id	sid	tid	token	lemma	pos
ejpam-5434	1	1	european	european	PROPN
ejpam-5434	1	2	journal	journal	PROPN
ejpam-5434	1	3	of	of	ADP
ejpam-5434	1	4	pure	pure	ADJ
ejpam-5434	1	5	and	and	CCONJ
ejpam-5434	1	6	applied	apply	VERB
ejpam-5434	1	7	mathematics	mathematic	NOUN
ejpam-5434	1	8	vol	vol	NOUN
ejpam-5434	1	9	.	.	PROPN
ejpam-5434	2	1	17	17	NUM
ejpam-5434	2	2	,	,	PUNCT
ejpam-5434	2	3	no	no	INTJ
ejpam-5434	2	4	.	.	NOUN
ejpam-5434	2	5	4	4	NUM
ejpam-5434	2	6	,	,	PUNCT
ejpam-5434	2	7	2024	2024	NUM
ejpam-5434	2	8	,	,	PUNCT
ejpam-5434	2	9	3156	3156	NUM
ejpam-5434	2	10	-	-	SYM
ejpam-5434	2	11	3166	3166	NUM
ejpam-5434	2	12	issn	issn	PROPN
ejpam-5434	2	13	1307	1307	NUM
ejpam-5434	2	14	-	-	SYM
ejpam-5434	2	15	5543	5543	NUM
ejpam-5434	2	16	–	–	PUNCT
ejpam-5434	3	1	ejpam.com	ejpam.com	X
ejpam-5434	3	2	published	publish	VERB
ejpam-5434	3	3	by	by	ADP
ejpam-5434	3	4	new	new	PROPN
ejpam-5434	3	5	york	york	PROPN
ejpam-5434	3	6	business	business	PROPN
ejpam-5434	3	7	global	global	PROPN
ejpam-5434	3	8	on	on	ADP
ejpam-5434	3	9	micro	micro	PROPN
ejpam-5434	3	10	pre	pre	PROPN
ejpam-5434	3	11	operators	operator	NOUN
ejpam-5434	3	12	in	in	ADP
ejpam-5434	3	13	micro	micro	ADJ
ejpam-5434	3	14	topological	topological	PROPN
ejpam-5434	3	15	spaces	space	NOUN
ejpam-5434	3	16	p.	p.	PROPN
ejpam-5434	3	17	sathishmohan1	sathishmohan1	PROPN
ejpam-5434	3	18	,	,	PUNCT
ejpam-5434	3	19	s.	s.	PROPN
ejpam-5434	3	20	stanley	stanley	PROPN
ejpam-5434	3	21	roshan1,∗	roshan1,∗	PROPN
ejpam-5434	3	22	,	,	PUNCT
ejpam-5434	3	23	k.	k.	PROPN
ejpam-5434	3	24	rajalakshmi2	rajalakshmi2	PROPN
ejpam-5434	3	25	,	,	PUNCT
ejpam-5434	3	26	s.	s.	PROPN
ejpam-5434	3	27	brindha3	brindha3	PROPN
ejpam-5434	3	28	,	,	PUNCT
ejpam-5434	3	29	g.	g.	PROPN
ejpam-5434	3	30	poongothai1	poongothai1	NOUN
ejpam-5434	3	31	1	1	NUM
ejpam-5434	3	32	department	department	NOUN
ejpam-5434	3	33	of	of	ADP
ejpam-5434	3	34	mathematics	mathematic	NOUN
ejpam-5434	3	35	,	,	PUNCT
ejpam-5434	3	36	kongunadu	kongunadu	ADJ
ejpam-5434	3	37	arts	art	NOUN
ejpam-5434	3	38	and	and	CCONJ
ejpam-5434	3	39	science	science	NOUN
ejpam-5434	3	40	college(autonomous	college(autonomous	PROPN
ejpam-5434	3	41	)	)	PUNCT
ejpam-5434	3	42	,	,	PUNCT
ejpam-5434	3	43	coimbatore-29	coimbatore-29	PROPN
ejpam-5434	3	44	,	,	PUNCT
ejpam-5434	3	45	tamil	tamil	PROPN
ejpam-5434	3	46	nadu	nadu	PROPN
ejpam-5434	3	47	,	,	PUNCT
ejpam-5434	3	48	india	india	PROPN
ejpam-5434	3	49	2	2	NUM
ejpam-5434	3	50	department	department	NOUN
ejpam-5434	3	51	of	of	ADP
ejpam-5434	3	52	science	science	NOUN
ejpam-5434	3	53	and	and	CCONJ
ejpam-5434	3	54	humanities	humanity	NOUN
ejpam-5434	3	55	,	,	PUNCT
ejpam-5434	3	56	sri	sri	PROPN
ejpam-5434	3	57	krishna	krishna	PROPN
ejpam-5434	3	58	college	college	PROPN
ejpam-5434	3	59	of	of	ADP
ejpam-5434	3	60	engineering	engineering	NOUN
ejpam-5434	3	61	and	and	CCONJ
ejpam-5434	3	62	technology	technology	NOUN
ejpam-5434	3	63	,	,	PUNCT
ejpam-5434	3	64	coimbatore-08	coimbatore-08	PROPN
ejpam-5434	3	65	,	,	PUNCT
ejpam-5434	3	66	tamil	tamil	PROPN
ejpam-5434	3	67	nadu	nadu	NOUN
ejpam-5434	3	68	,	,	PUNCT
ejpam-5434	3	69	india	india	PROPN
ejpam-5434	3	70	3	3	NUM
ejpam-5434	3	71	department	department	PROPN
ejpam-5434	3	72	of	of	ADP
ejpam-5434	3	73	mathematics	mathematic	NOUN
ejpam-5434	3	74	,	,	PUNCT
ejpam-5434	3	75	government	government	NOUN
ejpam-5434	3	76	arts	art	NOUN
ejpam-5434	3	77	and	and	CCONJ
ejpam-5434	3	78	science	science	PROPN
ejpam-5434	3	79	college	college	PROPN
ejpam-5434	3	80	,	,	PUNCT
ejpam-5434	3	81	mettupalayam-04	mettupalayam-04	PROPN
ejpam-5434	3	82	,	,	PUNCT
ejpam-5434	3	83	tamil	tamil	PROPN
ejpam-5434	3	84	nadu	nadu	PROPN
ejpam-5434	3	85	,	,	PUNCT
ejpam-5434	3	86	india	india	PROPN
ejpam-5434	3	87	abstract	abstract	NOUN
ejpam-5434	3	88	.	.	PUNCT
ejpam-5434	4	1	the	the	DET
ejpam-5434	4	2	basic	basic	ADJ
ejpam-5434	4	3	objective	objective	NOUN
ejpam-5434	4	4	of	of	ADP
ejpam-5434	4	5	this	this	DET
ejpam-5434	4	6	research	research	NOUN
ejpam-5434	4	7	work	work	NOUN
ejpam-5434	4	8	is	be	AUX
ejpam-5434	4	9	to	to	PART
ejpam-5434	4	10	introduce	introduce	VERB
ejpam-5434	4	11	and	and	CCONJ
ejpam-5434	4	12	investigate	investigate	VERB
ejpam-5434	4	13	the	the	DET
ejpam-5434	4	14	properties	property	NOUN
ejpam-5434	4	15	of	of	ADP
ejpam-5434	4	16	micro	micro	ADJ
ejpam-5434	4	17	pre	pre	NOUN
ejpam-5434	4	18	-	-	NOUN
ejpam-5434	4	19	frontier	frontier	ADJ
ejpam-5434	4	20	,	,	PUNCT
ejpam-5434	4	21	micro	micro	ADJ
ejpam-5434	4	22	pre	pre	ADJ
ejpam-5434	4	23	-	-	ADJ
ejpam-5434	4	24	exterior	exterior	ADJ
ejpam-5434	4	25	,	,	PUNCT
ejpam-5434	4	26	micro	micro	ADJ
ejpam-5434	4	27	pre	pre	NOUN
ejpam-5434	4	28	-	-	ADJ
ejpam-5434	4	29	border	border	ADJ
ejpam-5434	4	30	,	,	PUNCT
ejpam-5434	4	31	micro	micro	ADJ
ejpam-5434	4	32	pre	pre	NOUN
ejpam-5434	4	33	-	-	ADJ
ejpam-5434	4	34	kernel	kernel	ADJ
ejpam-5434	4	35	using	use	VERB
ejpam-5434	4	36	the	the	DET
ejpam-5434	4	37	concept	concept	NOUN
ejpam-5434	4	38	of	of	ADP
ejpam-5434	4	39	frontier	frontier	NOUN
ejpam-5434	4	40	,	,	PUNCT
ejpam-5434	4	41	exterior	exterior	ADJ
ejpam-5434	4	42	,	,	PUNCT
ejpam-5434	4	43	border	border	NOUN
ejpam-5434	4	44	and	and	CCONJ
ejpam-5434	4	45	kernel	kernel	NOUN
ejpam-5434	4	46	.	.	PUNCT
ejpam-5434	5	1	2020	2020	NUM
ejpam-5434	5	2	mathematics	mathematic	NOUN
ejpam-5434	5	3	subject	subject	NOUN
ejpam-5434	5	4	classifications	classification	NOUN
ejpam-5434	5	5	:	:	PUNCT
ejpam-5434	5	6	54a05	54a05	NUM
ejpam-5434	5	7	,	,	PUNCT
ejpam-5434	5	8	54a10	54a10	NUM
ejpam-5434	5	9	key	key	ADJ
ejpam-5434	5	10	words	word	NOUN
ejpam-5434	5	11	and	and	CCONJ
ejpam-5434	5	12	phrases	phrase	NOUN
ejpam-5434	5	13	:	:	PUNCT
ejpam-5434	5	14	micro	micro	ADJ
ejpam-5434	5	15	pre	pre	NOUN
ejpam-5434	5	16	-	-	NOUN
ejpam-5434	5	17	frontier	frontier	ADJ
ejpam-5434	5	18	,	,	PUNCT
ejpam-5434	5	19	micro	micro	ADJ
ejpam-5434	5	20	pre	pre	ADJ
ejpam-5434	5	21	-	-	ADJ
ejpam-5434	5	22	exterior	exterior	ADJ
ejpam-5434	5	23	,	,	PUNCT
ejpam-5434	5	24	micro	micro	ADJ
ejpam-5434	5	25	pre	pre	NOUN
ejpam-5434	5	26	-	-	ADJ
ejpam-5434	5	27	border	border	ADJ
ejpam-5434	5	28	,	,	PUNCT
ejpam-5434	5	29	micro	micro	ADJ
ejpam-5434	5	30	prekernel	prekernel	PROPN
ejpam-5434	5	31	1	1	NUM
