	321	2	,	,	PUNCT
ejpam-6135	321	3	(	(	PUNCT
ejpam-6135	321	4	f∗	f∗	NOUN
ejpam-6135	321	5	ζ	ζ	NOUN
ejpam-6135	321	6	)	)	PUNCT
ejpam-6135	321	7	−1	−1	NOUN
ejpam-6135	321	8	(	(	PUNCT
ejpam-6135	321	9	(	(	PUNCT
ejpam-6135	321	10	rζ	rζ	NOUN
ejpam-6135	321	11	−	−	PROPN
ejpam-6135	321	12	ε	ε	PROPN
ejpam-6135	321	13	,	,	PUNCT
ejpam-6135	321	14	rζ	rζ	X
ejpam-6135	321	15	+	+	CCONJ
ejpam-6135	321	16	ε	ε	PROPN
ejpam-6135	321	17	)	)	PUNCT
ejpam-6135	321	18	)	)	PUNCT
ejpam-6135	322	1	∈	∈	PROPN
ejpam-6135	322	2	e.	e.	PROPN
ejpam-6135	322	3	by	by	ADP
ejpam-6135	322	4	the	the	DET
ejpam-6135	322	5	above	above	ADJ
ejpam-6135	322	6	proposition	proposition	NOUN
ejpam-6135	322	7	7	7	NUM
ejpam-6135	322	8	,	,	PUNCT
ejpam-6135	322	9	{	{	PUNCT
ejpam-6135	322	10	pi	pi	NOUN
ejpam-6135	322	11	}	}	PUNCT
ejpam-6135	322	12	is	be	AUX
ejpam-6135	322	13	⊘	⊘	X
ejpam-6135	322	14	in	in	ADP
ejpam-6135	322	15	(	(	PUNCT
ejpam-6135	322	16	fζ	fζ	ADP
ejpam-6135	322	17	)	)	PUNCT
ejpam-6135	322	18	−1((rζ	−1((rζ	PROPN
ejpam-6135	322	19	−	−	PROPN
ejpam-6135	322	20	ε	ε	PROPN
ejpam-6135	322	21	,	,	PUNCT
ejpam-6135	322	22	rζ	rζ	NOUN
ejpam-6135	322	23	+	+	CCONJ
ejpam-6135	322	24	ε))∗	ε))∗	PROPN
ejpam-6135	322	25	,	,	PUNCT
ejpam-6135	322	26	thus	thus	ADV
ejpam-6135	322	27	(	(	PUNCT
ejpam-6135	322	28	fζ	fζ	ADP
ejpam-6135	322	29	)	)	PUNCT
ejpam-6135	322	30	−1((rζ	−1((rζ	PROPN
ejpam-6135	322	31	−	−	PROPN
ejpam-6135	322	32	ε	ε	PROPN
ejpam-6135	322	33	,	,	PUNCT
ejpam-6135	322	34	rζ	rζ	X
ejpam-6135	322	35	+	+	CCONJ
ejpam-6135	322	36	ε	ε	PROPN
ejpam-6135	322	37	)	)	PUNCT
ejpam-6135	322	38	)	)	PUNCT
ejpam-6135	323	1	∈	∈	PROPN
ejpam-6135	323	2	l	l	NOUN
ejpam-6135	323	3	proposition	proposition	NOUN
ejpam-6135	323	4	8	8	NUM
ejpam-6135	323	5	.	.	PUNCT
ejpam-6135	324	1	e	e	NOUN
ejpam-6135	324	2	and	and	CCONJ
ejpam-6135	324	3	l	l	NOUN
ejpam-6135	324	4	are	be	AUX
ejpam-6135	324	5	(	(	PUNCT
ejpam-6135	324	6	c	c	X
ejpam-6135	324	7	,	,	PUNCT
ejpam-6135	324	8	d	d	NOUN
ejpam-6135	324	9	)	)	PUNCT
ejpam-6135	324	10	if	if	SCONJ
ejpam-6135	324	11	−q	−q	ADJ
ejpam-6135	324	12	uniform	uniform	ADJ
ejpam-6135	324	13	ir∗	ir∗	NOUN
ejpam-6135	324	14	centred	centre	VERB
ejpam-6135	324	15	structure	structure	NOUN
ejpam-6135	324	16	open	open	ADJ
ejpam-6135	324	17	filter	filter	NOUN
ejpam-6135	324	18	on	on	ADP
ejpam-6135	324	19	p	p	NOUN
ejpam-6135	324	20	∗	∗	NOUN
ejpam-6135	324	21	x	x	PUNCT
ejpam-6135	324	22	and	and	CCONJ
ejpam-6135	324	23	px	px	X
ejpam-6135	324	24	respectively	respectively	ADV
ejpam-6135	324	25	.	.	PUNCT
ejpam-6135	325	1	proof	proof	NOUN
ejpam-6135	325	2	.	.	PUNCT
ejpam-6135	326	1	building	build	VERB
ejpam-6135	326	2	on	on	ADP
ejpam-6135	326	3	the	the	DET
ejpam-6135	326	4	proof	proof	NOUN
ejpam-6135	326	5	of	of	ADP
ejpam-6135	326	6	proposition	proposition	NOUN
ejpam-6135	326	7	1	1	NUM
ejpam-6135	326	8	and	and	CCONJ
ejpam-6135	326	9	corollary	corollary	ADJ
ejpam-6135	326	10	1	1	NUM
ejpam-6135	326	11	,	,	PUNCT
ejpam-6135	326	12	it	it	PRON
ejpam-6135	326	13	is	be	AUX
ejpam-6135	326	14	evident	evident	ADJ
ejpam-6135	326	15	that	that	SCONJ
ejpam-6135	326	16	e	e	NOUN
ejpam-6135	326	17	is	be	AUX
ejpam-6135	326	18	an	an	DET
ejpam-6135	326	19	(	(	PUNCT
ejpam-6135	326	20	c	c	NOUN
ejpam-6135	326	21	,	,	PUNCT
ejpam-6135	326	22	d	d	NOUN
ejpam-6135	326	23	)	)	PUNCT
ejpam-6135	326	24	if	if	SCONJ
ejpam-6135	326	25	−q	−q	ADJ
ejpam-6135	326	26	uniform	uniform	ADJ
ejpam-6135	326	27	ir∗	ir∗	NOUN
ejpam-6135	326	28	centred	centre	VERB
ejpam-6135	326	29	structure	structure	NOUN
ejpam-6135	326	30	filter	filter	NOUN
ejpam-6135	326	31	on	on	ADP
ejpam-6135	326	32	p	p	NOUN
ejpam-6135	326	33	∗	∗	NOUN
ejpam-6135	326	34	x.	x.	NOUN
ejpam-6135	326	35	by	by	ADP
ejpam-6135	326	36	corollary	corollary	ADJ
ejpam-6135	326	37	1	1	NUM
ejpam-6135	326	38	l	l	NOUN
ejpam-6135	326	39	̸=	̸=	PROPN
ejpam-6135	326	40	∅.	∅.	ADV
ejpam-6135	326	41	if	if	SCONJ
ejpam-6135	326	42	u	u	PROPN
ejpam-6135	326	43	,	,	PUNCT
ejpam-6135	326	44	v	v	NOUN
ejpam-6135	326	45	are	be	AUX
ejpam-6135	326	46	(	(	PUNCT
ejpam-6135	326	47	c	c	X
ejpam-6135	326	48	,	,	PUNCT
ejpam-6135	326	49	d	d	NOUN
ejpam-6135	326	50	)	)	PUNCT
ejpam-6135	326	51	if	if	SCONJ
ejpam-6135	326	52	−q	−q	ADJ
ejpam-6135	326	53	uniform	uniform	ADJ
ejpam-6135	326	54	ir∗	ir∗	NOUN
ejpam-6135	326	55	centred	centre	VERB
ejpam-6135	326	56	strcuture	strcuture	ADJ
ejpam-6135	326	57	open	open	ADJ
ejpam-6135	326	58	sets	set	NOUN
ejpam-6135	326	59	in	in	ADP
ejpam-6135	326	60	l	l	NOUN
ejpam-6135	326	61	,	,	PUNCT
ejpam-6135	326	62	then	then	ADV
ejpam-6135	326	63	u∗	u∗	ADJ
ejpam-6135	326	64	and	and	CCONJ
ejpam-6135	326	65	v	v	ADP
ejpam-6135	326	66	∗	∗	NOUN
ejpam-6135	326	67	∈	∈	PROPN
ejpam-6135	326	68	e.	e.	PROPN
ejpam-6135	326	69	since	since	SCONJ
ejpam-6135	326	70	(	(	PUNCT
ejpam-6135	326	71	u	u	PROPN
ejpam-6135	326	72	∩	∩	NOUN
ejpam-6135	326	73	v	v	NOUN
ejpam-6135	326	74	)	)	PUNCT
ejpam-6135	326	75	∗=	∗=	NOUN
ejpam-6135	326	76	u∗	u∗	PROPN
ejpam-6135	326	77	∩	∩	PROPN
ejpam-6135	326	78	v	v	ADP
ejpam-6135	326	79	∗	∗	NOUN
ejpam-6135	326	80	and	and	CCONJ
ejpam-6135	326	81	u∗	u∗	ADJ
ejpam-6135	326	82	∩	∩	NOUN
ejpam-6135	326	83	v	v	ADP
ejpam-6135	326	84	∗	∗	NOUN
ejpam-6135	326	85	∈	∈	NOUN
ejpam-6135	326	86	e	e	NOUN
ejpam-6135	326	87	thus	thus	ADV
ejpam-6135	326	88	u	u	PROPN
ejpam-6135	326	89	∩	∩	PROPN
ejpam-6135	326	90	v	v	ADP
ejpam-6135	326	91	∈	∈	PROPN
ejpam-6135	326	92	l.	l.	NOUN
ejpam-6135	326	93	if	if	SCONJ
ejpam-6135	326	94	w	w	PROPN
ejpam-6135	326	95	is	be	AUX
ejpam-6135	326	96	an	an	DET
ejpam-6135	326	97	(	(	PUNCT
ejpam-6135	326	98	c	c	NOUN
ejpam-6135	326	99	,	,	PUNCT
ejpam-6135	326	100	d	d	NOUN
ejpam-6135	326	101	)	)	PUNCT
ejpam-6135	326	102	if	if	SCONJ
ejpam-6135	326	103	−q	−q	ADJ
ejpam-6135	326	104	uniform	uniform	ADJ
ejpam-6135	326	105	ir∗	ir∗	NOUN
ejpam-6135	326	106	centred	centre	VERB
ejpam-6135	326	107	structure	structure	NOUN
ejpam-6135	326	108	open	open	NOUN
ejpam-6135	326	109	set	set	VERB
ejpam-6135	326	110	both	both	DET
ejpam-6135	326	111	w	w	PROPN
ejpam-6135	326	112	⊃	⊃	X
ejpam-6135	326	113	o	o	NOUN
ejpam-6135	326	114	and	and	CCONJ
ejpam-6135	326	115	w	w	PROPN
ejpam-6135	326	116	∗	∗	X
ejpam-6135	326	117	⊃	⊃	PROPN
ejpam-6135	326	118	ø∗.	ø∗.	VERB
ejpam-6135	326	119	hence	hence	ADV
ejpam-6135	326	120	it	it	PRON
ejpam-6135	326	121	is	be	AUX
ejpam-6135	326	122	implies	imply	VERB
ejpam-6135	326	123	that	that	SCONJ
ejpam-6135	326	124	w	w	NOUN
ejpam-6135	326	125	∗	∗	NOUN
ejpam-6135	326	126	∈	∈	NOUN
ejpam-6135	326	127	e	e	NOUN
ejpam-6135	326	128	and	and	CCONJ
ejpam-6135	326	129	w	w	PROPN
ejpam-6135	326	130	∈	∈	PROPN
ejpam-6135	326	131	l.	l.	NOUN
ejpam-6135	326	132	proposition	proposition	NOUN
ejpam-6135	326	133	9	9	NUM
ejpam-6135	326	134	.	.	PUNCT
ejpam-6135	327	1	the	the	DET
ejpam-6135	327	2	c	c	PROPN
ejpam-6135	327	3	net	net	NOUN
ejpam-6135	327	4	{	{	PUNCT
ejpam-6135	327	5	pi	pi	NOUN
ejpam-6135	327	6	}	}	PUNCT
ejpam-6135	327	7	converges	converge	NOUN
ejpam-6135	327	8	with	with	ADP
ejpam-6135	327	9	respect	respect	NOUN
ejpam-6135	327	10	to	to	ADP
ejpam-6135	327	11	p	p	NOUN
ejpam-6135	327	12	∗	∗	NOUN
ejpam-6135	327	13	x	x	X
ejpam-6135	327	14	.	.	PUNCT
ejpam-6135	328	1	proof	proof	NOUN
ejpam-6135	328	2	.	.	PUNCT
ejpam-6135	329	1	let	let	AUX
ejpam-6135	329	2	{	{	PUNCT
ejpam-6135	329	3	wk	wk	PART
ejpam-6135	329	4	}	}	PUNCT
ejpam-6135	329	5	be	be	AUX
ejpam-6135	329	6	the	the	DET
ejpam-6135	329	7	(	(	PUNCT
ejpam-6135	329	8	c	c	NOUN
ejpam-6135	329	9	,	,	PUNCT
ejpam-6135	329	10	d	d	NOUN
ejpam-6135	329	11	)	)	PUNCT
ejpam-6135	329	12	if	if	SCONJ
ejpam-6135	329	13	−q	−q	ADJ
ejpam-6135	329	14	uniform	uniform	ADJ
ejpam-6135	329	15	ir∗	ir∗	PROPN
ejpam-6135	329	16	basis	basis	NOUN
ejpam-6135	329	17	on	on	ADP
ejpam-6135	329	18	centred	centred	ADJ
ejpam-6135	329	19	structure	structure	NOUN
ejpam-6135	329	20	net	net	NOUN
ejpam-6135	329	21	l.	l.	PROPN
ejpam-6135	329	22	since	since	SCONJ
ejpam-6135	329	23	for	for	ADP
ejpam-6135	329	24	any	any	DET
ejpam-6135	329	25	α	α	NOUN
ejpam-6135	329	26	∈	∈	PROPN
ejpam-6135	329	27	δ	δ	PROPN
ejpam-6135	329	28	and	and	CCONJ
ejpam-6135	329	29	ε	ε	PROPN
ejpam-6135	329	30	>	>	X
ejpam-6135	329	31	0	0	PROPN
ejpam-6135	329	32	,	,	PUNCT
ejpam-6135	329	33	(	(	PUNCT
ejpam-6135	329	34	f−1	f−1	PROPN
ejpam-6135	329	35	ζ	ζ	NOUN
ejpam-6135	329	36	)	)	PUNCT
ejpam-6135	329	37	(	(	PUNCT
ejpam-6135	329	38	(	(	PUNCT
ejpam-6135	329	39	rζ	rζ	NOUN
ejpam-6135	329	40	−	−	PROPN
ejpam-6135	329	41	ε	ε	PROPN
ejpam-6135	329	42	,	,	PUNCT
ejpam-6135	329	43	rζ	rζ	X
ejpam-6135	329	44	+	+	CCONJ
ejpam-6135	329	45	ε	ε	PROPN
ejpam-6135	329	46	)	)	PUNCT
ejpam-6135	329	47	)	)	PUNCT
ejpam-6135	330	1	∈	∈	PROPN
ejpam-6135	330	2	l	l	NOUN
ejpam-6135	330	3	,	,	PUNCT
ejpam-6135	330	4	where	where	SCONJ
ejpam-6135	330	5	rζ	rζ	NOUN
ejpam-6135	330	6	=	=	NOUN
ejpam-6135	330	7	lim	lim	NOUN
ejpam-6135	330	8	{	{	PUNCT
ejpam-6135	330	9	f∗	f∗	PROPN
ejpam-6135	330	10	ζ	ζ	NOUN
ejpam-6135	330	11	pi	pi	NOUN
ejpam-6135	330	12	}	}	PUNCT
ejpam-6135	330	13	.	.	PUNCT
ejpam-6135	331	1	so	so	ADV
ejpam-6135	331	2	,	,	PUNCT
ejpam-6135	331	3	fζ(wk	fζ(wk	ADJ
ejpam-6135	331	4	)	)	PUNCT
ejpam-6135	331	5	converges	converge	NOUN
ejpam-6135	331	6	to	to	ADP
ejpam-6135	331	7	rζ	rζ	NOUN
ejpam-6135	331	8	∀	∀	NOUN
ejpam-6135	331	9	ζ	ζ	PROPN
ejpam-6135	331	10	∈	∈	PROPN
ejpam-6135	331	11	δ	δ	PROPN
ejpam-6135	331	12	.	.	PUNCT
ejpam-6135	332	1	i.e	i.e	PRON
ejpam-6135	332	2	{	{	PUNCT
ejpam-6135	332	3	wk	wk	INTJ
ejpam-6135	332	4	}	}	PUNCT
ejpam-6135	332	5	is	be	AUX
ejpam-6135	332	6	a	a	DET
ejpam-6135	332	7	c∗(px	c∗(px	NOUN
ejpam-6135	332	8	)	)	PUNCT
ejpam-6135	332	9	net	net	NOUN
ejpam-6135	332	10	.	.	PUNCT
ejpam-6135	333	1	since	since	SCONJ
ejpam-6135	333	2	(	(	PUNCT
ejpam-6135	333	3	c	c	X
ejpam-6135	333	4	,	,	PUNCT
ejpam-6135	333	5	d	d	NOUN
ejpam-6135	333	6	)	)	PUNCT
ejpam-6135	333	7	if	if	SCONJ
ejpam-6135	333	8	−q	−q	ADJ
ejpam-6135	333	9	uniform	uniform	ADJ
ejpam-6135	333	10	ir∗	ir∗	NOUN
ejpam-6135	333	11	centred	centre	VERB
ejpam-6135	333	12	structure	structure	NOUN
ejpam-6135	333	13	open	open	ADJ
ejpam-6135	333	14	filter	filter	NOUN
ejpam-6135	333	15	f{wk	f{wk	PROPN
ejpam-6135	333	16	}	}	PUNCT
ejpam-6135	333	17	formed	form	VERB
ejpam-6135	333	18	by	by	ADP
ejpam-6135	333	19	the	the	DET
ejpam-6135	333	20	c∗(px	c∗(px	NOUN
ejpam-6135	333	21	)	)	PUNCT
ejpam-6135	333	22	net	net	NOUN
ejpam-6135	333	23	{	{	PUNCT
ejpam-6135	333	24	wk	wk	NOUN
ejpam-6135	333	25	}	}	PUNCT
ejpam-6135	333	26	is	be	AUX
ejpam-6135	333	27	exactly	exactly	ADV
ejpam-6135	333	28	in	in	ADP
ejpam-6135	333	29	l.	l.	PROPN
ejpam-6135	333	30	so	so	ADV
ejpam-6135	333	31	,	,	PUNCT
ejpam-6135	333	32	if	if	SCONJ
ejpam-6135	333	33	{	{	PUNCT
ejpam-6135	333	34	wpk	wpk	PROPN
ejpam-6135	333	35	k	k	PROPN
ejpam-6135	333	36	}	}	PUNCT
ejpam-6135	333	37	is	be	AUX
ejpam-6135	333	38	the	the	DET
ejpam-6135	333	39	(	(	PUNCT
ejpam-6135	333	40	c	c	NOUN
ejpam-6135	333	41	,	,	PUNCT
ejpam-6135	333	42	d	d	NOUN
ejpam-6135	333	43	)	)	PUNCT
ejpam-6135	333	44	if	if	SCONJ
ejpam-6135	333	45	−q	−q	ADJ
ejpam-6135	333	46	uniform	uniform	ADJ
ejpam-6135	333	47	ir∗	ir∗	NOUN
ejpam-6135	333	48	centred	centre	VERB
ejpam-6135	333	49	structure	structure	NOUN
ejpam-6135	333	50	net	net	NOUN
ejpam-6135	333	51	according	accord	VERB
ejpam-6135	333	52	to	to	ADP
ejpam-6135	333	53	f{wk	f{wk	PROPN
ejpam-6135	333	54	}	}	PUNCT
ejpam-6135	333	55	,	,	PUNCT
ejpam-6135	333	56	then	then	ADV
ejpam-6135	333	57	{	{	PUNCT
ejpam-6135	333	58	wk}=	wk}=	NOUN
ejpam-6135	333	59	{	{	PUNCT
ejpam-6135	333	60	wpk	wpk	NOUN
ejpam-6135	333	61	k	k	PROPN
ejpam-6135	333	62	}	}	PUNCT
ejpam-6135	333	63	.	.	PUNCT
ejpam-6135	334	1	case	case	NOUN
ejpam-6135	334	2	1	1	NUM
ejpam-6135	334	3	:	:	PUNCT
ejpam-6135	334	4	if	if	SCONJ
ejpam-6135	334	5	{	{	PUNCT
ejpam-6135	334	6	wk	wk	INTJ
ejpam-6135	334	7	}	}	PUNCT
ejpam-6135	334	8	converges	converge	NOUN
ejpam-6135	334	9	to	to	ADP
ejpam-6135	334	10	an	an	DET
ejpam-6135	334	11	(	(	PUNCT
ejpam-6135	334	12	c	c	NOUN
ejpam-6135	334	13	,	,	PUNCT
ejpam-6135	334	14	d	d	NOUN
ejpam-6135	334	15	)	)	PUNCT
ejpam-6135	334	16	if	if	SCONJ
ejpam-6135	334	17	−q	−q	ADJ
ejpam-6135	334	18	uniform	uniform	ADJ
ejpam-6135	334	19	ir∗	ir∗	NOUN
ejpam-6135	334	20	centred	centre	VERB
ejpam-6135	334	21	structure	structure	NOUN
ejpam-6135	334	22	point	point	NOUN
ejpam-6135	334	23	p	p	NOUN
ejpam-6135	334	24	in	in	ADP
ejpam-6135	334	25	px	px	PROPN
ejpam-6135	334	26	.	.	PUNCT
ejpam-6135	335	1	let	let	VERB
ejpam-6135	335	2	u	u	PRON
ejpam-6135	335	3	∗	∗	NOUN
ejpam-6135	335	4	be	be	AUX
ejpam-6135	335	5	an	an	DET
ejpam-6135	335	6	(	(	PUNCT
ejpam-6135	335	7	c	c	NOUN
ejpam-6135	335	8	,	,	PUNCT
ejpam-6135	335	9	d	d	NOUN
ejpam-6135	335	10	)	)	PUNCT
ejpam-6135	335	11	if	if	SCONJ
ejpam-6135	335	12	−q	−q	ADJ
ejpam-6135	335	13	uniform	uniform	ADJ
ejpam-6135	335	14	ir∗	ir∗	NOUN
ejpam-6135	335	15	centred	centre	VERB
ejpam-6135	335	16	structure	structure	NOUN
ejpam-6135	335	17	open	open	NOUN
ejpam-6135	335	18	set	set	PROPN
ejpam-6135	335	19	b	b	PROPN
ejpam-6135	335	20	contains	contain	VERB
ejpam-6135	335	21	k(p	k(p	PROPN
ejpam-6135	335	22	)	)	PUNCT
ejpam-6135	335	23	,	,	PUNCT
ejpam-6135	335	24	then	then	ADV
ejpam-6135	335	25	p	p	PROPN
ejpam-6135	335	26	∈	∈	PROPN
ejpam-6135	335	27	u	u	NOUN
ejpam-6135	335	28	.here	.here	PROPN
ejpam-6135	335	29	,	,	PUNCT
ejpam-6135	335	30	u	u	NOUN
ejpam-6135	335	31	is	be	AUX
ejpam-6135	335	32	an	an	DET
ejpam-6135	335	33	(	(	PUNCT
ejpam-6135	335	34	c	c	NOUN
ejpam-6135	335	35	,	,	PUNCT
ejpam-6135	335	36	d	d	NOUN
ejpam-6135	335	37	)	)	PUNCT
ejpam-6135	335	38	if	if	SCONJ
ejpam-6135	335	39	−q	−q	ADJ
ejpam-6135	335	40	uniform	uniform	ADJ
ejpam-6135	335	41	ir∗	ir∗	NOUN
ejpam-6135	335	42	centred	centre	VERB
ejpam-6135	335	43	structure	structure	NOUN
ejpam-6135	335	44	open	open	ADJ
ejpam-6135	335	45	set	set	VERB
ejpam-6135	335	46	in	in	ADP
ejpam-6135	335	47	px	px	PROPN
ejpam-6135	335	48	.	.	PROPN
ejpam-6135	336	1	since	since	SCONJ
ejpam-6135	336	2	{	{	PUNCT
ejpam-6135	336	3	wk	wk	INTJ
ejpam-6135	336	4	}	}	PUNCT
ejpam-6135	336	5	converges	converge	NOUN
ejpam-6135	336	6	to	to	ADP
ejpam-6135	336	7	p	p	NOUN
ejpam-6135	336	8	,	,	PUNCT
ejpam-6135	336	9	by	by	ADP