ejpam-5434	5	32	.	.	PUNCT
ejpam-5434	6	1	introduction	introduction	PROPN
ejpam-5434	6	2	levine	levine	PROPN
ejpam-5434	6	3	’s	’s	PART
ejpam-5434	6	4	introduction	introduction	NOUN
ejpam-5434	6	5	of	of	ADP
ejpam-5434	6	6	generalized	generalized	ADJ
ejpam-5434	6	7	closed	closed	ADJ
ejpam-5434	6	8	sets	set	NOUN
ejpam-5434	6	9	in	in	ADP
ejpam-5434	6	10	1970	1970	NUM
ejpam-5434	6	11	[	[	X
ejpam-5434	6	12	3	3	NUM
ejpam-5434	6	13	]	]	PUNCT
ejpam-5434	6	14	,	,	PUNCT
ejpam-5434	6	15	providing	provide	VERB
ejpam-5434	6	16	a	a	DET
ejpam-5434	6	17	foundational	foundational	ADJ
ejpam-5434	6	18	framework	framework	NOUN
ejpam-5434	6	19	for	for	ADP
ejpam-5434	6	20	subsequent	subsequent	ADJ
ejpam-5434	6	21	developments	development	NOUN
ejpam-5434	6	22	.	.	PUNCT
ejpam-5434	7	1	lellis	lellis	PROPN
ejpam-5434	7	2	thivagar	thivagar	NOUN
ejpam-5434	8	1	[	[	X
ejpam-5434	8	2	1	1	NUM
ejpam-5434	8	3	]	]	PUNCT
ejpam-5434	8	4	,	,	PUNCT
ejpam-5434	8	5	further	far	ADV
ejpam-5434	8	6	expanded	expand	VERB
ejpam-5434	8	7	this	this	DET
ejpam-5434	8	8	framework	framework	NOUN
ejpam-5434	8	9	with	with	ADP
ejpam-5434	8	10	the	the	DET
ejpam-5434	8	11	introduction	introduction	NOUN
ejpam-5434	8	12	of	of	ADP
ejpam-5434	8	13	nano	nano	NOUN
ejpam-5434	8	14	topology	topology	NOUN
ejpam-5434	8	15	,	,	PUNCT
ejpam-5434	8	16	utilizing	utilize	VERB
ejpam-5434	8	17	approximations	approximation	NOUN
ejpam-5434	8	18	and	and	CCONJ
ejpam-5434	8	19	boundary	boundary	ADJ
ejpam-5434	8	20	regions	region	NOUN
ejpam-5434	8	21	of	of	ADP
ejpam-5434	8	22	a	a	DET
ejpam-5434	8	23	subset	subset	NOUN
ejpam-5434	8	24	of	of	ADP
ejpam-5434	8	25	a	a	DET
ejpam-5434	8	26	universe	universe	NOUN
ejpam-5434	8	27	using	use	VERB
ejpam-5434	8	28	an	an	DET
ejpam-5434	8	29	equivalence	equivalence	NOUN
ejpam-5434	8	30	relation	relation	NOUN
ejpam-5434	8	31	on	on	ADP
ejpam-5434	8	32	it	it	PRON
ejpam-5434	8	33	to	to	PART
ejpam-5434	8	34	define	define	VERB
ejpam-5434	8	35	nano	nano	NOUN
ejpam-5434	8	36	closed	close	VERB
ejpam-5434	8	37	sets	set	NOUN
ejpam-5434	8	38	,	,	PUNCT
ejpam-5434	8	39	nano	nano	NOUN
ejpam-5434	8	40	-	-	ADJ
ejpam-5434	8	41	interior	interior	ADJ
ejpam-5434	8	42	and	and	CCONJ
ejpam-5434	8	43	nano	nano	NOUN
ejpam-5434	8	44	-	-	PUNCT
ejpam-5434	8	45	closure	closure	NOUN
ejpam-5434	8	46	.	.	PUNCT
ejpam-5434	9	1	the	the	DET
ejpam-5434	9	2	exploration	exploration	NOUN
ejpam-5434	9	3	of	of	ADP
ejpam-5434	9	4	weak	weak	ADJ
ejpam-5434	9	5	forms	form	NOUN
ejpam-5434	9	6	of	of	ADP
ejpam-5434	9	7	nano	nano	VERB
ejpam-5434	9	8	open	open	ADJ
ejpam-5434	9	9	sets	set	NOUN
ejpam-5434	9	10	,	,	PUNCT
ejpam-5434	9	11	such	such	ADJ
ejpam-5434	9	12	as	as	ADP
ejpam-5434	9	13	nano	nano	NOUN
ejpam-5434	9	14	α	α	NOUN
ejpam-5434	9	15	-	-	ADJ
ejpam-5434	9	16	open	open	ADJ
ejpam-5434	9	17	sets	set	NOUN
ejpam-5434	9	18	,	,	PUNCT
ejpam-5434	9	19	nano	nano	NOUN
ejpam-5434	9	20	semi	semi	ADJ
ejpam-5434	9	21	-	-	ADJ
ejpam-5434	9	22	open	open	ADJ
ejpam-5434	9	23	sets	set	NOUN
ejpam-5434	9	24	,	,	PUNCT
ejpam-5434	9	25	nano	nano	ADJ
ejpam-5434	9	26	pre	pre	ADJ
ejpam-5434	9	27	-	-	ADJ
ejpam-5434	9	28	open	open	ADJ
ejpam-5434	9	29	sets	set	NOUN
ejpam-5434	9	30	,	,	PUNCT
ejpam-5434	9	31	and	and	CCONJ
ejpam-5434	9	32	nano	nano	NOUN
ejpam-5434	9	33	-	-	PUNCT
ejpam-5434	9	34	β	β	NOUN
ejpam-5434	9	35	-	-	ADJ
ejpam-5434	9	36	open	open	ADJ
ejpam-5434	9	37	sets	set	NOUN
ejpam-5434	9	38	,	,	PUNCT
ejpam-5434	9	39	was	be	AUX
ejpam-5434	9	40	undertaken	undertake	VERB
ejpam-5434	9	41	by	by	ADP
ejpam-5434	9	42	many	many	ADJ
ejpam-5434	9	43	authors	author	NOUN
ejpam-5434	9	44	adding	add	VERB
ejpam-5434	9	45	layers	layer	NOUN
ejpam-5434	9	46	of	of	ADP
ejpam-5434	9	47	complexity	complexity	NOUN
ejpam-5434	9	48	to	to	ADP
ejpam-5434	9	49	the	the	DET
ejpam-5434	9	50	existing	exist	VERB
ejpam-5434	9	51	theories	theory	NOUN
ejpam-5434	9	52	.	.	PUNCT
ejpam-5434	10	1	in	in	ADP
ejpam-5434	10	2	2013	2013	NUM
ejpam-5434	10	3	,	,	PUNCT
ejpam-5434	10	4	antony	antony	PROPN
ejpam-5434	10	5	rex	rex	PROPN
ejpam-5434	10	6	rodgio	rodgio	PROPN
ejpam-5434	10	7	et.al	et.al	PROPN
ejpam-5434	10	8	.	.	PUNCT
ejpam-5434	10	9	,[8	,[8	PROPN
ejpam-5434	10	10	]	]	PUNCT
ejpam-5434	10	11	defined	define	VERB
ejpam-5434	10	12	the	the	DET
ejpam-5434	10	13	properties	property	NOUN
ejpam-5434	10	14	of	of	ADP
ejpam-5434	10	15	β∗	β∗	NOUN
ejpam-5434	10	16	open	open	ADJ
ejpam-5434	10	17	sets	set	NOUN
ejpam-5434	10	18	like	like	ADP
ejpam-5434	10	19	frontier	frontier	NOUN
ejpam-5434	10	20	,	,	PUNCT
ejpam-5434	10	21	exterior	exterior	ADJ
ejpam-5434	10	22	and	and	CCONJ
ejpam-5434	10	23	border	border	NOUN
ejpam-5434	10	24	.	.	PUNCT
ejpam-5434	11	1	in	in	ADP
ejpam-5434	11	2	2018	2018	NUM
ejpam-5434	11	3	,	,	PUNCT
ejpam-5434	11	4	sathishmohan	sathishmohan	PROPN
ejpam-5434	11	5	et.al	et.al	PROPN
ejpam-5434	11	6	.	.	PUNCT
ejpam-5434	11	7	,	,	PUNCT
ejpam-5434	12	1	[	[	X
ejpam-5434	12	2	6	6	NUM
ejpam-5434	12	3	]	]	PUNCT
ejpam-5434	12	4	introduced	introduce	VERB
ejpam-5434	12	5	some	some	DET
ejpam-5434	12	6	properties	property	NOUN
ejpam-5434	12	7	of	of	ADP
ejpam-5434	12	8	nano	nano	NOUN
ejpam-5434	12	9	pre	pre	NOUN
ejpam-5434	12	10	-	-	NOUN
ejpam-5434	12	11	neighbourhoods	neighbourhood	NOUN
ejpam-5434	12	12	in	in	ADP
ejpam-5434	12	13	nano	nano	NOUN
ejpam-5434	12	14	topology	topology	NOUN
ejpam-5434	12	15	.	.	PUNCT
ejpam-5434	13	1	in	in	ADP
ejpam-5434	13	2	2019	2019	NUM
ejpam-5434	13	3	,	,	PUNCT
ejpam-5434	13	4	chandrasekar	chandrasekar	X
ejpam-5434	13	5	[	[	X
ejpam-5434	13	6	4	4	NUM
ejpam-5434	13	7	]	]	PUNCT
ejpam-5434	13	8	,	,	PUNCT
ejpam-5434	13	9	introduced	introduce	VERB
ejpam-5434	13	10	the	the	DET
ejpam-5434	13	11	concept	concept	NOUN
ejpam-5434	13	12	of	of	ADP
ejpam-5434	13	13	micro	micro	ADJ
ejpam-5434	13	14	topology	topology	NOUN
ejpam-5434	13	15	which	which	PRON
ejpam-5434	13	16	is	be	AUX
ejpam-5434	13	17	a	a	DET
ejpam-5434	13	18	simple	simple	ADJ
ejpam-5434	13	19	extension	extension	NOUN
ejpam-5434	13	20	of	of	ADP
ejpam-5434	13	21	nano	nano	NOUN
ejpam-5434	13	22	topology	topology	NOUN
ejpam-5434	13	23	,	,	PUNCT
ejpam-5434	13	24	with	with	ADP
ejpam-5434	13	25	a	a	DET
ejpam-5434	13	26	focus	focus	NOUN
ejpam-5434	13	27	on	on	ADP
ejpam-5434	13	28	micro	micro	ADJ
ejpam-5434	13	29	preopen	preopen	NOUN
ejpam-5434	13	30	and	and	CCONJ
ejpam-5434	13	31	micro	micro	NOUN
ejpam-5434	13	32	semi	semi	ADJ
ejpam-5434	13	33	-	-	ADJ
ejpam-5434	13	34	open	open	ADJ
ejpam-5434	13	35	sets	set	NOUN
ejpam-5434	13	36	.	.	PUNCT
ejpam-5434	14	1	chandrasekar	chandrasekar	NOUN
ejpam-5434	14	2	and	and	CCONJ
ejpam-5434	14	3	swathi	swathi	X
ejpam-5434	15	1	[	[	X
ejpam-5434	15	2	5	5	NUM
ejpam-5434	15	3	]	]	PUNCT
ejpam-5434	15	4	,	,	PUNCT
ejpam-5434	15	5	introduced	introduce	VERB
ejpam-5434	15	6	micro	micro	PROPN
ejpam-5434	15	7	α	α	PROPN
ejpam-5434	15	8	-	-	ADJ
ejpam-5434	15	9	open	open	ADJ
ejpam-5434	15	10	∗corresponding	∗corresponde	VERB
ejpam-5434	15	11	author	author	NOUN
ejpam-5434	15	12	.	.	PUNCT
ejpam-5434	16	1	doi	doi	NOUN
ejpam-5434	16	2	:	:	PUNCT
ejpam-5434	16	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5434	https://doi.org/10.29020/nybg.ejpam.v17i4.5434	NOUN
ejpam-5434	16	4	email	email	NOUN
ejpam-5434	16	5	addresses	address	NOUN
ejpam-5434	16	6	:	:	PUNCT
ejpam-5434	16	7	sathishmohan@kongunaducollege.ac.in	sathishmohan@kongunaducollege.ac.in	PROPN
ejpam-5434	16	8	(	(	PUNCT
ejpam-5434	16	9	p.	p.	NOUN
ejpam-5434	16	10	sathishmohan	sathishmohan	PROPN
ejpam-5434	16	11	)	)	PUNCT
ejpam-5434	16	12	,	,	PUNCT
ejpam-5434	16	13	stanleyroshan20@gmail.com	stanleyroshan20@gmail.com	X
ejpam-5434	16	14	(	(	PUNCT
ejpam-5434	16	15	s.	s.	PROPN
ejpam-5434	16	16	stanley	stanley	PROPN
ejpam-5434	16	17	roshan	roshan	PROPN
ejpam-5434	16	18	)	)	PUNCT
ejpam-5434	16	19	,	,	PUNCT
ejpam-5434	16	20	rajalakshmikandhasamy@gmail.com	rajalakshmikandhasamy@gmail.com	X
ejpam-5434	16	21	(	(	PUNCT
ejpam-5434	16	22	k.	k.	NOUN
ejpam-5434	16	23	rajalakshmi	rajalakshmi	PROPN
ejpam-5434	16	24	)	)	PUNCT
ejpam-5434	16	25	,	,	PUNCT
ejpam-5434	16	26	brindha.sagashra@gmail.com	brindha.sagashra@gmail.com	X
ejpam-5434	16	27	(	(	PUNCT
ejpam-5434	16	28	s.	s.	PROPN
ejpam-5434	16	29	brindha	brindha	PROPN
ejpam-5434	16	30	)	)	PUNCT
ejpam-5434	16	31	,	,	PUNCT
ejpam-5434	16	32	gpkpoongothai@gmail.com	gpkpoongothai@gmail.com	X
ejpam-5434	16	33	(	(	PUNCT
ejpam-5434	16	34	g.	g.	PROPN
ejpam-5434	16	35	poongothai	poongothai	PROPN
ejpam-5434	16	36	)	)	PUNCT
ejpam-5434	16	37	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5434	17	1	3156	3156	NUM
ejpam-5434	17	2	copyright	copyright	NOUN
ejpam-5434	17	3	:	:	PUNCT
ejpam-5434	17	4	©	©	PROPN
ejpam-5434	17	5	2024	2024	NUM
ejpam-5434	17	6	the	the	DET
ejpam-5434	17	7	author(s	author(s	NOUN
ejpam-5434	17	8	)	)	PUNCT
ejpam-5434	17	9	.	.	PUNCT
ejpam-5434	18	1	(	(	PUNCT
ejpam-5434	18	2	cc	cc	NOUN
ejpam-5434	18	3	by	by	ADP
ejpam-5434	18	4	-	-	PUNCT
ejpam-5434	18	5	nc	nc	PROPN
ejpam-5434	18	6	4.0	4.0	NUM
ejpam-5434	18	7	)	)	PUNCT
ejpam-5434	18	8	s.	s.	PROPN
ejpam-5434	18	9	stanley	stanley	PROPN
ejpam-5434	18	10	roshan	roshan	PROPN
ejpam-5434	18	11	et	et	PROPN
ejpam-5434	18	12	al	al	PROPN
ejpam-5434	18	13	.	.	PUNCT
ejpam-5434	18	14	/	/	SYM
ejpam-5434	18	15	eur	eur	PROPN
ejpam-5434	18	16	.	.	PUNCT
ejpam-5434	19	1	j.	j.	PROPN
ejpam-5434	19	2	pure	pure	PROPN
ejpam-5434	19	3	appl	appl	PROPN
ejpam-5434	19	4	.	.	PROPN
ejpam-5434	19	5	math	math	PROPN
ejpam-5434	19	6	,	,	PUNCT
ejpam-5434	19	7	17	17	NUM
ejpam-5434	19	8	(	(	PUNCT
ejpam-5434	19	9	4	4	NUM
ejpam-5434	19	10	)	)	PUNCT
ejpam-5434	19	11	(	(	PUNCT
ejpam-5434	19	12	2024	2024	NUM
ejpam-5434	19	13	)	)	PUNCT
ejpam-5434	19	14	,	,	PUNCT
ejpam-5434	19	15	3156	3156	NUM
ejpam-5434	19	16	-	-	SYM
ejpam-5434	19	17	3166	3166	NUM
ejpam-5434	19	18	3157	3157	NUM
ejpam-5434	19	19	sets	set	NOUN
ejpam-5434	19	20	and	and	CCONJ
ejpam-5434	19	21	studied	study	VERB
ejpam-5434	19	22	the	the	DET
ejpam-5434	19	23	basic	basic	ADJ
ejpam-5434	19	24	properties	property	NOUN
ejpam-5434	19	25	.	.	PUNCT
ejpam-5434	20	1	recently	recently	ADV
ejpam-5434	20	2	in	in	ADP
ejpam-5434	20	3	2020	2020	NUM
ejpam-5434	20	4	,	,	PUNCT
ejpam-5434	20	5	hariwan	hariwan	X
ejpam-5434	20	6	z.ibrahim	z.ibrahim	PRON
ejpam-5434	20	7	[	[	X
ejpam-5434	20	8	9	9	NUM
ejpam-5434	20	9	]	]	PUNCT
ejpam-5434	20	10	,	,	PUNCT
ejpam-5434	20	11	introduced	introduce	VERB
ejpam-5434	20	12	micro	micro	ADV
ejpam-5434	20	13	β	β	NOUN
ejpam-5434	20	14	-	-	ADJ
ejpam-5434	20	15	open	open	ADJ
ejpam-5434	20	16	sets	set	NOUN
ejpam-5434	20	17	in	in	ADP
ejpam-5434	20	18	micro	micro	ADJ
ejpam-5434	20	19	topological	topological	ADJ
ejpam-5434	20	20	spaces	space	NOUN
ejpam-5434	20	21	.	.	PUNCT
ejpam-5434	21	1	the	the	DET
ejpam-5434	21	2	aim	aim	NOUN
ejpam-5434	21	3	of	of	ADP
ejpam-5434	21	4	this	this	DET
ejpam-5434	21	5	paper	paper	NOUN
ejpam-5434	21	6	is	be	AUX
ejpam-5434	21	7	to	to	PART
ejpam-5434	21	8	introduce	introduce	VERB
ejpam-5434	21	9	and	and	CCONJ
ejpam-5434	21	10	investigate	investigate	VERB
ejpam-5434	21	11	the	the	DET
ejpam-5434	21	12	properties	property	NOUN
ejpam-5434	21	13	of	of	ADP
ejpam-5434	21	14	micro	micro	ADJ
ejpam-5434	21	15	pre	pre	NOUN
ejpam-5434	21	16	-	-	NOUN
ejpam-5434	21	17	frontier	frontier	ADJ
ejpam-5434	21	18	,	,	PUNCT
ejpam-5434	21	19	micro	micro	ADJ
ejpam-5434	21	20	pre	pre	ADJ
ejpam-5434	21	21	-	-	ADJ
ejpam-5434	21	22	exterior	exterior	ADJ
ejpam-5434	21	23	,	,	PUNCT
ejpam-5434	21	24	micro	micro	ADJ
ejpam-5434	21	25	pre	pre	ADJ
ejpam-5434	21	26	-	-	ADJ
ejpam-5434	21	27	border	border	ADJ
ejpam-5434	21	28	and	and	CCONJ
ejpam-5434	21	29	micro	micro	ADJ
ejpam-5434	21	30	pre	pre	NOUN
ejpam-5434	21	31	-	-	ADJ
ejpam-5434	21	32	kernel	kernel	ADJ
ejpam-5434	21	33	using	use	VERB
ejpam-5434	21	34	the	the	DET
ejpam-5434	21	35	notion	notion	NOUN
ejpam-5434	21	36	of	of	ADP
ejpam-5434	21	37	frontier	frontier	NOUN
ejpam-5434	21	38	,	,	PUNCT
ejpam-5434	21	39	exterior	exterior	ADJ
ejpam-5434	21	40	,	,	PUNCT
ejpam-5434	21	41	border	border	NOUN
ejpam-5434	21	42	and	and	CCONJ
ejpam-5434	21	43	kernel	kernel	NOUN
ejpam-5434	21	44	to	to	PART
ejpam-5434	21	45	obtain	obtain	VERB
ejpam-5434	21	46	their	their	PRON
ejpam-5434	21	47	basic	basic	ADJ
ejpam-5434	21	48	results	result	NOUN
ejpam-5434	21	49	.	.	PUNCT
ejpam-5434	22	1	the	the	DET
ejpam-5434	22	2	basic	basic	ADJ
ejpam-5434	22	3	definitions	definition	NOUN
ejpam-5434	22	4	used	use	VERB
ejpam-5434	22	5	in	in	ADP
ejpam-5434	22	6	this	this	DET