ejpam-6135	336	10	considering	consider	VERB
ejpam-6135	336	11	definition	definition	NOUN
ejpam-6135	336	12	31	31	NUM
ejpam-6135	336	13	,	,	PUNCT
ejpam-6135	336	14	u	u	NOUN
ejpam-6135	336	15	in	in	ADP
ejpam-6135	336	16	l	l	NOUN
ejpam-6135	336	17	and	and	CCONJ
ejpam-6135	336	18	therefore	therefore	ADV
ejpam-6135	336	19	u∗	u∗	ADV
ejpam-6135	336	20	is	be	AUX
ejpam-6135	336	21	in	in	ADP
ejpam-6135	336	22	e.	e.	PROPN
ejpam-6135	336	23	it	it	PRON
ejpam-6135	336	24	states	state	VERB
ejpam-6135	336	25	that	that	SCONJ
ejpam-6135	336	26	{	{	PUNCT
ejpam-6135	336	27	pi	pi	NOUN
ejpam-6135	336	28	}	}	PUNCT
ejpam-6135	336	29	converged	converge	VERB
ejpam-6135	336	30	to	to	ADP
ejpam-6135	336	31	k(p	k(p	PROPN
ejpam-6135	336	32	)	)	PUNCT
ejpam-6135	336	33	in	in	ADP
ejpam-6135	336	34	p	p	NOUN
ejpam-6135	336	35	∗	∗	NOUN
ejpam-6135	336	36	x.	x.	NOUN
ejpam-6135	336	37	s.	s.	PROPN
ejpam-6135	336	38	thirukumaran	thirukumaran	PROPN
ejpam-6135	336	39	,	,	PUNCT
ejpam-6135	336	40	g.	g.	PROPN
ejpam-6135	336	41	k.	k.	PROPN
ejpam-6135	336	42	revathi	revathi	PROPN
ejpam-6135	336	43	/	/	SYM
ejpam-6135	336	44	eur	eur	PROPN
ejpam-6135	336	45	.	.	PUNCT
ejpam-6135	337	1	j.	j.	PROPN
ejpam-6135	337	2	pure	pure	PROPN
ejpam-6135	337	3	appl	appl	PROPN
ejpam-6135	337	4	.	.	PROPN
ejpam-6135	337	5	math	math	PROPN
ejpam-6135	337	6	,	,	PUNCT
ejpam-6135	337	7	18	18	NUM
ejpam-6135	337	8	(	(	PUNCT
ejpam-6135	337	9	2	2	NUM
ejpam-6135	337	10	)	)	PUNCT
ejpam-6135	337	11	(	(	PUNCT
ejpam-6135	337	12	2025	2025	NUM
ejpam-6135	337	13	)	)	PUNCT
ejpam-6135	337	14	,	,	PUNCT
ejpam-6135	337	15	6135	6135	NUM
ejpam-6135	337	16	15	15	NUM
ejpam-6135	337	17	of	of	ADP
ejpam-6135	337	18	17	17	NUM
ejpam-6135	337	19	case	case	NOUN
ejpam-6135	337	20	2	2	NUM
ejpam-6135	337	21	:	:	PUNCT
ejpam-6135	337	22	if	if	SCONJ
ejpam-6135	337	23	{	{	PUNCT
ejpam-6135	337	24	wk	wk	INTJ
ejpam-6135	337	25	}	}	PUNCT
ejpam-6135	337	26	diverges	diverge	VERB
ejpam-6135	337	27	to	to	ADP
ejpam-6135	337	28	{	{	PUNCT
ejpam-6135	337	29	px	px	INTJ
ejpam-6135	337	30	}	}	PUNCT
ejpam-6135	337	31	then	then	ADV
ejpam-6135	337	32	{	{	PUNCT
ejpam-6135	337	33	w∗	w∗	PROPN
ejpam-6135	337	34	k}=	k}=	PROPN
ejpam-6135	337	35	{	{	PUNCT
ejpam-6135	337	36	wpk	wpk	PROPN
ejpam-6135	337	37	k	k	PROPN
ejpam-6135	337	38	}	}	PUNCT
ejpam-6135	337	39	∗	∗	NOUN
ejpam-6135	337	40	is	be	AUX
ejpam-6135	337	41	in	in	ADP
ejpam-6135	337	42	yp	yp	PROPN
ejpam-6135	337	43	.	.	PUNCT
ejpam-6135	338	1	for	for	ADP
ejpam-6135	338	2	all	all	PRON
ejpam-6135	338	3	u	u	NOUN
ejpam-6135	338	4	∗	∗	NOUN
ejpam-6135	338	5	is	be	AUX
ejpam-6135	338	6	in	in	ADP
ejpam-6135	338	7	b	b	NOUN
ejpam-6135	338	8	containing	contain	VERB
ejpam-6135	338	9	{	{	PUNCT
ejpam-6135	338	10	wpk	wpk	PROPN
ejpam-6135	338	11	k	k	PROPN
ejpam-6135	338	12	}	}	PUNCT
ejpam-6135	338	13	is	be	AUX
ejpam-6135	338	14	⊘	⊘	X
ejpam-6135	338	15	in	in	ADP
ejpam-6135	338	16	u	u	NOUN
ejpam-6135	338	17	in	in	ADP
ejpam-6135	338	18	px	px	X
ejpam-6135	338	19	then	then	ADV
ejpam-6135	338	20	by	by	ADP
ejpam-6135	338	21	definition	definition	NOUN
ejpam-6135	338	22	32	32	NUM
ejpam-6135	338	23	implies	imply	VERB
ejpam-6135	338	24	that	that	SCONJ
ejpam-6135	338	25	u	u	PROPN
ejpam-6135	338	26	in	in	ADP
ejpam-6135	338	27	l	l	PROPN
ejpam-6135	338	28	and	and	CCONJ
ejpam-6135	338	29	therefore	therefore	ADV
ejpam-6135	338	30	u∗	u∗	ADV
ejpam-6135	338	31	is	be	AUX
ejpam-6135	338	32	in	in	ADP
ejpam-6135	338	33	e	e	PROPN
ejpam-6135	338	34	.	.	PUNCT
ejpam-6135	339	1	thus	thus	ADV
ejpam-6135	339	2	{	{	PUNCT
ejpam-6135	339	3	pi	pi	NOUN
ejpam-6135	339	4	}	}	PUNCT
ejpam-6135	339	5	converges	converge	NOUN
ejpam-6135	339	6	to	to	ADP
ejpam-6135	339	7	{	{	PUNCT
ejpam-6135	339	8	wpk	wpk	PROPN
ejpam-6135	339	9	k	k	PROPN
ejpam-6135	339	10	}	}	PUNCT
ejpam-6135	339	11	∗=	∗=	NOUN
ejpam-6135	339	12	{	{	PUNCT
ejpam-6135	339	13	wk}∗	wk}∗	NOUN
ejpam-6135	339	14	∈	∈	NOUN
ejpam-6135	339	15	p	p	NOUN
ejpam-6135	339	16	∗	∗	NOUN
ejpam-6135	339	17	x.	x.	NOUN
ejpam-6135	339	18	proposition	proposition	NOUN
ejpam-6135	339	19	10	10	NUM
ejpam-6135	339	20	.	.	PUNCT
ejpam-6135	340	1	(	(	PUNCT
ejpam-6135	340	2	p	p	NOUN
ejpam-6135	340	3	∗	∗	NOUN
ejpam-6135	340	4	x	x	NOUN
ejpam-6135	340	5	,	,	PUNCT
ejpam-6135	340	6	k	k	NOUN
ejpam-6135	340	7	)	)	PUNCT
ejpam-6135	340	8	is	be	AUX
ejpam-6135	340	9	an	an	DET
ejpam-6135	340	10	(	(	PUNCT
ejpam-6135	340	11	c	c	NOUN
ejpam-6135	340	12	,	,	PUNCT
ejpam-6135	340	13	d	d	NOUN
ejpam-6135	340	14	)	)	PUNCT
ejpam-6135	340	15	if	if	SCONJ
ejpam-6135	340	16	−q	−q	ADJ
ejpam-6135	340	17	uniform	uniform	ADJ
ejpam-6135	340	18	ir∗	ir∗	NOUN
ejpam-6135	340	19	centred	centre	VERB
ejpam-6135	340	20	structure	structure	NOUN
ejpam-6135	340	21	compactification	compactification	NOUN
ejpam-6135	340	22	of	of	ADP
ejpam-6135	340	23	px	px	PROPN
ejpam-6135	340	24	.	.	PROPN
ejpam-6135	340	25	proof	proof	NOUN
ejpam-6135	340	26	.	.	PUNCT
ejpam-6135	341	1	a	a	DET
ejpam-6135	341	2	family	family	NOUN
ejpam-6135	341	3	of	of	ADP
ejpam-6135	341	4	c	c	PROPN
ejpam-6135	341	5	is	be	AUX
ejpam-6135	341	6	said	say	VERB
ejpam-6135	341	7	to	to	PART
ejpam-6135	341	8	be	be	AUX
ejpam-6135	341	9	bdd	bdd	PROPN
ejpam-6135	341	10	real	real	ADV
ejpam-6135	341	11	-	-	PUNCT
ejpam-6135	341	12	valued	value	VERB
ejpam-6135	341	13	continuous	continuous	ADJ
ejpam-6135	341	14	functions	function	NOUN
ejpam-6135	341	15	on	on	ADP
ejpam-6135	341	16	p∗	p∗	PROPN
ejpam-6135	341	17	x	x	X
ejpam-6135	341	18	and	and	CCONJ
ejpam-6135	341	19	for	for	ADP
ejpam-6135	341	20	all	all	DET
ejpam-6135	341	21	c	c	PROPN
ejpam-6135	341	22	net	net	NOUN
ejpam-6135	341	23	{	{	PUNCT
ejpam-6135	341	24	pi	pi	NOUN
ejpam-6135	341	25	}	}	PUNCT
ejpam-6135	341	26	converges	converge	NOUN
ejpam-6135	341	27	to	to	ADP
ejpam-6135	341	28	p	p	NOUN
ejpam-6135	341	29	∗	∗	NOUN
ejpam-6135	341	30	x.	x.	NOUN
ejpam-6135	341	31	from	from	ADP
ejpam-6135	341	32	the	the	DET
ejpam-6135	341	33	definition	definition	NOUN
ejpam-6135	341	34	28	28	NUM
ejpam-6135	341	35	,	,	PUNCT
ejpam-6135	341	36	p	p	NOUN
ejpam-6135	341	37	∗	∗	NOUN
ejpam-6135	341	38	x	x	X
ejpam-6135	341	39	is	be	AUX
ejpam-6135	341	40	an	an	DET
ejpam-6135	341	41	(	(	PUNCT
ejpam-6135	341	42	c	c	NOUN
ejpam-6135	341	43	,	,	PUNCT
ejpam-6135	341	44	d	d	NOUN
ejpam-6135	341	45	)	)	PUNCT
ejpam-6135	341	46	if	if	SCONJ
ejpam-6135	341	47	−q	−q	ADJ
ejpam-6135	341	48	uniform	uniform	ADJ
ejpam-6135	341	49	ir∗	ir∗	NOUN
ejpam-6135	341	50	centred	centre	VERB
ejpam-6135	341	51	structure	structure	NOUN
ejpam-6135	341	52	compact	compact	ADJ
ejpam-6135	341	53	space	space	NOUN
ejpam-6135	341	54	.	.	PUNCT
ejpam-6135	342	1	here	here	ADV
ejpam-6135	342	2	,	,	PUNCT
ejpam-6135	342	3	the	the	DET
ejpam-6135	342	4	proposition	proposition	NOUN
ejpam-6135	342	5	6	6	NUM
ejpam-6135	342	6	,	,	PUNCT
ejpam-6135	342	7	implies	imply	VERB
ejpam-6135	342	8	that	that	SCONJ
ejpam-6135	342	9	(	(	PUNCT
ejpam-6135	342	10	p	p	NOUN
ejpam-6135	342	11	∗	∗	NOUN
ejpam-6135	342	12	x	x	NOUN
ejpam-6135	342	13	,	,	PUNCT
ejpam-6135	342	14	k	k	NOUN
ejpam-6135	342	15	)	)	PUNCT
ejpam-6135	342	16	is	be	AUX
ejpam-6135	342	17	an	an	DET