ejpam-5434	22	7	paper	paper	NOUN
ejpam-5434	22	8	is	be	AUX
ejpam-5434	22	9	given	give	VERB
ejpam-5434	22	10	below	below	ADV
ejpam-5434	22	11	.	.	PUNCT
ejpam-5434	23	1	definition	definition	NOUN
ejpam-5434	23	2	1	1	NUM
ejpam-5434	23	3	.	.	PUNCT
ejpam-5434	24	1	[	[	X
ejpam-5434	24	2	1	1	X
ejpam-5434	24	3	]	]	PUNCT
ejpam-5434	24	4	let	let	VERB
ejpam-5434	24	5	u	u	PRON
ejpam-5434	24	6	be	be	AUX
ejpam-5434	24	7	the	the	DET
ejpam-5434	24	8	universe	universe	NOUN
ejpam-5434	24	9	,	,	PUNCT
ejpam-5434	24	10	r	r	NOUN
ejpam-5434	24	11	be	be	VERB
ejpam-5434	24	12	an	an	DET
ejpam-5434	24	13	equivalence	equivalence	NOUN
ejpam-5434	24	14	relation	relation	NOUN
ejpam-5434	24	15	on	on	ADP
ejpam-5434	24	16	u	u	NOUN
ejpam-5434	24	17	and	and	CCONJ
ejpam-5434	24	18	τr(x	τr(x	NUM
ejpam-5434	24	19	)	)	PUNCT
ejpam-5434	25	1	=	=	PRON
ejpam-5434	25	2	{	{	PUNCT
ejpam-5434	25	3	u	u	NOUN
ejpam-5434	25	4	,	,	PUNCT
ejpam-5434	25	5	∅	∅	NOUN
ejpam-5434	25	6	,	,	PUNCT
ejpam-5434	25	7	lr(x	lr(x	PROPN
ejpam-5434	25	8	)	)	PUNCT
ejpam-5434	25	9	,	,	PUNCT
ejpam-5434	25	10	ur(x	ur(x	PROPN
ejpam-5434	25	11	)	)	PUNCT
ejpam-5434	25	12	,	,	PUNCT
ejpam-5434	25	13	br(x	br(x	NOUN
ejpam-5434	25	14	)	)	PUNCT
ejpam-5434	25	15	}	}	PUNCT
ejpam-5434	25	16	where	where	SCONJ
ejpam-5434	25	17	x	x	X
ejpam-5434	25	18	⊆	⊆	NUM
ejpam-5434	25	19	u	u	NOUN
ejpam-5434	25	20	.	.	PUNCT
ejpam-5434	25	21	τr(x	τr(x	PUNCT
ejpam-5434	25	22	)	)	PUNCT
ejpam-5434	25	23	satisfies	satisfy	VERB
ejpam-5434	25	24	the	the	DET
ejpam-5434	25	25	following	follow	VERB
ejpam-5434	25	26	axioms	axiom	NOUN
ejpam-5434	25	27	:	:	PUNCT
ejpam-5434	25	28	(	(	PUNCT
ejpam-5434	25	29	i	i	NOUN
ejpam-5434	25	30	)	)	PUNCT
ejpam-5434	25	31	u	u	NOUN
ejpam-5434	25	32	∈	∈	PROPN
ejpam-5434	25	33	τr(x	τr(x	NUM
ejpam-5434	25	34	)	)	PUNCT
ejpam-5434	25	35	and	and	CCONJ
ejpam-5434	25	36	∅	∅	NOUN
ejpam-5434	25	37	∈	∈	PROPN
ejpam-5434	25	38	τr(x	τr(x	NUM
ejpam-5434	25	39	)	)	PUNCT
ejpam-5434	25	40	.	.	PUNCT
ejpam-5434	26	1	(	(	PUNCT
ejpam-5434	26	2	ii	ii	X
ejpam-5434	26	3	)	)	PUNCT
ejpam-5434	26	4	the	the	DET
ejpam-5434	26	5	union	union	NOUN
ejpam-5434	26	6	of	of	ADP
ejpam-5434	26	7	elements	element	NOUN
ejpam-5434	26	8	of	of	ADP
ejpam-5434	26	9	any	any	DET
ejpam-5434	26	10	sub	sub	NOUN
ejpam-5434	26	11	collection	collection	NOUN
ejpam-5434	26	12	of	of	ADP
ejpam-5434	26	13	τr(x	τr(x	NUM
ejpam-5434	26	14	)	)	PUNCT
ejpam-5434	26	15	is	be	AUX
ejpam-5434	26	16	in	in	ADP
ejpam-5434	26	17	τr(x	τr(x	NUM
ejpam-5434	26	18	)	)	PUNCT
ejpam-5434	26	19	.	.	PUNCT
ejpam-5434	27	1	(	(	PUNCT
ejpam-5434	27	2	iii	iii	X
ejpam-5434	27	3	)	)	PUNCT
ejpam-5434	27	4	the	the	DET
ejpam-5434	27	5	intersection	intersection	NOUN
ejpam-5434	27	6	of	of	ADP
ejpam-5434	27	7	the	the	DET
ejpam-5434	27	8	elements	element	NOUN
ejpam-5434	27	9	of	of	ADP
ejpam-5434	27	10	any	any	DET
ejpam-5434	27	11	finite	finite	ADJ
ejpam-5434	27	12	sub	sub	NOUN
ejpam-5434	27	13	collection	collection	NOUN
ejpam-5434	27	14	of	of	ADP
ejpam-5434	27	15	τr(x	τr(x	NUM
ejpam-5434	27	16	)	)	PUNCT
ejpam-5434	27	17	is	be	AUX
ejpam-5434	27	18	in	in	ADP
ejpam-5434	27	19	τr(x	τr(x	NUM
ejpam-5434	27	20	)	)	PUNCT
ejpam-5434	27	21	.	.	PUNCT
ejpam-5434	28	1	that	that	PRON
ejpam-5434	28	2	is	be	AUX
ejpam-5434	28	3	,	,	PUNCT
ejpam-5434	28	4	τr(x	τr(x	NUM
ejpam-5434	28	5	)	)	PUNCT
ejpam-5434	28	6	forms	form	VERB
ejpam-5434	28	7	a	a	DET
ejpam-5434	28	8	topology	topology	NOUN
ejpam-5434	28	9	on	on	ADP
ejpam-5434	28	10	u	u	PROPN
ejpam-5434	28	11	is	be	AUX
ejpam-5434	28	12	called	call	VERB
ejpam-5434	28	13	the	the	DET
ejpam-5434	28	14	nano	nano	NOUN
ejpam-5434	28	15	topology	topology	NOUN
ejpam-5434	28	16	on	on	ADP
ejpam-5434	28	17	u	u	NOUN
ejpam-5434	28	18	with	with	ADP
ejpam-5434	28	19	respect	respect	NOUN
ejpam-5434	28	20	to	to	ADP
ejpam-5434	28	21	x.	x.	PROPN
ejpam-5434	28	22	{	{	PUNCT
ejpam-5434	28	23	u	u	PROPN
ejpam-5434	28	24	,	,	PUNCT
ejpam-5434	28	25	τr(x	τr(x	NUM
ejpam-5434	28	26	)	)	PUNCT
ejpam-5434	28	27	}	}	PUNCT
ejpam-5434	28	28	is	be	AUX
ejpam-5434	28	29	called	call	VERB
ejpam-5434	28	30	the	the	DET
ejpam-5434	28	31	nano	nano	NOUN
ejpam-5434	28	32	topological	topological	ADJ
ejpam-5434	28	33	space	space	NOUN
ejpam-5434	28	34	.	.	PUNCT
ejpam-5434	29	1	definition	definition	NOUN
ejpam-5434	29	2	2	2	NUM
ejpam-5434	29	3	.	.	PUNCT
ejpam-5434	30	1	[	[	X
ejpam-5434	30	2	4	4	X
ejpam-5434	30	3	]	]	X
ejpam-5434	30	4	let	let	VERB
ejpam-5434	30	5	{	{	PUNCT
ejpam-5434	30	6	u	u	NOUN
ejpam-5434	30	7	,	,	PUNCT
ejpam-5434	30	8	τr(x	τr(x	NUM
ejpam-5434	30	9	)	)	PUNCT
ejpam-5434	30	10	}	}	PUNCT
ejpam-5434	30	11	is	be	AUX
ejpam-5434	30	12	a	a	DET
ejpam-5434	30	13	nano	nano	ADJ
ejpam-5434	30	14	topological	topological	ADJ
ejpam-5434	30	15	space	space	NOUN
ejpam-5434	30	16	here	here	ADV
ejpam-5434	30	17	µr(x	µr(x	X
ejpam-5434	30	18	)	)	PUNCT
ejpam-5434	31	1	=	=	SYM
ejpam-5434	31	2	{	{	PUNCT
ejpam-5434	31	3	n	n	CCONJ
ejpam-5434	31	4	∪(n	∪(n	NOUN
ejpam-5434	31	5	′∩µ	′∩µ	NOUN
ejpam-5434	31	6	)	)	PUNCT
ejpam-5434	31	7	:	:	PUNCT
ejpam-5434	31	8	n	n	CCONJ
ejpam-5434	31	9	,	,	PUNCT
ejpam-5434	31	10	n	n	NOUN
ejpam-5434	31	11	′	′	NUM
ejpam-5434	31	12	∈	∈	PROPN
ejpam-5434	31	13	τr(x	τr(x	NUM
ejpam-5434	31	14	)	)	PUNCT
ejpam-5434	31	15	}	}	PUNCT
ejpam-5434	31	16	and	and	CCONJ
ejpam-5434	31	17	called	call	VERB
ejpam-5434	31	18	it	it	PRON
ejpam-5434	31	19	micro	micro	ADJ
ejpam-5434	31	20	topology	topology	NOUN
ejpam-5434	31	21	of	of	ADP
ejpam-5434	31	22	τr(x	τr(x	NUM
ejpam-5434	31	23	)	)	PUNCT
ejpam-5434	31	24	by	by	ADP
ejpam-5434	31	25	µ	µ	PRON
ejpam-5434	31	26	where	where	SCONJ
ejpam-5434	31	27	µ	µ	NOUN
ejpam-5434	31	28	/∈	/∈	NOUN
ejpam-5434	31	29	τr(x	τr(x	NUM
ejpam-5434	31	30	)	)	PUNCT
ejpam-5434	31	31	.	.	PUNCT
ejpam-5434	32	1	definition	definition	NOUN
ejpam-5434	32	2	3	3	NUM
ejpam-5434	32	3	.	.	PUNCT
ejpam-5434	33	1	[	[	X
ejpam-5434	33	2	4	4	X
ejpam-5434	33	3	]	]	X
ejpam-5434	33	4	the	the	DET
ejpam-5434	33	5	micro	micro	PROPN
ejpam-5434	33	6	topology	topology	PROPN
ejpam-5434	33	7	µr(x	µr(x	X
ejpam-5434	33	8	)	)	PUNCT
ejpam-5434	33	9	satisfies	satisfy	VERB
ejpam-5434	33	10	the	the	DET
ejpam-5434	33	11	following	follow	VERB
ejpam-5434	33	12	axioms	axiom	NOUN
ejpam-5434	33	13	.	.	PUNCT