ejpam-6135	342	18	(	(	PUNCT
ejpam-6135	342	19	c	c	NOUN
ejpam-6135	342	20	,	,	PUNCT
ejpam-6135	342	21	d	d	NOUN
ejpam-6135	342	22	)	)	PUNCT
ejpam-6135	342	23	if	if	SCONJ
ejpam-6135	342	24	−q	−q	ADJ
ejpam-6135	342	25	uniform	uniform	ADJ
ejpam-6135	342	26	ir∗	ir∗	NOUN
ejpam-6135	342	27	centred	centre	VERB
ejpam-6135	342	28	structure	structure	NOUN
ejpam-6135	342	29	compactification	compactification	NOUN
ejpam-6135	342	30	of	of	ADP
ejpam-6135	342	31	px	px	PROPN
ejpam-6135	342	32	.	.	PROPN
ejpam-6135	342	33	proposition	proposition	NOUN
ejpam-6135	342	34	11	11	NUM
ejpam-6135	342	35	.	.	PUNCT
ejpam-6135	343	1	let	let	VERB
ejpam-6135	343	2	c(p	c(p	PROPN
ejpam-6135	343	3	∗	∗	PROPN
ejpam-6135	343	4	x	x	X
ejpam-6135	343	5	)	)	PUNCT
ejpam-6135	343	6	be	be	VERB
ejpam-6135	343	7	the	the	DET
ejpam-6135	343	8	collection	collection	NOUN
ejpam-6135	343	9	of	of	ADP
ejpam-6135	343	10	all	all	DET
ejpam-6135	343	11	real	real	ADV
ejpam-6135	343	12	valued	value	VERB
ejpam-6135	343	13	continuous	continuous	ADJ
ejpam-6135	343	14	functions	function	NOUN
ejpam-6135	343	15	on	on	ADP
ejpam-6135	343	16	p	p	NOUN
ejpam-6135	343	17	∗	∗	NOUN
ejpam-6135	343	18	x	x	X
ejpam-6135	343	19	.	.	PUNCT
ejpam-6135	344	1	then	then	ADV
ejpam-6135	344	2	c(p	c(p	NOUN
ejpam-6135	344	3	∗	∗	NOUN
ejpam-6135	344	4	x)=	x)=	PROPN
ejpam-6135	344	5	c=	c=	NOUN
ejpam-6135	344	6	{	{	PUNCT
ejpam-6135	344	7	f∗	f∗	NOUN
ejpam-6135	344	8	ζ	ζ	NOUN
ejpam-6135	344	9	:	:	PUNCT
ejpam-6135	344	10	fζ	fζ	PROPN
ejpam-6135	344	11	∈	∈	PROPN
ejpam-6135	344	12	c∗(px	c∗(px	NOUN
ejpam-6135	344	13	)	)	PUNCT
ejpam-6135	344	14	}	}	PUNCT
ejpam-6135	344	15	proof	proof	NOUN
ejpam-6135	344	16	.	.	PUNCT
ejpam-6135	345	1	let	let	VERB
ejpam-6135	345	2	g	g	PROPN
ejpam-6135	345	3	∈	∈	PROPN
ejpam-6135	345	4	c(p	c(p	PROPN
ejpam-6135	345	5	∗	∗	NOUN
ejpam-6135	345	6	x	x	NOUN
ejpam-6135	345	7	)	)	PUNCT
ejpam-6135	345	8	.	.	PUNCT
ejpam-6135	346	1	since	since	SCONJ
ejpam-6135	346	2	p∗	p∗	PROPN
ejpam-6135	346	3	x	x	PUNCT
ejpam-6135	346	4	is	be	AUX
ejpam-6135	346	5	an	an	DET
ejpam-6135	346	6	(	(	PUNCT
ejpam-6135	346	7	c	c	NOUN
ejpam-6135	346	8	,	,	PUNCT
ejpam-6135	346	9	d	d	NOUN
ejpam-6135	346	10	)	)	PUNCT
ejpam-6135	346	11	if	if	SCONJ
ejpam-6135	346	12	−q	−q	ADJ
ejpam-6135	346	13	uniform	uniform	ADJ
ejpam-6135	346	14	ir∗	ir∗	NOUN
ejpam-6135	346	15	centred	centre	VERB
ejpam-6135	346	16	structure	structure	NOUN
ejpam-6135	346	17	compact	compact	ADJ
ejpam-6135	346	18	,	,	PUNCT
ejpam-6135	346	19	so	so	SCONJ
ejpam-6135	346	20	g	g	PROPN
ejpam-6135	346	21	◦	◦	NOUN
ejpam-6135	346	22	k	k	PROPN
ejpam-6135	346	23	∈	∈	PROPN
ejpam-6135	346	24	c(p	c(p	PROPN
ejpam-6135	346	25	∗	∗	NOUN
ejpam-6135	346	26	x	x	NOUN
ejpam-6135	346	27	)	)	PUNCT
ejpam-6135	346	28	.	.	PUNCT
ejpam-6135	347	1	by	by	ADP
ejpam-6135	347	2	proposition	proposition	NOUN
ejpam-6135	347	3	5	5	NUM
ejpam-6135	347	4	and	and	CCONJ
ejpam-6135	347	5	6	6	NUM
ejpam-6135	347	6	along	along	ADP
ejpam-6135	347	7	with	with	ADP
ejpam-6135	347	8	based	base	VERB
ejpam-6135	347	9	on	on	ADP
ejpam-6135	347	10	the	the	DET
ejpam-6135	347	11	continuity	continuity	NOUN
ejpam-6135	347	12	of	of	ADP
ejpam-6135	347	13	g	g	NOUN
ejpam-6135	347	14	,	,	PUNCT
ejpam-6135	347	15	it	it	PRON
ejpam-6135	347	16	follows	follow	VERB
ejpam-6135	347	17	that	that	SCONJ
ejpam-6135	347	18	(	(	PUNCT
ejpam-6135	347	19	g	g	NOUN
ejpam-6135	347	20	◦	◦	NOUN
ejpam-6135	347	21	k)∗({wpi	k)∗({wpi	NOUN
ejpam-6135	347	22	k	k	NOUN
ejpam-6135	347	23	}	}	PUNCT
ejpam-6135	347	24	)	)	PUNCT
ejpam-6135	348	1	=	=	SYM
ejpam-6135	348	2	lim	lim	PROPN
ejpam-6135	348	3	{	{	PUNCT
ejpam-6135	348	4	(	(	PUNCT
ejpam-6135	348	5	g	g	ADP
ejpam-6135	348	6	◦	◦	NOUN
ejpam-6135	348	7	k)(wpi	k)(wpi	X
ejpam-6135	348	8	i	i	NOUN
ejpam-6135	348	9	)	)	PUNCT
ejpam-6135	348	10	}	}	PUNCT
ejpam-6135	348	11	=	=	SYM
ejpam-6135	348	12	lim	lim	PROPN
ejpam-6135	348	13	{	{	PUNCT
ejpam-6135	348	14	g(k(wpi	g(k(wpi	PROPN
ejpam-6135	348	15	k	k	PROPN
ejpam-6135	348	16	)	)	PUNCT
ejpam-6135	348	17	)	)	PUNCT
ejpam-6135	348	18	}	}	PUNCT
ejpam-6135	349	1	=	=	X
ejpam-6135	349	2	g(lim	g(lim	X
ejpam-6135	349	3	{	{	PUNCT
ejpam-6135	349	4	k(wpi	k(wpi	PROPN
ejpam-6135	349	5	k	k	PROPN
ejpam-6135	349	6	)	)	PUNCT
ejpam-6135	349	7	}	}	PUNCT
ejpam-6135	349	8	)	)	PUNCT
ejpam-6135	349	9	=	=	NOUN
ejpam-6135	349	10	g({wpi	g({wpi	NOUN
ejpam-6135	349	11	k	k	ADJ
ejpam-6135	349	12	}	}	PUNCT
ejpam-6135	349	13	∗	∗	NOUN
ejpam-6135	349	14	)	)	PUNCT
ejpam-6135	349	15	∀	∀	X
ejpam-6135	349	16	{	{	PUNCT
ejpam-6135	349	17	wpi	wpi	NOUN
ejpam-6135	349	18	k	k	PROPN
ejpam-6135	349	19	}	}	PUNCT
ejpam-6135	349	20	∈	∈	PROPN
ejpam-6135	349	21	yp	yp	PROPN
ejpam-6135	349	22	and	and	CCONJ
ejpam-6135	349	23	(	(	PUNCT
ejpam-6135	349	24	g	g	PROPN
ejpam-6135	349	25	◦	◦	NOUN
ejpam-6135	349	26	k)∗	k)∗	PROPN
ejpam-6135	349	27	(	(	PUNCT
ejpam-6135	349	28	k(p	k(p	PROPN
ejpam-6135	349	29	)	)	PUNCT
ejpam-6135	349	30	)	)	PUNCT
ejpam-6135	349	31	=	=	PRON
ejpam-6135	349	32	(	(	PUNCT
ejpam-6135	349	33	g	g	PROPN
ejpam-6135	349	34	◦	◦	NOUN
ejpam-6135	349	35	k)∗	k)∗	NOUN
ejpam-6135	349	36	(	(	PUNCT
ejpam-6135	349	37	p	p	NOUN
ejpam-6135	349	38	)	)	PUNCT
ejpam-6135	349	39	=	=	SYM
ejpam-6135	349	40	g(k(p	g(k(p	PROPN
ejpam-6135	349	41	)	)	PUNCT
ejpam-6135	349	42	)	)	PUNCT
ejpam-6135	349	43	∀	∀	X
ejpam-6135	350	1	p	p	X
ejpam-6135	350	2	∈	∈	PROPN
ejpam-6135	350	3	px	px	NOUN
ejpam-6135	350	4	.	.	PUNCT
ejpam-6135	351	1	it	it	PRON
ejpam-6135	351	2	is	be	AUX
ejpam-6135	351	3	stated	state	VERB
ejpam-6135	351	4	that	that	SCONJ
ejpam-6135	351	5	,	,	PUNCT
ejpam-6135	351	6	c(p	c(p	NOUN
ejpam-6135	351	7	∗	∗	NOUN
ejpam-6135	351	8	x	x	NOUN
ejpam-6135	351	9	)	)	PUNCT
ejpam-6135	351	10	⊂	⊂	PRON
ejpam-6135	351	11	c=	c=	VERB
ejpam-6135	351	12	{	{	PUNCT
ejpam-6135	351	13	f∗	f∗	NOUN
ejpam-6135	351	14	ζ	ζ	NOUN
ejpam-6135	351	15	:	:	PUNCT
ejpam-6135	351	16	fζ	fζ	PROPN
ejpam-6135	351	17	∈	∈	PROPN
ejpam-6135	351	18	c∗(px	c∗(px	NOUN
ejpam-6135	351	19	)	)	PUNCT
ejpam-6135	351	20	}	}	PUNCT
ejpam-6135	351	21	.	.	PUNCT
ejpam-6135	352	1	7	7	X
ejpam-6135	352	2	.	.	NOUN
ejpam-6135	352	3	results	result	NOUN
ejpam-6135	352	4	and	and	CCONJ
ejpam-6135	352	5	discussions	discussion	NOUN
ejpam-6135	352	6	the	the	DET
ejpam-6135	352	7	(	(	PUNCT
ejpam-6135	352	8	c	c	NOUN
ejpam-6135	352	9	,	,	PUNCT
ejpam-6135	352	10	d	d	NOUN
ejpam-6135	352	11	)	)	PUNCT
ejpam-6135	352	12	if	if	SCONJ
ejpam-6135	352	13	−q	−q	ADJ
ejpam-6135	352	14	uniform	uniform	ADJ
ejpam-6135	352	15	ir∗	ir∗	NOUN
ejpam-6135	352	16	centred	centre	VERB
ejpam-6135	352	17	structure	structure	NOUN
ejpam-6135	352	18	compactification	compactification	NOUN
ejpam-6135	352	19	is	be	AUX
ejpam-6135	352	20	an	an	DET
ejpam-6135	352	21	unique	unique	ADJ
ejpam-6135	352	22	approach	approach	NOUN
ejpam-6135	352	23	of	of	ADP
ejpam-6135	352	24	compactification	compactification	NOUN
ejpam-6135	352	25	methods	method	NOUN
ejpam-6135	352	26	compared	compare	VERB
ejpam-6135	352	27	to	to	ADP
ejpam-6135	352	28	others	other	NOUN
ejpam-6135	352	29	.	.	PUNCT
ejpam-6135	353	1	here	here	ADV
ejpam-6135	353	2	,	,	PUNCT