ejpam-5434	34	1	(	(	PUNCT
ejpam-5434	34	2	i	i	NOUN
ejpam-5434	34	3	)	)	PUNCT
ejpam-5434	34	4	u	u	PROPN
ejpam-5434	34	5	∈	∈	PROPN
ejpam-5434	34	6	µr(x	µr(x	NUM
ejpam-5434	34	7	)	)	PUNCT
ejpam-5434	34	8	and	and	CCONJ
ejpam-5434	34	9	∅	∅	NOUN
ejpam-5434	34	10	∈	∈	PROPN
ejpam-5434	34	11	µr(x	µr(x	PRON
ejpam-5434	34	12	)	)	PUNCT
ejpam-5434	34	13	(	(	PUNCT
ejpam-5434	34	14	ii	ii	NOUN
ejpam-5434	34	15	)	)	PUNCT
ejpam-5434	34	16	the	the	DET
ejpam-5434	34	17	union	union	NOUN
ejpam-5434	34	18	of	of	ADP
ejpam-5434	34	19	elements	element	NOUN
ejpam-5434	34	20	of	of	ADP
ejpam-5434	34	21	any	any	DET
ejpam-5434	34	22	sub	sub	NOUN
ejpam-5434	34	23	collection	collection	NOUN
ejpam-5434	34	24	of	of	ADP
ejpam-5434	34	25	µr(x	µr(x	X
ejpam-5434	34	26	)	)	PUNCT
ejpam-5434	34	27	is	be	AUX
ejpam-5434	34	28	in	in	ADP
ejpam-5434	34	29	µr(x	µr(x	NUM
ejpam-5434	34	30	)	)	PUNCT
ejpam-5434	34	31	.	.	PUNCT
ejpam-5434	35	1	(	(	PUNCT
ejpam-5434	35	2	iii	iii	X
ejpam-5434	35	3	)	)	PUNCT
ejpam-5434	35	4	the	the	DET
ejpam-5434	35	5	intersection	intersection	NOUN
ejpam-5434	35	6	of	of	ADP
ejpam-5434	35	7	the	the	DET
ejpam-5434	35	8	elements	element	NOUN
ejpam-5434	35	9	of	of	ADP
ejpam-5434	35	10	any	any	DET
ejpam-5434	35	11	finite	finite	ADJ
ejpam-5434	35	12	sub	sub	NOUN
ejpam-5434	35	13	collection	collection	NOUN
ejpam-5434	35	14	of	of	ADP
ejpam-5434	35	15	µr(x	µr(x	X
ejpam-5434	35	16	)	)	PUNCT
ejpam-5434	35	17	is	be	AUX
ejpam-5434	35	18	in	in	ADP
ejpam-5434	35	19	µr(x	µr(x	NUM
ejpam-5434	35	20	)	)	PUNCT
ejpam-5434	35	21	.	.	PUNCT
ejpam-5434	36	1	then	then	ADV
ejpam-5434	36	2	µr(x	µr(x	NUM
ejpam-5434	36	3	)	)	PUNCT
ejpam-5434	36	4	is	be	AUX
ejpam-5434	36	5	called	call	VERB
ejpam-5434	36	6	micro	micro	ADJ
ejpam-5434	36	7	topology	topology	NOUN
ejpam-5434	36	8	on	on	ADP
ejpam-5434	36	9	u	u	NOUN
ejpam-5434	36	10	with	with	ADP
ejpam-5434	36	11	respect	respect	NOUN
ejpam-5434	36	12	to	to	ADP
ejpam-5434	36	13	x.	x.	NOUN
ejpam-5434	36	14	the	the	DET
ejpam-5434	36	15	triplet	triplet	NOUN
ejpam-5434	36	16	(	(	PUNCT
ejpam-5434	36	17	u	u	NOUN
ejpam-5434	36	18	,	,	PUNCT
ejpam-5434	36	19	τr(x	τr(x	NUM
ejpam-5434	36	20	)	)	PUNCT
ejpam-5434	36	21	,	,	PUNCT
ejpam-5434	36	22	µr(x	µr(x	X
ejpam-5434	36	23	)	)	PUNCT
ejpam-5434	36	24	)	)	PUNCT
ejpam-5434	36	25	is	be	AUX
ejpam-5434	36	26	called	call	VERB
ejpam-5434	36	27	micro	micro	ADJ
ejpam-5434	36	28	topological	topological	ADJ
ejpam-5434	36	29	spaces	space	NOUN
ejpam-5434	36	30	and	and	CCONJ
ejpam-5434	36	31	the	the	DET
ejpam-5434	36	32	elements	element	NOUN
ejpam-5434	36	33	of	of	ADP
ejpam-5434	36	34	µr(x	µr(x	NOUN
ejpam-5434	36	35	)	)	PUNCT
ejpam-5434	36	36	are	be	AUX
ejpam-5434	36	37	called	call	VERB
ejpam-5434	36	38	micro	micro	ADJ
ejpam-5434	36	39	open	open	ADJ
ejpam-5434	36	40	sets	set	NOUN
ejpam-5434	36	41	and	and	CCONJ
ejpam-5434	36	42	the	the	DET
ejpam-5434	36	43	complement	complement	NOUN
ejpam-5434	36	44	of	of	ADP
ejpam-5434	36	45	a	a	DET
ejpam-5434	36	46	micro	micro	ADJ
ejpam-5434	36	47	open	open	ADJ
ejpam-5434	36	48	set	set	NOUN
ejpam-5434	36	49	is	be	AUX
ejpam-5434	36	50	called	call	VERB
ejpam-5434	36	51	a	a	DET
ejpam-5434	36	52	micro	micro	NOUN
ejpam-5434	36	53	closed	close	VERB
ejpam-5434	36	54	set	set	NOUN
ejpam-5434	36	55	.	.	PUNCT
ejpam-5434	37	1	definition	definition	NOUN
ejpam-5434	37	2	4	4	NUM
ejpam-5434	37	3	.	.	PUNCT
ejpam-5434	38	1	[	[	X
ejpam-5434	38	2	4	4	X
ejpam-5434	38	3	]	]	X
ejpam-5434	38	4	the	the	DET
ejpam-5434	38	5	micro	micro	ADJ
ejpam-5434	38	6	closure	closure	NOUN
ejpam-5434	38	7	of	of	ADP
ejpam-5434	38	8	a	a	DET
ejpam-5434	38	9	set	set	NOUN
ejpam-5434	38	10	a	a	PRON
ejpam-5434	38	11	is	be	AUX
ejpam-5434	38	12	denoted	denote	VERB
ejpam-5434	38	13	by	by	ADP
ejpam-5434	38	14	mic	mic	NOUN
ejpam-5434	38	15	-	-	PUNCT
ejpam-5434	38	16	cl(a	cl(a	NUM
ejpam-5434	38	17	)	)	PUNCT
ejpam-5434	38	18	and	and	CCONJ
ejpam-5434	38	19	is	be	AUX
ejpam-5434	38	20	defined	define	VERB
ejpam-5434	38	21	as	as	ADP
ejpam-5434	38	22	mic	mic	NOUN
ejpam-5434	38	23	-	-	PUNCT
ejpam-5434	38	24	cl(a	cl(a	NUM
ejpam-5434	38	25	)	)	PUNCT
ejpam-5434	38	26	=	=	PUNCT
ejpam-5434	39	1	∩{b	∩{b	PROPN
ejpam-5434	39	2	:	:	PUNCT
ejpam-5434	39	3	b	b	NOUN
ejpam-5434	39	4	is	be	AUX
ejpam-5434	39	5	micro	micro	ADV
ejpam-5434	39	6	closed	close	VERB
ejpam-5434	39	7	and	and	CCONJ
ejpam-5434	39	8	a	a	DET
ejpam-5434	39	9	⊆	⊆	NUM
ejpam-5434	39	10	b	b	NOUN
ejpam-5434	39	11	}	}	PUNCT
ejpam-5434	39	12	.	.	PUNCT
ejpam-5434	40	1	the	the	DET
ejpam-5434	40	2	micro	micro	ADJ
ejpam-5434	40	3	interior	interior	PROPN
ejpam-5434	40	4	of	of	ADP
ejpam-5434	40	5	a	a	DET
ejpam-5434	40	6	set	set	NOUN
ejpam-5434	40	7	a	a	PRON
ejpam-5434	40	8	is	be	AUX
ejpam-5434	40	9	denoted	denote	VERB
ejpam-5434	40	10	by	by	ADP
ejpam-5434	40	11	mic	mic	ADJ
ejpam-5434	40	12	-	-	PUNCT
ejpam-5434	40	13	int(a	int(a	NOUN
ejpam-5434	40	14	)	)	PUNCT
ejpam-5434	40	15	and	and	CCONJ
ejpam-5434	40	16	is	be	AUX
ejpam-5434	40	17	defined	define	VERB
ejpam-5434	40	18	as	as	ADP
ejpam-5434	40	19	mic	mic	ADJ
ejpam-5434	40	20	-	-	PUNCT
ejpam-5434	40	21	int(a	int(a	NOUN
ejpam-5434	40	22	)	)	PUNCT
ejpam-5434	41	1	=	=	PUNCT
ejpam-5434	41	2	∪{b	∪{b	NOUN
ejpam-5434	41	3	:	:	PUNCT
ejpam-5434	41	4	b	b	X
ejpam-5434	41	5	is	be	AUX
ejpam-5434	41	6	micro	micro	ADV
ejpam-5434	41	7	open	open	ADJ
ejpam-5434	41	8	and	and	CCONJ
ejpam-5434	41	9	a	a	DET
ejpam-5434	41	10	⊇	⊇	ADJ
ejpam-5434	41	11	b	b	NOUN
ejpam-5434	41	12	}	}	PUNCT
ejpam-5434	41	13	.	.	PUNCT
ejpam-5434	42	1	definition	definition	NOUN
ejpam-5434	42	2	5	5	NUM
ejpam-5434	42	3	.	.	PUNCT
ejpam-5434	43	1	[	[	X
ejpam-5434	43	2	7	7	X
ejpam-5434	43	3	]	]	X
ejpam-5434	43	4	the	the	DET
ejpam-5434	43	5	union	union	NOUN
ejpam-5434	43	6	of	of	ADP
ejpam-5434	43	7	all	all	DET
ejpam-5434	43	8	micro	micro	ADJ
ejpam-5434	43	9	pre	pre	ADJ
ejpam-5434	43	10	-	-	ADJ
ejpam-5434	43	11	open	open	ADJ
ejpam-5434	43	12	sets	set	NOUN
ejpam-5434	43	13	which	which	PRON
ejpam-5434	43	14	are	be	AUX
ejpam-5434	43	15	contained	contain	VERB
ejpam-5434	43	16	in	in	ADP
ejpam-5434	43	17	a	a	PRON
ejpam-5434	43	18	is	be	AUX
ejpam-5434	43	19	called	call	VERB
ejpam-5434	43	20	the	the	DET
ejpam-5434	43	21	micro	micro	ADJ
ejpam-5434	43	22	pre	pre	NOUN