ejpam-6135	353	3	it	it	PRON
ejpam-6135	353	4	was	be	AUX
ejpam-6135	353	5	studied	study	VERB
ejpam-6135	353	6	with	with	ADP
ejpam-6135	353	7	the	the	DET
ejpam-6135	353	8	irreducibility	irreducibility	NOUN
ejpam-6135	353	9	,	,	PUNCT
ejpam-6135	353	10	centred	centred	ADJ
ejpam-6135	353	11	systems	system	NOUN
ejpam-6135	353	12	,	,	PUNCT
ejpam-6135	353	13	compact	compact	ADJ
ejpam-6135	353	14	spaces	space	NOUN
ejpam-6135	353	15	,	,	PUNCT
ejpam-6135	353	16	nets	net	NOUN
ejpam-6135	353	17	and	and	CCONJ
ejpam-6135	353	18	filters	filter	NOUN
ejpam-6135	353	19	etc	etc	X
ejpam-6135	353	20	.	.	X
ejpam-6135	353	21	,	,	PUNCT
ejpam-6135	353	22	also	also	ADV
ejpam-6135	353	23	with	with	ADP
ejpam-6135	353	24	convergence	convergence	NOUN
ejpam-6135	353	25	using	use	VERB
ejpam-6135	353	26	boundedness	boundedness	NOUN
ejpam-6135	353	27	and	and	CCONJ
ejpam-6135	353	28	continous	continous	ADJ
ejpam-6135	353	29	functions	function	NOUN
ejpam-6135	353	30	.	.	PUNCT
ejpam-6135	354	1	while	while	SCONJ
ejpam-6135	354	2	comparing	compare	VERB
ejpam-6135	354	3	to	to	ADP
ejpam-6135	354	4	other	other	ADJ
ejpam-6135	354	5	compactifications	compactification	NOUN
ejpam-6135	354	6	as	as	SCONJ
ejpam-6135	354	7	mentioned	mention	VERB
ejpam-6135	354	8	in	in	ADP
ejpam-6135	354	9	section-2	section-2	NUM
ejpam-6135	354	10	literature	literature	NOUN
ejpam-6135	354	11	survey	survey	NOUN
ejpam-6135	354	12	.	.	PUNCT
ejpam-6135	355	1	fan	fan	NOUN
ejpam-6135	355	2	-	-	PUNCT
ejpam-6135	355	3	gottesmann	gottesmann	NOUN
ejpam-6135	355	4	compactification	compactification	NOUN
ejpam-6135	355	5	deals	deal	NOUN
ejpam-6135	355	6	with	with	ADP
ejpam-6135	355	7	clopen	clopen	ADJ
ejpam-6135	355	8	open	open	ADJ
ejpam-6135	355	9	sets	set	NOUN
ejpam-6135	355	10	with	with	ADP
ejpam-6135	355	11	filters	filter	NOUN
ejpam-6135	355	12	and	and	CCONJ
ejpam-6135	355	13	nets	net	NOUN
ejpam-6135	355	14	alongs	along	NOUN
ejpam-6135	355	15	with	with	ADP
ejpam-6135	355	16	convergence	convergence	NOUN
ejpam-6135	355	17	not	not	PART
ejpam-6135	355	18	using	use	VERB
ejpam-6135	355	19	the	the	DET
ejpam-6135	355	20	boundedness	boundedness	NOUN
ejpam-6135	355	21	.	.	PUNCT
ejpam-6135	356	1	also	also	ADV
ejpam-6135	356	2	,	,	PUNCT
ejpam-6135	356	3	some	some	PRON
ejpam-6135	356	4	of	of	ADP
ejpam-6135	356	5	the	the	DET
ejpam-6135	356	6	compactifications	compactification	NOUN
ejpam-6135	356	7	make	make	VERB
ejpam-6135	356	8	a	a	DET
ejpam-6135	356	9	way	way	NOUN
ejpam-6135	356	10	to	to	ADP
ejpam-6135	356	11	conceptual	conceptual	ADJ
ejpam-6135	356	12	ideas	idea	NOUN
ejpam-6135	356	13	of	of	ADP
ejpam-6135	356	14	framing	frame	VERB
ejpam-6135	356	15	from	from	ADP
ejpam-6135	356	16	noncompact	noncompact	ADJ
ejpam-6135	356	17	spaces	space	NOUN
ejpam-6135	356	18	to	to	ADP
ejpam-6135	356	19	compact	compact	ADJ
ejpam-6135	356	20	spaces	space	NOUN
ejpam-6135	356	21	and	and	CCONJ
ejpam-6135	356	22	others	other	NOUN
ejpam-6135	356	23	.	.	PUNCT
ejpam-6135	357	1	apart	apart	ADV
ejpam-6135	357	2	from	from	ADP
ejpam-6135	357	3	all	all	DET
ejpam-6135	357	4	these	these	PRON
ejpam-6135	357	5	,	,	PUNCT
ejpam-6135	357	6	(	(	PUNCT
ejpam-6135	357	7	c	c	X
ejpam-6135	357	8	,	,	PUNCT
ejpam-6135	357	9	d	d	NOUN
ejpam-6135	357	10	)	)	PUNCT
ejpam-6135	357	11	if	if	SCONJ
ejpam-6135	357	12	−q	−q	ADJ
ejpam-6135	357	13	uniform	uniform	ADJ
ejpam-6135	357	14	ir∗	ir∗	NOUN
ejpam-6135	357	15	centred	centre	VERB
ejpam-6135	357	16	structure	structure	NOUN
ejpam-6135	357	17	compactification	compactification	NOUN
ejpam-6135	357	18	is	be	AUX
ejpam-6135	357	19	unique	unique	ADJ
ejpam-6135	357	20	one	one	NUM
ejpam-6135	357	21	which	which	PRON
ejpam-6135	357	22	is	be	AUX
ejpam-6135	357	23	being	be	AUX
ejpam-6135	357	24	centred	centre	VERB
ejpam-6135	357	25	system	system	NOUN
ejpam-6135	357	26	and	and	CCONJ
ejpam-6135	357	27	irreducible	irreducible	ADJ
ejpam-6135	357	28	sets	set	NOUN
ejpam-6135	357	29	.	.	PUNCT
ejpam-6135	358	1	8	8	X
ejpam-6135	358	2	.	.	X
ejpam-6135	358	3	conclusion	conclusion	NOUN
ejpam-6135	358	4	this	this	DET
ejpam-6135	358	5	research	research	NOUN
ejpam-6135	358	6	work	work	NOUN
ejpam-6135	358	7	will	will	AUX
ejpam-6135	358	8	lead	lead	VERB
ejpam-6135	358	9	to	to	ADP
ejpam-6135	358	10	a	a	DET
ejpam-6135	358	11	fine	fine	ADJ
ejpam-6135	358	12	understanding	understanding	NOUN
ejpam-6135	358	13	about	about	ADP
ejpam-6135	358	14	(	(	PUNCT
ejpam-6135	358	15	c	c	X
ejpam-6135	358	16	,	,	PUNCT
ejpam-6135	358	17	d	d	NOUN
ejpam-6135	358	18	)	)	PUNCT
ejpam-6135	358	19	if	if	SCONJ
ejpam-6135	358	20	−q	−q	ADJ
ejpam-6135	358	21	uniform	uniform	ADJ
ejpam-6135	358	22	ir∗	ir∗	NOUN
ejpam-6135	358	23	centred	centre	VERB
ejpam-6135	358	24	structure	structure	NOUN
ejpam-6135	358	25	space	space	NOUN
ejpam-6135	358	26	and	and	CCONJ
ejpam-6135	358	27	its	its	PRON
ejpam-6135	358	28	properties	property	NOUN
ejpam-6135	358	29	.	.	PUNCT
ejpam-6135	359	1	it	it	PRON
ejpam-6135	359	2	enhances	enhance	VERB
ejpam-6135	359	3	the	the	DET
ejpam-6135	359	4	theoretical	theoretical	ADJ
ejpam-6135	359	5	approaches	approach	NOUN
ejpam-6135	359	6	to	to	ADP
ejpam-6135	359	7	various	various	ADJ
ejpam-6135	359	8	contexts	context	NOUN
ejpam-6135	359	9	in	in	ADP
ejpam-6135	359	10	compactifications	compactification	NOUN
ejpam-6135	359	11	.	.	PUNCT
ejpam-6135	360	1	the	the	DET
ejpam-6135	360	2	inter	inter	NOUN
ejpam-6135	360	3	-	-	NOUN
ejpam-6135	360	4	relations	relation	NOUN
ejpam-6135	360	5	between	between	ADP
ejpam-6135	360	6	(	(	PUNCT
ejpam-6135	360	7	c	c	NOUN
ejpam-6135	360	8	,	,	PUNCT
ejpam-6135	360	9	d	d	NOUN
ejpam-6135	360	10	)	)	PUNCT
ejpam-6135	360	11	if	if	SCONJ
ejpam-6135	360	12	−q	−q	ADJ
ejpam-6135	360	13	uniform	uniform	ADJ
ejpam-6135	360	14	ir∗	ir∗	NOUN
ejpam-6135	360	15	centred	centre	VERB
ejpam-6135	360	16	structure	structure	NOUN
ejpam-6135	360	17	nets	net	NOUN
ejpam-6135	360	18	and	and	CCONJ
ejpam-6135	360	19	(	(	PUNCT
ejpam-6135	360	20	c	c	X
ejpam-6135	360	21	,	,	PUNCT
ejpam-6135	360	22	d	d	NOUN
ejpam-6135	360	23	)	)	PUNCT
ejpam-6135	360	24	if	if	SCONJ
ejpam-6135	360	25	−q	−q	ADJ
ejpam-6135	360	26	uniform	uniform	ADJ
ejpam-6135	360	27	ir∗	ir∗	NOUN
ejpam-6135	360	28	centred	centre	VERB
ejpam-6135	360	29	structure	structure	NOUN
ejpam-6135	360	30	filters	filter	NOUN
ejpam-6135	360	31	provide	provide	VERB
ejpam-6135	360	32	a	a	DET
ejpam-6135	360	33	robust	robust	ADJ
ejpam-6135	360	34	theoretical	theoretical	ADJ
ejpam-6135	360	35	framework	framework	NOUN
ejpam-6135	360	36	for	for	ADP
ejpam-6135	360	37	understanding	understanding	NOUN
ejpam-6135	360	38	(	(	PUNCT
ejpam-6135	360	39	c	c	NOUN
ejpam-6135	360	40	,	,	PUNCT
ejpam-6135	360	41	d	d	NOUN
ejpam-6135	360	42	)	)	PUNCT
ejpam-6135	360	43	if	if	SCONJ
ejpam-6135	360	44	−q	−q	ADJ
ejpam-6135	360	45	uniform	uniform	ADJ
ejpam-6135	360	46	ir∗	ir∗	NOUN
ejpam-6135	360	47	centred	centre	VERB
ejpam-6135	360	48	structure	structure	NOUN
ejpam-6135	360	49	compactness	compactness	NOUN
ejpam-6135	360	50	in	in	ADP
ejpam-6135	360	51	various	various	ADJ
ejpam-6135	360	52	types	type	NOUN
ejpam-6135	360	53	of	of	ADP
ejpam-6135	360	54	spaces	space	NOUN
ejpam-6135	360	55	.	.	PUNCT
ejpam-6135	361	1	likewise	likewise	ADV
ejpam-6135	361	2	,	,	PUNCT
ejpam-6135	361	3	(	(	PUNCT
ejpam-6135	361	4	c	c	X
ejpam-6135	361	5	,	,	PUNCT
ejpam-6135	361	6	d	d	NOUN
ejpam-6135	361	7	)	)	PUNCT
ejpam-6135	361	8	if	if	SCONJ
ejpam-6135	361	9	−q	−q	ADJ
ejpam-6135	361	10	uniform	uniform	ADJ
ejpam-6135	361	11	ir∗	ir∗	NOUN
ejpam-6135	361	12	centred	centre	VERB
ejpam-6135	361	13	structure	structure	NOUN
ejpam-6135	361	14	nets	net	NOUN
ejpam-6135	361	15	provides	provide	VERB
ejpam-6135	361	16	a	a	DET
ejpam-6135	361	17	way	way	NOUN
ejpam-6135	361	18	to	to	PART
ejpam-6135	361	19	generalize	generalize	VERB
ejpam-6135	361	20	sequences	sequence	NOUN
ejpam-6135	361	21	and	and	CCONJ
ejpam-6135	361	22	convergence	convergence	NOUN
ejpam-6135	361	23	in	in	ADP
ejpam-6135	361	24	(	(	PUNCT
ejpam-6135	361	25	c	c	X
ejpam-6135	361	26	,	,	PUNCT
ejpam-6135	361	27	d	d	NOUN
ejpam-6135	361	28	)	)	PUNCT
ejpam-6135	361	29	s.	s.	PROPN
ejpam-6135	361	30	thirukumaran	thirukumaran	PROPN
ejpam-6135	361	31	,	,	PUNCT
ejpam-6135	361	32	g.	g.	PROPN
ejpam-6135	361	33	k.	k.	PROPN
ejpam-6135	361	34	revathi	revathi	PROPN
ejpam-6135	361	35	/	/	SYM
ejpam-6135	361	36	eur	eur	PROPN
ejpam-6135	361	37	.	.	PUNCT
ejpam-6135	362	1	j.	j.	PROPN
ejpam-6135	362	2	pure	pure	PROPN
ejpam-6135	362	3	appl	appl	PROPN
ejpam-6135	362	4	.	.	PROPN
ejpam-6135	362	5	math	math	PROPN
ejpam-6135	362	6	,	,	PUNCT
ejpam-6135	362	7	18	18	NUM
ejpam-6135	362	8	(	(	PUNCT
ejpam-6135	362	9	2	2	NUM
ejpam-6135	362	10	)	)	PUNCT
ejpam-6135	362	11	(	(	PUNCT
ejpam-6135	362	12	2025	2025	NUM
ejpam-6135	362	13	)	)	PUNCT
ejpam-6135	362	14	,	,	PUNCT
ejpam-6135	362	15	6135	6135	NUM
ejpam-6135	362	16	16	16	NUM
ejpam-6135	362	17	of	of	ADP
ejpam-6135	362	18	17	17	NUM
ejpam-6135	362	19	if	if	SCONJ
ejpam-6135	362	20	−q	−q	ADJ
ejpam-6135	362	21	uniform	uniform	ADJ
ejpam-6135	362	22	topological	topological	ADJ
ejpam-6135	362	23	space	space	NOUN
ejpam-6135	362	24	while	while	SCONJ
ejpam-6135	362	25	(	(	PUNCT
ejpam-6135	362	26	c	c	X
ejpam-6135	362	27	,	,	PUNCT
ejpam-6135	362	28	d	d	NOUN
ejpam-6135	362	29	)	)	PUNCT
ejpam-6135	362	30	if	if	SCONJ
ejpam-6135	362	31	−q	−q	ADJ
ejpam-6135	362	32	uniform	uniform	ADJ
ejpam-6135	362	33	ir∗	ir∗	NOUN
ejpam-6135	362	34	centred	centre	VERB
ejpam-6135	362	35	structure	structure	NOUN
ejpam-6135	362	36	filters	filter	NOUN
ejpam-6135	362	37	discussed	discuss	VERB
ejpam-6135	362	38	a	a	DET
ejpam-6135	362	39	framework	framework	NOUN
ejpam-6135	362	40	for	for	ADP
ejpam-6135	362	41	convergence	convergence	NOUN
ejpam-6135	362	42	and	and	CCONJ
ejpam-6135	362	43	compactness	compactness	NOUN
ejpam-6135	362	44	.	.	PUNCT
ejpam-6135	363	1	it	it	PRON
ejpam-6135	363	2	will	will	AUX
ejpam-6135	363	3	lead	lead	VERB
ejpam-6135	363	4	to	to	ADP
ejpam-6135	363	5	applications	application	NOUN
ejpam-6135	363	6	of	of	ADP
ejpam-6135	363	7	compactifications	compactification	NOUN
ejpam-6135	363	8	on	on	ADP
ejpam-6135	363	9	various	various	ADJ
ejpam-6135	363	10	fields	field	NOUN
ejpam-6135	363	11	.	.	PUNCT
ejpam-6135	364	1	future	future	ADJ
ejpam-6135	364	2	framework	framework	NOUN
ejpam-6135	364	3	of	of	ADP
ejpam-6135	364	4	(	(	PUNCT
ejpam-6135	364	5	c	c	X
ejpam-6135	364	6	,	,	PUNCT
ejpam-6135	364	7	d	d	NOUN
ejpam-6135	364	8	)	)	PUNCT
ejpam-6135	364	9	if	if	SCONJ
ejpam-6135	364	10	−q	−q	ADJ
ejpam-6135	364	11	uniform	uniform	ADJ
ejpam-6135	364	12	ir∗	ir∗	NOUN
ejpam-6135	364	13	centred	centre	VERB
ejpam-6135	364	14	structure	structure	NOUN
ejpam-6135	364	15	compactification	compactification	NOUN
ejpam-6135	364	16	can	can	AUX
ejpam-6135	364	17	be	be	AUX
ejpam-6135	364	18	explored	explore	VERB
ejpam-6135	364	19	into	into	ADP
ejpam-6135	364	20	category	category	NOUN
ejpam-6135	364	21	theory	theory	NOUN
ejpam-6135	364	22	,	,	PUNCT
ejpam-6135	364	23	fixed	fix	VERB
ejpam-6135	364	24	point	point	NOUN
ejpam-6135	364	25	theory	theory	NOUN
ejpam-6135	364	26	along	along	ADP
ejpam-6135	364	27	with	with	ADP
ejpam-6135	364	28	metric	metric	ADJ
ejpam-6135	364	29	spaces	space	NOUN
ejpam-6135	364	30	.	.	PUNCT
ejpam-6135	365	1	acknowledgements	acknowledgement	NOUN
ejpam-6135	365	2	the	the	DET
ejpam-6135	365	3	authors	author	NOUN
ejpam-6135	365	4	are	be	AUX
ejpam-6135	365	5	highly	highly	ADV
ejpam-6135	365	6	thankful	thankful	ADJ
ejpam-6135	365	7	to	to	ADP
ejpam-6135	365	8	the	the	DET
ejpam-6135	365	9	referees	referee	NOUN
ejpam-6135	365	10	and	and	CCONJ
ejpam-6135	365	11	editors	editor	NOUN
ejpam-6135	365	12	for	for	ADP
ejpam-6135	365	13	their	their	PRON
ejpam-6135	365	14	valuable	valuable	ADJ
ejpam-6135	365	15	comments	comment	NOUN
ejpam-6135	365	16	and	and	CCONJ
ejpam-6135	365	17	suggestions	suggestion	NOUN
ejpam-6135	365	18	to	to	ADP
ejpam-6135	365	19	our	our	PRON
ejpam-6135	365	20	article	article	NOUN
ejpam-6135	365	21	.	.	PUNCT
ejpam-6135	366	1	references	reference	NOUN
ejpam-6135	366	2	[	[	X
ejpam-6135	366	3	1	1	NUM
ejpam-6135	366	4	]	]	PUNCT
ejpam-6135	366	5	lotfi	lotfi	PROPN
ejpam-6135	366	6	asker	asker	PROPN
ejpam-6135	366	7	zadeh	zadeh	PROPN
ejpam-6135	366	8	.	.	PUNCT
ejpam-6135	366	9	fuzzy	fuzzy	ADJ
ejpam-6135	366	10	sets	set	NOUN
ejpam-6135	366	11	.	.	PUNCT
ejpam-6135	367	1	information	information	NOUN
ejpam-6135	367	2	and	and	CCONJ
ejpam-6135	367	3	control	control	NOUN
ejpam-6135	367	4	,	,	PUNCT
ejpam-6135	367	5	8(3):338–353	8(3):338–353	NUM
ejpam-6135	367	6	,	,	PUNCT
ejpam-6135	367	7	1965	1965	NUM
ejpam-6135	367	8	.	.	PUNCT
ejpam-6135	368	1	[	[	X
ejpam-6135	368	2	2	2	NUM
ejpam-6135	368	3	]	]	X
ejpam-6135	368	4	hans	han	NOUN
ejpam-6135	368	5	-	-	PUNCT
ejpam-6135	368	6	jürgen	jürgen	PROPN
ejpam-6135	368	7	zimmermann	zimmermann	PROPN
ejpam-6135	368	8	.	.	PUNCT
ejpam-6135	369	1	fuzzy	fuzzy	ADJ
ejpam-6135	369	2	set	set	PROPN
ejpam-6135	369	3	theory	theory	NOUN
ejpam-6135	369	4	—	—	PUNCT
ejpam-6135	369	5	and	and	CCONJ
ejpam-6135	369	6	its	its	PRON
ejpam-6135	369	7	applications	application	NOUN
ejpam-6135	369	8	.	.	PUNCT
ejpam-6135	370	1	springer	springer	NOUN
ejpam-6135	370	2	science	science	PROPN
ejpam-6135	370	3	&	&	CCONJ
ejpam-6135	370	4	business	business	NOUN
ejpam-6135	370	5	media	medium	NOUN
ejpam-6135	370	6	,	,	PUNCT
ejpam-6135	370	7	2011	2011	NUM
ejpam-6135	370	8	.	.	PUNCT
ejpam-6135	371	1	[	[	X
ejpam-6135	371	2	3	3	X
ejpam-6135	371	3	]	]	X
ejpam-6135	371	4	krassimir	krassimir	PROPN
ejpam-6135	371	5	t	t	PROPN
ejpam-6135	371	6	atanassov	atanassov	NOUN
ejpam-6135	371	7	.	.	PUNCT
ejpam-6135	372	1	on	on	ADP
ejpam-6135	372	2	intuitionistic	intuitionistic	ADJ
ejpam-6135	372	3	fuzzy	fuzzy	ADJ
ejpam-6135	372	4	sets	set	NOUN
ejpam-6135	372	5	theory	theory	NOUN
ejpam-6135	372	6	,	,	PUNCT
ejpam-6135	372	7	volume	volume	NOUN
ejpam-6135	372	8	283	283	NUM
ejpam-6135	372	9	.	.	PUNCT
ejpam-6135	373	1	springer	springer	NOUN
ejpam-6135	373	2	,	,	PUNCT
ejpam-6135	373	3	2012	2012	NUM
ejpam-6135	373	4	.	.	PUNCT
ejpam-6135	374	1	[	[	X
ejpam-6135	374	2	4	4	NUM
ejpam-6135	374	3	]	]	X
ejpam-6135	374	4	chin	chin	PROPN
ejpam-6135	374	5	-	-	PUNCT
ejpam-6135	374	6	liang	liang	PROPN