ejpam-5434	43	23	-	-	ADJ
ejpam-5434	43	24	interior	interior	ADJ
ejpam-5434	43	25	of	of	ADP
ejpam-5434	43	26	a	a	PRON
ejpam-5434	43	27	and	and	CCONJ
ejpam-5434	43	28	is	be	AUX
ejpam-5434	43	29	denoted	denote	VERB
ejpam-5434	43	30	by	by	ADP
ejpam-5434	43	31	mic	mic	ADJ
ejpam-5434	43	32	-	-	PUNCT
ejpam-5434	43	33	pint(a	pint(a	NOUN
ejpam-5434	43	34	)	)	PUNCT
ejpam-5434	43	35	or	or	CCONJ
ejpam-5434	43	36	by	by	ADP
ejpam-5434	43	37	mic	mic	ADJ
ejpam-5434	43	38	-	-	PUNCT
ejpam-5434	43	39	pa∗.	pa∗.	NOUN
ejpam-5434	43	40	as	as	ADP
ejpam-5434	43	41	the	the	DET
ejpam-5434	43	42	union	union	NOUN
ejpam-5434	43	43	of	of	ADP
ejpam-5434	43	44	micro	micro	PROPN
ejpam-5434	43	45	pre	pre	ADJ
ejpam-5434	43	46	-	-	ADJ
ejpam-5434	43	47	open	open	ADJ
ejpam-5434	43	48	sets	set	NOUN
ejpam-5434	43	49	is	be	AUX
ejpam-5434	43	50	micro	micro	ADJ
ejpam-5434	43	51	pre	pre	ADJ
ejpam-5434	43	52	-	-	ADJ
ejpam-5434	43	53	open	open	ADJ
ejpam-5434	43	54	,	,	PUNCT
ejpam-5434	43	55	mic	mic	ADJ
ejpam-5434	43	56	-	-	PUNCT
ejpam-5434	43	57	pa∗	pa∗	NOUN
ejpam-5434	43	58	is	be	AUX
ejpam-5434	43	59	micro	micro	ADJ
ejpam-5434	43	60	pre	pre	ADJ
ejpam-5434	43	61	-	-	ADJ
ejpam-5434	43	62	open	open	ADJ
ejpam-5434	43	63	always	always	ADV
ejpam-5434	43	64	.	.	PUNCT
ejpam-5434	44	1	micro	micro	VERB
ejpam-5434	44	2	pre	pre	ADJ
ejpam-5434	44	3	-	-	ADJ
ejpam-5434	44	4	open	open	ADJ
ejpam-5434	44	5	is	be	AUX
ejpam-5434	44	6	denoted	denote	VERB
ejpam-5434	44	7	by	by	ADP
ejpam-5434	44	8	mic	mic	ADJ
ejpam-5434	44	9	-	-	PUNCT
ejpam-5434	44	10	po(u	po(u	ADJ
ejpam-5434	44	11	)	)	PUNCT
ejpam-5434	44	12	and	and	CCONJ
ejpam-5434	44	13	micro	micro	ADJ
ejpam-5434	44	14	pre	pre	ADJ
ejpam-5434	44	15	-	-	ADJ
ejpam-5434	44	16	closed	closed	ADJ
ejpam-5434	44	17	is	be	AUX
ejpam-5434	44	18	denoted	denote	VERB
ejpam-5434	44	19	by	by	ADP
ejpam-5434	44	20	mic	mic	ADJ
ejpam-5434	44	21	-	-	PUNCT
ejpam-5434	44	22	pf(u	pf(u	NUM
ejpam-5434	44	23	)	)	PUNCT
ejpam-5434	44	24	.	.	PUNCT
ejpam-5434	45	1	definition	definition	NOUN
ejpam-5434	45	2	6	6	NUM
ejpam-5434	45	3	.	.	PUNCT
ejpam-5434	46	1	[	[	X
ejpam-5434	46	2	7	7	X
ejpam-5434	46	3	]	]	X
ejpam-5434	46	4	the	the	DET
ejpam-5434	46	5	intersection	intersection	NOUN
ejpam-5434	46	6	of	of	ADP
ejpam-5434	46	7	micro	micro	ADJ
ejpam-5434	46	8	pre	pre	ADJ
ejpam-5434	46	9	-	-	ADJ
ejpam-5434	46	10	closed	closed	ADJ
ejpam-5434	46	11	sets	set	NOUN
ejpam-5434	46	12	containing	contain	VERB
ejpam-5434	46	13	a	a	DET
ejpam-5434	46	14	set	set	NOUN
ejpam-5434	46	15	a	a	PRON
ejpam-5434	46	16	is	be	AUX
ejpam-5434	46	17	called	call	VERB
ejpam-5434	46	18	the	the	DET
ejpam-5434	46	19	micro	micro	ADJ
ejpam-5434	46	20	pre	pre	NOUN
ejpam-5434	46	21	-	-	NOUN
ejpam-5434	46	22	closure	closure	NOUN
ejpam-5434	46	23	of	of	ADP
ejpam-5434	46	24	a	a	PRON
ejpam-5434	46	25	and	and	CCONJ
ejpam-5434	46	26	is	be	AUX
ejpam-5434	46	27	denoted	denote	VERB
ejpam-5434	46	28	by	by	ADP
ejpam-5434	46	29	mic	mic	ADJ
ejpam-5434	46	30	-	-	PUNCT
ejpam-5434	46	31	pcl(a	pcl(a	NOUN
ejpam-5434	46	32	)	)	PUNCT
ejpam-5434	46	33	or	or	CCONJ
ejpam-5434	46	34	by	by	ADP
ejpam-5434	46	35	mic	mic	ADJ
ejpam-5434	46	36	-	-	PUNCT
ejpam-5434	46	37	pa∗.	pa∗.	NOUN
ejpam-5434	46	38	definition	definition	NOUN
ejpam-5434	46	39	7	7	NUM
ejpam-5434	46	40	.	.	PUNCT
ejpam-5434	47	1	[	[	X
ejpam-5434	47	2	4	4	X
ejpam-5434	47	3	]	]	X
ejpam-5434	47	4	let	let	VERB
ejpam-5434	47	5	(	(	PUNCT
ejpam-5434	47	6	u	u	NOUN
ejpam-5434	47	7	,	,	PUNCT
ejpam-5434	47	8	τr(x	τr(x	NUM
ejpam-5434	47	9	)	)	PUNCT
ejpam-5434	47	10	,	,	PUNCT
ejpam-5434	47	11	µr(x	µr(x	X
ejpam-5434	47	12	)	)	PUNCT
ejpam-5434	47	13	)	)	PUNCT
ejpam-5434	47	14	be	be	AUX
ejpam-5434	47	15	a	a	DET
ejpam-5434	47	16	micro	micro	ADJ
ejpam-5434	47	17	topological	topological	ADJ
ejpam-5434	47	18	space	space	NOUN
ejpam-5434	47	19	and	and	CCONJ
ejpam-5434	47	20	a	a	DET
ejpam-5434	47	21	⊆	⊆	NUM
ejpam-5434	47	22	u	u	NOUN
ejpam-5434	47	23	.	.	PUNCT
ejpam-5434	48	1	then	then	ADV
ejpam-5434	48	2	a	a	PRON
ejpam-5434	48	3	is	be	AUX
ejpam-5434	48	4	called	call	VERB
ejpam-5434	48	5	micro	micro	ADJ
ejpam-5434	48	6	pre	pre	ADJ
ejpam-5434	48	7	-	-	ADJ
ejpam-5434	48	8	open	open	ADJ
ejpam-5434	48	9	if	if	SCONJ
ejpam-5434	48	10	a	a	DET
ejpam-5434	48	11	⊆	⊆	NUM
ejpam-5434	48	12	mic	mic	ADJ
ejpam-5434	48	13	-	-	PUNCT
ejpam-5434	48	14	int(mic	int(mic	NOUN
ejpam-5434	48	15	-	-	PUNCT
ejpam-5434	48	16	cl(a	cl(a	NUM
ejpam-5434	48	17	)	)	PUNCT
ejpam-5434	48	18	)	)	PUNCT
ejpam-5434	48	19	.	.	PUNCT
ejpam-5434	49	1	s.	s.	PROPN
ejpam-5434	49	2	stanley	stanley	PROPN
ejpam-5434	49	3	roshan	roshan	PROPN
ejpam-5434	49	4	et	et	PROPN
ejpam-5434	49	5	al	al	PROPN
ejpam-5434	49	6	.	.	PUNCT
ejpam-5434	49	7	/	/	SYM
ejpam-5434	49	8	eur	eur	PROPN
ejpam-5434	49	9	.	.	PUNCT
ejpam-5434	50	1	j.	j.	PROPN
ejpam-5434	50	2	pure	pure	PROPN
ejpam-5434	50	3	appl	appl	PROPN
ejpam-5434	50	4	.	.	PROPN
ejpam-5434	50	5	math	math	PROPN
ejpam-5434	50	6	,	,	PUNCT
ejpam-5434	50	7	17	17	NUM
ejpam-5434	50	8	(	(	PUNCT
ejpam-5434	50	9	4	4	NUM
ejpam-5434	50	10	)	)	PUNCT
ejpam-5434	50	11	(	(	PUNCT
ejpam-5434	50	12	2024	2024	NUM
ejpam-5434	50	13	)	)	PUNCT
ejpam-5434	50	14	,	,	PUNCT
ejpam-5434	50	15	3156	3156	NUM
ejpam-5434	50	16	-	-	SYM
ejpam-5434	50	17	3166	3166	NUM
ejpam-5434	50	18	3158	3158	NUM
ejpam-5434	50	19	definition	definition	NOUN
ejpam-5434	50	20	8	8	NUM
ejpam-5434	50	21	.	.	PUNCT
ejpam-5434	51	1	[	[	X
ejpam-5434	51	2	2	2	X
ejpam-5434	51	3	]	]	PUNCT
ejpam-5434	51	4	a	a	DET
ejpam-5434	51	5	point	point	NOUN
ejpam-5434	51	6	x	x	X
ejpam-5434	51	7	∈	∈	NOUN
ejpam-5434	51	8	x	x	PUNCT
ejpam-5434	51	9	is	be	AUX
ejpam-5434	51	10	said	say	VERB
ejpam-5434	51	11	to	to	PART
ejpam-5434	51	12	be	be	AUX
ejpam-5434	51	13	limit	limit	NOUN
ejpam-5434	51	14	point	point	NOUN
ejpam-5434	51	15	of	of	ADP
ejpam-5434	51	16	a	a	DET
ejpam-5434	51	17	if	if	SCONJ
ejpam-5434	51	18	every	every	DET
ejpam-5434	51	19	neighborhood	neighborhood	NOUN
ejpam-5434	51	20	of	of	ADP
ejpam-5434	51	21	x	x	PART
ejpam-5434	51	22	intersects	intersect	VERB
ejpam-5434	51	23	a	a	PRON
ejpam-5434	51	24	in	in	ADP
ejpam-5434	51	25	some	some	DET
ejpam-5434	51	26	point	point	NOUN
ejpam-5434	51	27	other	other	ADJ
ejpam-5434	51	28	than	than	ADP
ejpam-5434	51	29	x	x	PRON
ejpam-5434	51	30	itself	itself	PRON
ejpam-5434	51	31	.	.	PUNCT
ejpam-5434	52	1	definition	definition	NOUN
ejpam-5434	52	2	9	9	NUM
ejpam-5434	52	3	.	.	PUNCT
ejpam-5434	53	1	[	[	X
ejpam-5434	53	2	2	2	X
ejpam-5434	53	3	]	]	PUNCT
ejpam-5434	53	4	the	the	DET
ejpam-5434	53	5	set	set	NOUN
ejpam-5434	53	6	of	of	ADP
ejpam-5434	53	7	all	all	DET
ejpam-5434	53	8	limit	limit	NOUN
ejpam-5434	53	9	points	point	NOUN
ejpam-5434	53	10	of	of	ADP
ejpam-5434	53	11	a	a	PRON
ejpam-5434	53	12	is	be	AUX
ejpam-5434	53	13	called	call	VERB
ejpam-5434	53	14	the	the	DET
ejpam-5434	53	15	derived	derive	VERB
ejpam-5434	53	16	set	set	NOUN
ejpam-5434	53	17	of	of	ADP
ejpam-5434	53	18	a	a	PRON
ejpam-5434	53	19	and	and	CCONJ
ejpam-5434	53	20	it	it	PRON
ejpam-5434	53	21	denoted	denote	VERB
ejpam-5434	53	22	by	by	ADP
ejpam-5434	53	23	d(a	d(a	PROPN
ejpam-5434	53	24	)	)	PUNCT
ejpam-5434	53	25	.	.	PUNCT
ejpam-5434	54	1	definition	definition	NOUN
ejpam-5434	54	2	10	10	NUM
ejpam-5434	54	3	.	.	PUNCT
ejpam-5434	55	1	[	[	X
ejpam-5434	55	2	7	7	X
ejpam-5434	55	3	]	]	X
ejpam-5434	55	4	a	a	DET
ejpam-5434	55	5	point	point	NOUN
ejpam-5434	55	6	x	x	X
ejpam-5434	55	7	∈	∈	NOUN
ejpam-5434	55	8	u	u	NOUN
ejpam-5434	55	9	is	be	AUX
ejpam-5434	55	10	said	say	VERB
ejpam-5434	55	11	to	to	PART
ejpam-5434	55	12	be	be	AUX
ejpam-5434	55	13	a	a	DET
ejpam-5434	55	14	micro	micro	ADJ
ejpam-5434	55	15	pre	pre	ADJ
ejpam-5434	55	16	-	-	ADJ
ejpam-5434	55	17	limit	limit	ADJ
ejpam-5434	55	18	point	point	NOUN
ejpam-5434	55	19	of	of	ADP
ejpam-5434	55	20	a	a	DET
ejpam-5434	55	21	iff	iff	NOUN
ejpam-5434	55	22	for	for	ADP
ejpam-5434	55	23	each	each	DET
ejpam-5434	55	24	u	u	PROPN
ejpam-5434	55	25	∈	∈	PROPN
ejpam-5434	55	26	mic	mic	ADJ
ejpam-5434	55	27	-	-	PUNCT
ejpam-5434	55	28	po(u	po(u	ADJ
ejpam-5434	55	29	)	)	PUNCT
ejpam-5434	55	30	,	,	PUNCT
ejpam-5434	55	31	u	u	NOUN
ejpam-5434	55	32	∩	∩	NOUN
ejpam-5434	55	33	(	(	PUNCT
ejpam-5434	55	34	a−	a−	X
ejpam-5434	55	35	{	{	PUNCT
ejpam-5434	55	36	x	x	NOUN
ejpam-5434	55	37	}	}	PUNCT
ejpam-5434	55	38	)	)	PUNCT
ejpam-5434	55	39	̸=	̸=	PROPN
ejpam-5434	55	40	∅.	∅.	PRON
ejpam-5434	55	41	definition	definition	NOUN
ejpam-5434	55	42	11	11	NUM
ejpam-5434	55	43	.	.	PUNCT
ejpam-5434	56	1	[	[	X
ejpam-5434	56	2	7	7	X
ejpam-5434	56	3	]	]	PUNCT
ejpam-5434	56	4	the	the	DET
ejpam-5434	56	5	set	set	NOUN
ejpam-5434	56	6	of	of	ADP
ejpam-5434	56	7	all	all	DET
ejpam-5434	56	8	micro	micro	ADJ
ejpam-5434	56	9	pre	pre	ADJ
ejpam-5434	56	10	-	-	ADJ
ejpam-5434	56	11	limit	limit	ADJ
ejpam-5434	56	12	points	point	NOUN
ejpam-5434	56	13	of	of	ADP
ejpam-5434	56	14	a	a	PRON
ejpam-5434	56	15	is	be	AUX
ejpam-5434	56	16	said	say	VERB
ejpam-5434	56	17	to	to	PART
ejpam-5434	56	18	be	be	AUX
ejpam-5434	56	19	the	the	DET
ejpam-5434	56	20	micro	micro	ADJ
ejpam-5434	56	21	pre	pre	ADJ
ejpam-5434	56	22	-	-	ADJ
ejpam-5434	56	23	derived	derived	ADJ
ejpam-5434	56	24	set	set	NOUN
ejpam-5434	56	25	of	of	ADP
ejpam-5434	56	26	a	a	PRON
ejpam-5434	56	27	and	and	CCONJ
ejpam-5434	56	28	in	in	ADP
ejpam-5434	56	29	denoted	denote	VERB
ejpam-5434	56	30	by	by	ADP
ejpam-5434	56	31	mic	mic	ADJ
ejpam-5434	56	32	-	-	PUNCT
ejpam-5434	56	33	pd(a	pd(a	NOUN
ejpam-5434	56	34	)	)	PUNCT
ejpam-5434	56	35	.	.	PUNCT
ejpam-5434	57	1	2	2	X
ejpam-5434	57	2	.	.	X
ejpam-5434	57	3	micro	micro	ADJ
ejpam-5434	57	4	pre	pre	NOUN
ejpam-5434	57	5	-	-	NOUN
ejpam-5434	57	6	frontier	frontier	NOUN
ejpam-5434	57	7	in	in	ADP
ejpam-5434	57	8	this	this	DET
ejpam-5434	57	9	section	section	NOUN
ejpam-5434	57	10	,	,	PUNCT
ejpam-5434	57	11	we	we	PRON
ejpam-5434	57	12	define	define	VERB
ejpam-5434	57	13	and	and	CCONJ
ejpam-5434	57	14	study	study	VERB
ejpam-5434	57	15	the	the	DET
ejpam-5434	57	16	notions	notion	NOUN
ejpam-5434	57	17	of	of	ADP
ejpam-5434	57	18	micro	micro	ADJ
ejpam-5434	57	19	pre	pre	NOUN
ejpam-5434	57	20	-	-	NOUN
ejpam-5434	57	21	frontier	frontier	NOUN
ejpam-5434	57	22	and	and	CCONJ
ejpam-5434	57	23	obtain	obtain	VERB
ejpam-5434	57	24	its	its	PRON
ejpam-5434	57	25	basic	basic	ADJ
ejpam-5434	57	26	properties	property	NOUN
ejpam-5434	57	27	.	.	PUNCT
ejpam-5434	58	1	definition	definition	NOUN
ejpam-5434	58	2	12	12	NUM
ejpam-5434	58	3	.	.	PUNCT
ejpam-5434	59	1	micro	micro	ADJ
ejpam-5434	59	2	pre	pre	NOUN
ejpam-5434	59	3	-	-	NOUN
ejpam-5434	59	4	frontier	frontier	NOUN
ejpam-5434	59	5	of	of	ADP
ejpam-5434	59	6	a	a	DET
ejpam-5434	59	7	⊂	⊂	PROPN
ejpam-5434	59	8	u	u	NOUN
ejpam-5434	59	9	is	be	AUX
ejpam-5434	59	10	defined	define	VERB
ejpam-5434	59	11	as	as	ADP
ejpam-5434	59	12	mic	mic	ADJ
ejpam-5434	59	13	-	-	PUNCT
ejpam-5434	59	14	pa∗−	pa∗−	NOUN
ejpam-5434	59	15	mic	mic	ADJ
ejpam-5434	59	16	-	-	PUNCT
ejpam-5434	59	17	pa∗	pa∗	NOUN
ejpam-5434	59	18	and	and	CCONJ
ejpam-5434	59	19	is	be	AUX
ejpam-5434	59	20	denoted	denote	VERB
ejpam-5434	59	21	by	by	ADP
ejpam-5434	59	22	mic	mic	ADJ
ejpam-5434	59	23	-	-	PUNCT
ejpam-5434	59	24	pfr(a	pfr(a	NOUN
ejpam-5434	59	25	)	)	PUNCT
ejpam-5434	59	26	.	.	PUNCT
ejpam-5434	60	1	it	it	PRON
ejpam-5434	60	2	is	be	AUX
ejpam-5434	60	3	obvious	obvious	ADJ
ejpam-5434	60	4	that	that	SCONJ
ejpam-5434	60	5	mic	mic	ADJ
ejpam-5434	60	6	-	-	PUNCT
ejpam-5434	60	7	pfr(a	pfr(a	NOUN
ejpam-5434	60	8	)	)	PUNCT
ejpam-5434	60	9	⊆	⊆	NUM
ejpam-5434	60	10	mic	mic	NOUN
ejpam-5434	60	11	-	-	PUNCT
ejpam-5434	60	12	fr(a	fr(a	NUM
ejpam-5434	60	13	)	)	PUNCT
ejpam-5434	60	14	,	,	PUNCT
ejpam-5434	60	15	the	the	DET
ejpam-5434	60	16	micro	micro	PROPN
ejpam-5434	60	17	frontier	frontier	NOUN
ejpam-5434	60	18	of	of	ADP
ejpam-5434	60	19	a.	a.	NOUN
ejpam-5434	60	20	but	but	CCONJ
ejpam-5434	60	21	in	in	ADP
ejpam-5434	60	22	general	general	ADJ
ejpam-5434	60	23	the	the	DET
ejpam-5434	60	24	converse	converse	NOUN
ejpam-5434	60	25	may	may	AUX
ejpam-5434	60	26	not	not	PART
ejpam-5434	60	27	be	be	AUX
ejpam-5434	60	28	true	true	ADJ
ejpam-5434	60	29	.	.	PUNCT
ejpam-5434	61	1	micro	micro	ADJ
ejpam-5434	61	2	pre	pre	ADJ
ejpam-5434	61	3	-	-	ADJ
ejpam-5434	61	4	interior(a	interior(a	ADJ
ejpam-5434	61	5	)	)	PUNCT
ejpam-5434	61	6	is	be	AUX
ejpam-5434	61	7	denoted	denote	VERB
ejpam-5434	61	8	as	as	ADP
ejpam-5434	61	9	mic	mic	ADJ
ejpam-5434	61	10	-	-	PUNCT
ejpam-5434	61	11	pa∗	pa∗	NOUN
ejpam-5434	61	12	and	and	CCONJ
ejpam-5434	61	13	micro	micro	ADJ