ejpam-6135	374	7	chang	chang	PROPN
ejpam-6135	374	8	.	.	PUNCT
ejpam-6135	375	1	fuzzy	fuzzy	ADJ
ejpam-6135	375	2	topological	topological	ADJ
ejpam-6135	375	3	spaces	space	NOUN
ejpam-6135	375	4	.	.	PUNCT
ejpam-6135	376	1	journal	journal	PROPN
ejpam-6135	376	2	of	of	ADP
ejpam-6135	376	3	mathematical	mathematical	ADJ
ejpam-6135	376	4	analysis	analysis	NOUN
ejpam-6135	376	5	and	and	CCONJ
ejpam-6135	376	6	applications	application	NOUN
ejpam-6135	376	7	,	,	PUNCT
ejpam-6135	376	8	24(1):182–190	24(1):182–190	NUM
ejpam-6135	376	9	,	,	PUNCT
ejpam-6135	376	10	1968	1968	NUM
ejpam-6135	376	11	.	.	PUNCT
ejpam-6135	377	1	[	[	X
ejpam-6135	377	2	5	5	NUM
ejpam-6135	377	3	]	]	X
ejpam-6135	377	4	doǧan	doǧan	NOUN
ejpam-6135	377	5	çoker	çoker	NOUN
ejpam-6135	377	6	.	.	PUNCT
ejpam-6135	378	1	an	an	DET
ejpam-6135	378	2	introduction	introduction	NOUN
ejpam-6135	378	3	to	to	ADP
ejpam-6135	378	4	intuitionistic	intuitionistic	ADJ
ejpam-6135	378	5	fuzzy	fuzzy	ADJ
ejpam-6135	378	6	topological	topological	ADJ
ejpam-6135	378	7	spaces	space	NOUN
ejpam-6135	378	8	.	.	PUNCT
ejpam-6135	379	1	fuzzy	fuzzy	ADJ
ejpam-6135	379	2	sets	set	NOUN
ejpam-6135	379	3	and	and	CCONJ
ejpam-6135	379	4	systems	system	NOUN
ejpam-6135	379	5	,	,	PUNCT
ejpam-6135	379	6	88(1):81–89	88(1):81–89	NUM
ejpam-6135	379	7	,	,	PUNCT
ejpam-6135	379	8	1997	1997	NUM
ejpam-6135	379	9	.	.	PUNCT
ejpam-6135	380	1	[	[	X
ejpam-6135	380	2	6	6	NUM
ejpam-6135	380	3	]	]	PUNCT
ejpam-6135	380	4	bruce	bruce	PROPN
ejpam-6135	380	5	hutton	hutton	PROPN
ejpam-6135	380	6	.	.	PUNCT
ejpam-6135	381	1	normality	normality	NOUN
ejpam-6135	381	2	in	in	ADP
ejpam-6135	381	3	fuzzy	fuzzy	ADJ
ejpam-6135	381	4	topological	topological	ADJ
ejpam-6135	381	5	spaces	space	NOUN
ejpam-6135	381	6	.	.	PUNCT
ejpam-6135	382	1	journal	journal	PROPN
ejpam-6135	382	2	of	of	ADP
ejpam-6135	382	3	mathematical	mathematical	ADJ
ejpam-6135	382	4	analysis	analysis	NOUN
ejpam-6135	382	5	and	and	CCONJ
ejpam-6135	382	6	applications	application	NOUN
ejpam-6135	382	7	,	,	PUNCT
ejpam-6135	382	8	50(1):74–79	50(1):74–79	NUM
ejpam-6135	382	9	,	,	PUNCT
ejpam-6135	382	10	1975	1975	NUM
ejpam-6135	382	11	.	.	PUNCT
ejpam-6135	383	1	[	[	X
ejpam-6135	383	2	7	7	X
ejpam-6135	383	3	]	]	X
ejpam-6135	383	4	bruce	bruce	PROPN
ejpam-6135	383	5	hutton	hutton	PROPN
ejpam-6135	383	6	.	.	PUNCT
ejpam-6135	384	1	uniformities	uniformity	NOUN
ejpam-6135	384	2	on	on	ADP
ejpam-6135	384	3	fuzzy	fuzzy	ADJ
ejpam-6135	384	4	topological	topological	ADJ
ejpam-6135	384	5	spaces	space	NOUN
ejpam-6135	384	6	.	.	PUNCT
ejpam-6135	385	1	journal	journal	PROPN
ejpam-6135	385	2	of	of	ADP
ejpam-6135	385	3	mathematical	mathematical	ADJ
ejpam-6135	385	4	analysis	analysis	NOUN
ejpam-6135	385	5	and	and	CCONJ
ejpam-6135	385	6	applications	application	NOUN
ejpam-6135	385	7	,	,	PUNCT
ejpam-6135	385	8	58(3):559–571	58(3):559–571	PROPN
ejpam-6135	385	9	,	,	PUNCT
ejpam-6135	385	10	1977	1977	NUM
ejpam-6135	385	11	.	.	PUNCT
ejpam-6135	386	1	[	[	X
ejpam-6135	386	2	8	8	NUM
ejpam-6135	386	3	]	]	X
ejpam-6135	386	4	r	r	NOUN
ejpam-6135	386	5	narmada	narmada	PROPN
ejpam-6135	386	6	devi	devi	PROPN
ejpam-6135	386	7	,	,	PUNCT
ejpam-6135	386	8	e	e	NOUN
ejpam-6135	386	9	roja	roja	NOUN
ejpam-6135	386	10	,	,	PUNCT
ejpam-6135	386	11	and	and	CCONJ
ejpam-6135	386	12	mkuma	mkuma	NOUN
ejpam-6135	386	13	.	.	PUNCT
ejpam-6135	387	1	a	a	DET
ejpam-6135	387	2	new	new	ADJ
ejpam-6135	387	3	view	view	NOUN
ejpam-6135	387	4	on	on	ADP
ejpam-6135	387	5	intuitionistic	intuitionistic	ADJ
ejpam-6135	387	6	fuzzy	fuzzy	ADJ
ejpam-6135	387	7	c	c	NOUN
ejpam-6135	387	8	structure	structure	NOUN
ejpam-6135	387	9	compactification	compactification	NOUN
ejpam-6135	387	10	.	.	PUNCT
ejpam-6135	388	1	annals	annal	NOUN
ejpam-6135	388	2	of	of	ADP
ejpam-6135	388	3	fuzzy	fuzzy	ADJ
ejpam-6135	388	4	mathematics	mathematic	NOUN
ejpam-6135	388	5	and	and	CCONJ
ejpam-6135	388	6	informatics	informatic	NOUN
ejpam-6135	388	7	,	,	PUNCT
ejpam-6135	388	8	5(3):571–582	5(3):571–582	NUM
ejpam-6135	388	9	,	,	PUNCT
ejpam-6135	388	10	2013	2013	NUM
ejpam-6135	388	11	.	.	PUNCT
ejpam-6135	389	1	[	[	X
ejpam-6135	389	2	9	9	NUM
ejpam-6135	389	3	]	]	X
ejpam-6135	389	4	gk	gk	PROPN
ejpam-6135	389	5	revathi	revathi	PROPN
ejpam-6135	389	6	,	,	PUNCT
ejpam-6135	389	7	r	r	PROPN
ejpam-6135	389	8	narmada	narmada	PROPN
ejpam-6135	389	9	devi	devi	PROPN
ejpam-6135	389	10	,	,	PUNCT
ejpam-6135	389	11	and	and	CCONJ
ejpam-6135	389	12	e	e	PROPN
ejpam-6135	389	13	roja	roja	NOUN
ejpam-6135	389	14	.	.	PUNCT
ejpam-6135	390	1	intuitionistic	intuitionistic	ADJ
ejpam-6135	390	2	fuzzy	fuzzy	ADJ
ejpam-6135	390	3	rough	rough	ADJ
ejpam-6135	390	4	centred	centred	ADJ
ejpam-6135	390	5	texture	texture	ADJ
ejpam-6135	390	6	wallman	wallman	NOUN
ejpam-6135	390	7	type	type	NOUN
ejpam-6135	390	8	compactification	compactification	NOUN
ejpam-6135	390	9	.	.	PUNCT
ejpam-6135	391	1	annals	annal	NOUN
ejpam-6135	391	2	of	of	ADP
ejpam-6135	391	3	fuzzy	fuzzy	ADJ
ejpam-6135	391	4	mathematics	mathematic	NOUN
ejpam-6135	391	5	and	and	CCONJ
ejpam-6135	391	6	informatics	informatic	NOUN
ejpam-6135	391	7	,	,	PUNCT
ejpam-6135	391	8	7(4):699–714	7(4):699–714	PROPN
ejpam-6135	391	9	,	,	PUNCT
ejpam-6135	391	10	2014	2014	NUM
ejpam-6135	391	11	.	.	PUNCT
ejpam-6135	392	1	[	[	X
ejpam-6135	392	2	10	10	NUM
ejpam-6135	392	3	]	]	X
ejpam-6135	392	4	gk	gk	PROPN
ejpam-6135	392	5	revathi	revathi	PROPN
ejpam-6135	392	6	,	,	PUNCT
ejpam-6135	392	7	e	e	NOUN
ejpam-6135	392	8	roja	roja	NOUN
ejpam-6135	392	9	,	,	PUNCT
ejpam-6135	392	10	and	and	CCONJ
ejpam-6135	392	11	mk	mk	PROPN
ejpam-6135	392	12	uma	uma	PROPN
ejpam-6135	392	13	.	.	PROPN
ejpam-6135	393	1	semigroup	semigroup	PROPN
ejpam-6135	393	2	compactification	compactification	NOUN
ejpam-6135	393	3	in	in	ADP
ejpam-6135	393	4	an	an	DET
ejpam-6135	393	5	intuitionistic	intuitionistic	ADJ
ejpam-6135	393	6	fuzzy	fuzzy	ADJ
ejpam-6135	393	7	convergence	convergence	NOUN
ejpam-6135	393	8	topological	topological	ADJ
ejpam-6135	393	9	space	space	NOUN
ejpam-6135	393	10	.	.	PUNCT
ejpam-6135	394	1	italian	italian	ADJ
ejpam-6135	394	2	journal	journal	NOUN
ejpam-6135	394	3	of	of	ADP
ejpam-6135	394	4	pure	pure	ADJ
ejpam-6135	394	5	and	and	CCONJ
ejpam-6135	394	6	applied	applied	ADJ
ejpam-6135	394	7	mathematics	mathematic	NOUN
ejpam-6135	394	8	,	,	PUNCT
ejpam-6135	394	9	(	(	PUNCT
ejpam-6135	394	10	35):9–22	35):9–22	NUM
ejpam-6135	394	11	,	,	PUNCT
ejpam-6135	394	12	2015	2015	NUM
ejpam-6135	394	13	.	.	PUNCT
ejpam-6135	395	1	[	[	X
ejpam-6135	395	2	11	11	NUM
ejpam-6135	395	3	]	]	PUNCT
ejpam-6135	395	4	ceren	ceren	PROPN
ejpam-6135	395	5	sultan	sultan	PROPN
ejpam-6135	395	6	elmali	elmali	PROPN
ejpam-6135	395	7	and	and	CCONJ
ejpam-6135	395	8	tamer	tame	ADJ
ejpam-6135	395	9	ugur	ugur	NOUN
ejpam-6135	395	10	.	.	PUNCT
ejpam-6135	396	1	fan	fan	NOUN
ejpam-6135	396	2	-	-	PUNCT
ejpam-6135	396	3	gottesman	gottesman	NOUN
ejpam-6135	396	4	compactifications	compactification	NOUN
ejpam-6135	396	5	and	and	CCONJ
ejpam-6135	396	6	stone	stone	NOUN
ejpam-6135	396	7	space	space	NOUN
ejpam-6135	396	8	.	.	PUNCT
ejpam-6135	397	1	sigma	sigma	PROPN
ejpam-6135	397	2	,	,	PUNCT
ejpam-6135	397	3	10(2):143–147	10(2):143–147	PROPN
ejpam-6135	397	4	,	,	PUNCT
ejpam-6135	397	5	2019	2019	NUM
ejpam-6135	397	6	.	.	PUNCT
ejpam-6135	398	1	[	[	X
ejpam-6135	398	2	12	12	NUM
ejpam-6135	398	3	]	]	PUNCT
ejpam-6135	398	4	boris	boris	PROPN
ejpam-6135	398	5	vladimirovich	vladimirovich	PROPN
ejpam-6135	398	6	sorin	sorin	PROPN
ejpam-6135	398	7	.	.	PUNCT
ejpam-6135	399	1	compactifications	compactification	NOUN
ejpam-6135	399	2	of	of	ADP
ejpam-6135	399	3	homeomorphism	homeomorphism	PROPN
ejpam-6135	399	4	groups	group	NOUN
ejpam-6135	399	5	of	of	ADP
ejpam-6135	399	6	linearly	linearly	ADV
ejpam-6135	399	7	ordered	order	VERB
ejpam-6135	399	8	compacta	compacta	NOUN
ejpam-6135	399	9	.	.	PUNCT
ejpam-6135	400	1	mathematical	mathematical	ADJ
ejpam-6135	400	2	notes	note	NOUN
ejpam-6135	400	3	,	,	PUNCT
ejpam-6135	400	4	112(1):126–141	112(1):126–141	NUM
ejpam-6135	400	5	,	,	PUNCT
ejpam-6135	400	6	2022	2022	NUM
ejpam-6135	400	7	.	.	PUNCT
ejpam-6135	401	1	[	[	X
ejpam-6135	401	2	13	13	NUM
ejpam-6135	401	3	]	]	SYM
ejpam-6135	401	4	g	g	PROPN
ejpam-6135	401	5	bezhanishvili	bezhanishvili	NOUN
ejpam-6135	401	6	and	and	CCONJ
ejpam-6135	401	7	j	j	PROPN
ejpam-6135	401	8	harding	harding	PROPN
ejpam-6135	401	9	.	.	PUNCT
ejpam-6135	402	1	duality	duality	NOUN
ejpam-6135	402	2	theory	theory	NOUN
ejpam-6135	402	3	for	for	ADP
ejpam-6135	402	4	the	the	DET
ejpam-6135	402	5	category	category	NOUN
ejpam-6135	402	6	of	of	ADP
ejpam-6135	402	7	stable	stable	ADJ
ejpam-6135	402	8	compactifications	compactification	NOUN
ejpam-6135	402	9	.	.	PUNCT
ejpam-6135	403	1	in	in	ADP
ejpam-6135	403	2	topology	topology	NOUN
ejpam-6135	403	3	proc	proc	NOUN
ejpam-6135	403	4	,	,	PUNCT
ejpam-6135	403	5	volume	volume	NOUN
ejpam-6135	403	6	61	61	NUM
ejpam-6135	403	7	,	,	PUNCT
ejpam-6135	403	8	pages	page	NOUN
ejpam-6135	403	9	1–13	1–13	NOUN
ejpam-6135	403	10	,	,	PUNCT
ejpam-6135	403	11	2023	2023	NUM
ejpam-6135	403	12	.	.	PUNCT
ejpam-6135	404	1	[	[	X
ejpam-6135	404	2	14	14	NUM
ejpam-6135	404	3	]	]	X
ejpam-6135	404	4	j	j	PROPN
ejpam-6135	404	5	flachsmeyer	flachsmeyer	NOUN
ejpam-6135	404	6	and	and	CCONJ
ejpam-6135	404	7	f	f	PROPN
ejpam-6135	404	8	terpe	terpe	NOUN
ejpam-6135	404	9	.	.	PUNCT
ejpam-6135	405	1	some	some	DET
ejpam-6135	405	2	applications	application	NOUN
ejpam-6135	405	3	of	of	ADP
ejpam-6135	405	4	the	the	DET
ejpam-6135	405	5	theory	theory	NOUN
ejpam-6135	405	6	of	of	ADP
ejpam-6135	405	7	compactifications	compactification	NOUN
ejpam-6135	405	8	of	of	ADP
ejpam-6135	405	9	topological	topological	ADJ
ejpam-6135	405	10	spaces	space	NOUN
ejpam-6135	405	11	and	and	CCONJ
ejpam-6135	405	12	measure	measure	NOUN
ejpam-6135	405	13	theory	theory	NOUN
ejpam-6135	405	14	.	.	PUNCT
ejpam-6135	406	1	russian	russian	ADJ
ejpam-6135	406	2	mathematical	mathematical	ADJ
ejpam-6135	406	3	surveys	survey	NOUN
ejpam-6135	406	4	,	,	PUNCT
ejpam-6135	406	5	32(5):133	32(5):133	NUM
ejpam-6135	406	6	,	,	PUNCT
ejpam-6135	406	7	1977	1977	NUM
ejpam-6135	406	8	.	.	PUNCT
ejpam-6135	407	1	s.	s.	PROPN
ejpam-6135	407	2	thirukumaran	thirukumaran	PROPN
ejpam-6135	407	3	,	,	PUNCT
ejpam-6135	407	4	g.	g.	PROPN
ejpam-6135	407	5	k.	k.	PROPN
ejpam-6135	407	6	revathi	revathi	PROPN
ejpam-6135	407	7	/	/	SYM
ejpam-6135	407	8	eur	eur	PROPN
ejpam-6135	407	9	.	.	PUNCT
ejpam-6135	408	1	j.	j.	PROPN
ejpam-6135	408	2	pure	pure	PROPN
ejpam-6135	408	3	appl	appl	PROPN
ejpam-6135	408	4	.	.	PROPN
ejpam-6135	408	5	math	math	PROPN
ejpam-6135	408	6	,	,	PUNCT
ejpam-6135	408	7	18	18	NUM
ejpam-6135	408	8	(	(	PUNCT
ejpam-6135	408	9	2	2	NUM
ejpam-6135	408	10	)	)	PUNCT
ejpam-6135	408	11	(	(	PUNCT
ejpam-6135	408	12	2025	2025	NUM
ejpam-6135	408	13	)	)	PUNCT
ejpam-6135	408	14	,	,	PUNCT
ejpam-6135	408	15	6135	6135	NUM
ejpam-6135	408	16	17	17	NUM
ejpam-6135	408	17	of	of	ADP
ejpam-6135	408	18	17	17	NUM
ejpam-6135	408	19	[	[	SYM
ejpam-6135	408	20	15	15	NUM
ejpam-6135	408	21	]	]	X
ejpam-6135	408	22	klaus	klaus	PROPN
ejpam-6135	408	23	g	g	PROPN
ejpam-6135	408	24	witz	witz	PROPN
ejpam-6135	408	25	.	.	PUNCT
ejpam-6135	409	1	applications	application	NOUN
ejpam-6135	409	2	of	of	ADP
ejpam-6135	409	3	a	a	DET
ejpam-6135	409	4	compactification	compactification	NOUN
ejpam-6135	409	5	for	for	ADP
ejpam-6135	409	6	bounded	bounded	ADJ
ejpam-6135	409	7	operator	operator	NOUN
ejpam-6135	409	8	semigroups	semigroup	NOUN
ejpam-6135	409	9	.	.	PUNCT
ejpam-6135	410	1	illinois	illinois	PROPN
ejpam-6135	410	2	journal	journal	PROPN
ejpam-6135	410	3	of	of	ADP
ejpam-6135	410	4	mathematics	mathematics	PROPN
ejpam-6135	410	5	,	,	PUNCT
ejpam-6135	410	6	8(4):685–696	8(4):685–696	NUM
ejpam-6135	410	7	,	,	PUNCT
ejpam-6135	410	8	1964	1964	NUM
ejpam-6135	410	9	.	.	PUNCT
ejpam-6135	411	1	[	[	X
ejpam-6135	411	2	16	16	NUM
ejpam-6135	411	3	]	]	X
ejpam-6135	411	4	nestor	nestor	PROPN
ejpam-6135	411	5	djintelbe	djintelbe	PROPN
ejpam-6135	411	6	and	and	CCONJ
ejpam-6135	411	7	michel	michel	PROPN
ejpam-6135	411	8	coste	coste	PROPN
ejpam-6135	411	9	.	.	PUNCT
ejpam-6135	412	1	compactification	compactification	NOUN
ejpam-6135	412	2	of	of	ADP
ejpam-6135	412	3	the	the	DET
ejpam-6135	412	4	group	group	NOUN
ejpam-6135	412	5	of	of	ADP
ejpam-6135	412	6	rigid	rigid	ADJ
ejpam-6135	412	7	motions	motion	NOUN
ejpam-6135	412	8	and	and	CCONJ
ejpam-6135	412	9	applications	application	NOUN
ejpam-6135	412	10	to	to	ADP
ejpam-6135	412	11	robotics	robotic	NOUN
ejpam-6135	412	12	.	.	PUNCT
ejpam-6135	413	1	journal	journal	NOUN
ejpam-6135	413	2	of	of	ADP
ejpam-6135	413	3	pure	pure	ADJ
ejpam-6135	413	4	and	and	CCONJ
ejpam-6135	413	5	applied	applied	ADJ
ejpam-6135	413	6	algebra	algebra	NOUN
ejpam-6135	413	7	,	,	PUNCT
ejpam-6135	413	8	225(7):106604	225(7):106604	PROPN
ejpam-6135	413	9	,	,	PUNCT
ejpam-6135	413	10	2021	2021	NUM
ejpam-6135	413	11	.	.	PUNCT
ejpam-6135	414	1	[	[	X
ejpam-6135	414	2	17	17	NUM
ejpam-6135	414	3	]	]	X
ejpam-6135	414	4	gk	gk	PROPN
ejpam-6135	414	5	revathi	revathi	PROPN
ejpam-6135	414	6	,	,	PUNCT
ejpam-6135	414	7	e	e	NOUN
ejpam-6135	414	8	roja	roja	NOUN
ejpam-6135	414	9	,	,	PUNCT
ejpam-6135	414	10	and	and	CCONJ
ejpam-6135	414	11	mk	mk	PROPN
ejpam-6135	414	12	uma	uma	PROPN
ejpam-6135	414	13	.	.	PUNCT
ejpam-6135	415	1	a	a	DET
ejpam-6135	415	2	new	new	ADJ
ejpam-6135	415	3	approach	approach	NOUN
ejpam-6135	415	4	to	to	ADP
ejpam-6135	415	5	intuitionistic	intuitionistic	ADJ
ejpam-6135	415	6	fuzzy	fuzzy	ADJ
ejpam-6135	415	7	quasi	quasi	ADJ
ejpam-6135	415	8	uniform	uniform	NOUN
ejpam-6135	415	9	regular	regular	ADJ
ejpam-6135	415	10	gδ	gδ	NOUN
ejpam-6135	415	11	compactness	compactness	NOUN
ejpam-6135	415	12	.	.	PUNCT
ejpam-6135	416	1	international	international	ADJ
ejpam-6135	416	2	journal	journal	PROPN
ejpam-6135	416	3	of	of	ADP
ejpam-6135	416	4	mathematics	mathematics	PROPN
ejpam-6135	416	5	sciences	science	NOUN
ejpam-6135	416	6	and	and	CCONJ
ejpam-6135	416	7	applications	application	NOUN
ejpam-6135	416	8	,	,	PUNCT
ejpam-6135	416	9	2	2	NUM
ejpam-6135	416	10	,	,	PUNCT
ejpam-6135	416	11	2012	2012	NUM
ejpam-6135	416	12	.	.	PUNCT