ejpam-5434	61	14	pre	pre	NOUN
ejpam-5434	61	15	-	-	NOUN
ejpam-5434	61	16	closure	closure	NOUN
ejpam-5434	61	17	is	be	AUX
ejpam-5434	61	18	denoted	denote	VERB
ejpam-5434	61	19	as	as	ADP
ejpam-5434	61	20	mic	mic	ADJ
ejpam-5434	61	21	-	-	PUNCT
ejpam-5434	61	22	pa∗.	pa∗.	ADJ
ejpam-5434	61	23	example	example	NOUN
ejpam-5434	62	1	1	1	X
ejpam-5434	62	2	.	.	PUNCT
ejpam-5434	62	3	let	let	VERB
ejpam-5434	62	4	u	u	PRON
ejpam-5434	62	5	=	=	X
ejpam-5434	62	6	{	{	PUNCT
ejpam-5434	62	7	a	a	PRON
ejpam-5434	62	8	,	,	PUNCT
ejpam-5434	62	9	b	b	NOUN
ejpam-5434	62	10	,	,	PUNCT
ejpam-5434	62	11	c	c	NOUN
ejpam-5434	62	12	,	,	PUNCT
ejpam-5434	62	13	d	d	NOUN
ejpam-5434	62	14	}	}	PUNCT
ejpam-5434	62	15	,	,	PUNCT
ejpam-5434	62	16	u\r	u\r	X
ejpam-5434	62	17	=	=	PRON
ejpam-5434	62	18	{	{	PUNCT
ejpam-5434	62	19	{	{	PUNCT
ejpam-5434	62	20	a	a	X
ejpam-5434	62	21	,	,	PUNCT
ejpam-5434	62	22	c	c	NOUN
ejpam-5434	62	23	}	}	PUNCT
ejpam-5434	62	24	,	,	PUNCT
ejpam-5434	62	25	{	{	PUNCT
ejpam-5434	62	26	b	b	X
ejpam-5434	62	27	,	,	PUNCT
ejpam-5434	62	28	d	d	NOUN
ejpam-5434	62	29	}	}	PUNCT
ejpam-5434	62	30	}	}	PUNCT
ejpam-5434	62	31	,	,	PUNCT
ejpam-5434	62	32	x	x	X
ejpam-5434	62	33	=	=	PRON
ejpam-5434	62	34	{	{	PUNCT
ejpam-5434	62	35	a	a	X
ejpam-5434	62	36	,	,	PUNCT
ejpam-5434	62	37	c	c	NOUN
ejpam-5434	62	38	}	}	PUNCT
ejpam-5434	62	39	,	,	PUNCT
ejpam-5434	62	40	τr(x	τr(x	NUM
ejpam-5434	62	41	)	)	PUNCT
ejpam-5434	63	1	=	=	PRON
ejpam-5434	63	2	{	{	PUNCT
ejpam-5434	63	3	u	u	NOUN
ejpam-5434	63	4	,	,	PUNCT
ejpam-5434	63	5	∅	∅	NOUN
ejpam-5434	63	6	,	,	PUNCT
ejpam-5434	63	7	{	{	PUNCT
ejpam-5434	63	8	a	a	PRON
ejpam-5434	63	9	,	,	PUNCT
ejpam-5434	63	10	c	c	NOUN
ejpam-5434	63	11	}	}	PUNCT
ejpam-5434	63	12	}	}	PUNCT
ejpam-5434	63	13	,	,	PUNCT
ejpam-5434	63	14	µ	µ	X
ejpam-5434	63	15	=	=	SYM
ejpam-5434	63	16	{	{	PUNCT
ejpam-5434	63	17	b	b	NOUN
ejpam-5434	63	18	}	}	PUNCT
ejpam-5434	63	19	and	and	CCONJ
ejpam-5434	63	20	µr(x	µr(x	NUM
ejpam-5434	63	21	)	)	PUNCT
ejpam-5434	63	22	=	=	SYM
ejpam-5434	63	23	{	{	PUNCT
ejpam-5434	63	24	u	u	NOUN
ejpam-5434	63	25	,	,	PUNCT
ejpam-5434	63	26	∅	∅	NOUN
ejpam-5434	63	27	,	,	PUNCT
ejpam-5434	63	28	{	{	PUNCT
ejpam-5434	63	29	b	b	NOUN
ejpam-5434	63	30	}	}	PUNCT
ejpam-5434	63	31	,	,	PUNCT
ejpam-5434	63	32	{	{	PUNCT
ejpam-5434	63	33	a	a	X
ejpam-5434	63	34	,	,	PUNCT
ejpam-5434	63	35	c	c	NOUN
ejpam-5434	63	36	}	}	PUNCT
ejpam-5434	63	37	,	,	PUNCT
ejpam-5434	63	38	{	{	PUNCT
ejpam-5434	63	39	a	a	PRON
ejpam-5434	63	40	,	,	PUNCT
ejpam-5434	63	41	b	b	NOUN
ejpam-5434	63	42	,	,	PUNCT
ejpam-5434	63	43	c	c	NOUN
ejpam-5434	63	44	}	}	PUNCT
ejpam-5434	63	45	}	}	PUNCT
ejpam-5434	63	46	.	.	PUNCT
ejpam-5434	64	1	if	if	SCONJ
ejpam-5434	64	2	a	a	PRON
ejpam-5434	64	3	=	=	X
ejpam-5434	64	4	{	{	PUNCT
ejpam-5434	64	5	b	b	NOUN
ejpam-5434	64	6	,	,	PUNCT
ejpam-5434	64	7	c	c	NOUN
ejpam-5434	64	8	}	}	PUNCT
ejpam-5434	64	9	then	then	ADV
ejpam-5434	64	10	,	,	PUNCT
ejpam-5434	64	11	mic	mic	NOUN
ejpam-5434	64	12	-	-	PUNCT
ejpam-5434	64	13	cl(a	cl(a	NUM
ejpam-5434	64	14	)	)	PUNCT
ejpam-5434	64	15	=	=	SYM
ejpam-5434	64	16	{	{	PUNCT
ejpam-5434	64	17	u	u	NOUN
ejpam-5434	64	18	}	}	PUNCT
ejpam-5434	64	19	and	and	CCONJ
ejpam-5434	64	20	mic	mic	ADJ
ejpam-5434	64	21	-	-	PUNCT
ejpam-5434	64	22	int(a	int(a	NOUN
ejpam-5434	64	23	)	)	PUNCT
ejpam-5434	64	24	=	=	NOUN
ejpam-5434	64	25	{	{	PUNCT
ejpam-5434	64	26	b	b	NOUN
ejpam-5434	64	27	}	}	PUNCT
ejpam-5434	64	28	,	,	PUNCT
ejpam-5434	64	29	mic	mic	ADJ
ejpam-5434	64	30	-	-	PUNCT
ejpam-5434	64	31	pcl(a	pcl(a	NOUN
ejpam-5434	64	32	)	)	PUNCT
ejpam-5434	64	33	=	=	SYM
ejpam-5434	64	34	{	{	PUNCT
ejpam-5434	64	35	b	b	PROPN
ejpam-5434	64	36	,	,	PUNCT
ejpam-5434	64	37	c	c	X
ejpam-5434	64	38	,	,	PUNCT
ejpam-5434	64	39	d	d	NOUN
ejpam-5434	64	40	}	}	PUNCT
ejpam-5434	64	41	and	and	CCONJ
ejpam-5434	64	42	mic	mic	ADJ
ejpam-5434	64	43	-	-	PUNCT
ejpam-5434	64	44	pint(a	pint(a	NOUN
ejpam-5434	64	45	)	)	PUNCT
ejpam-5434	64	46	=	=	PUNCT
ejpam-5434	64	47	{	{	PUNCT
ejpam-5434	64	48	b	b	NOUN
ejpam-5434	64	49	,	,	PUNCT
ejpam-5434	64	50	c	c	NOUN
ejpam-5434	64	51	}	}	PUNCT
ejpam-5434	64	52	,	,	PUNCT
ejpam-5434	64	53	where	where	SCONJ
ejpam-5434	64	54	mic	mic	NOUN
ejpam-5434	64	55	-	-	PUNCT
ejpam-5434	64	56	fr(a	fr(a	NUM
ejpam-5434	64	57	)	)	PUNCT
ejpam-5434	65	1	=	=	PRON
ejpam-5434	65	2	{	{	PUNCT
ejpam-5434	65	3	a	a	X
ejpam-5434	65	4	,	,	PUNCT
ejpam-5434	65	5	c	c	NOUN
ejpam-5434	65	6	,	,	PUNCT
ejpam-5434	65	7	d	d	NOUN
ejpam-5434	65	8	}	}	PUNCT
ejpam-5434	65	9	and	and	CCONJ
ejpam-5434	65	10	mic	mic	ADJ
ejpam-5434	65	11	-	-	PUNCT
ejpam-5434	65	12	pfr(a	pfr(a	NOUN
ejpam-5434	65	13	)	)	PUNCT
ejpam-5434	65	14	=	=	PUNCT
ejpam-5434	65	15	{	{	PUNCT
ejpam-5434	65	16	d	d	NOUN
ejpam-5434	65	17	}	}	PUNCT
ejpam-5434	65	18	.	.	PUNCT
ejpam-5434	66	1	this	this	PRON
ejpam-5434	66	2	shows	show	VERB
ejpam-5434	66	3	that	that	SCONJ
ejpam-5434	66	4	mic	mic	ADJ
ejpam-5434	66	5	-	-	PUNCT
ejpam-5434	66	6	fr(a	fr(a	NUM
ejpam-5434	66	7	)	)	PUNCT
ejpam-5434	66	8	̸⊂	̸⊂	ADV
ejpam-5434	66	9	mic	mic	ADJ
ejpam-5434	66	10	-	-	PUNCT
ejpam-5434	66	11	pfr(a	pfr(a	NOUN
ejpam-5434	66	12	)	)	PUNCT
ejpam-5434	66	13	.	.	PUNCT
ejpam-5434	67	1	lemma	lemma	PROPN
ejpam-5434	67	2	1	1	NUM
ejpam-5434	67	3	.	.	PUNCT
ejpam-5434	68	1	for	for	ADP
ejpam-5434	68	2	a	a	DET
ejpam-5434	68	3	subset	subset	NOUN
ejpam-5434	68	4	a	a	PRON
ejpam-5434	68	5	of	of	ADP
ejpam-5434	68	6	a	a	DET
ejpam-5434	68	7	space	space	NOUN
ejpam-5434	68	8	u	u	NOUN
ejpam-5434	68	9	,	,	PUNCT
ejpam-5434	68	10	(	(	PUNCT
ejpam-5434	68	11	i	i	NOUN
ejpam-5434	68	12	)	)	PUNCT
ejpam-5434	68	13	mic	mic	ADJ
ejpam-5434	68	14	-	-	PUNCT
ejpam-5434	68	15	pa∗	pa∗	NOUN
ejpam-5434	68	16	=	=	SYM
ejpam-5434	68	17	mic	mic	ADJ
ejpam-5434	68	18	-	-	PUNCT
ejpam-5434	68	19	pa∗	pa∗	NOUN
ejpam-5434	68	20	∪	∪	ADJ
ejpam-5434	68	21	mic	mic	NOUN
ejpam-5434	68	22	-	-	PUNCT
ejpam-5434	68	23	pfr(a	pfr(a	NOUN
ejpam-5434	68	24	)	)	PUNCT
ejpam-5434	68	25	.	.	PUNCT
ejpam-5434	69	1	(	(	PUNCT
ejpam-5434	69	2	ii	ii	NOUN
ejpam-5434	69	3	)	)	PUNCT
ejpam-5434	69	4	mic	mic	ADJ
ejpam-5434	69	5	-	-	PUNCT
ejpam-5434	69	6	pa∗	pa∗	NOUN
ejpam-5434	69	7	∩	∩	ADJ
ejpam-5434	69	8	mic	mic	NOUN
ejpam-5434	69	9	-	-	PUNCT
ejpam-5434	69	10	pfr(a	pfr(a	NOUN
ejpam-5434	69	11	)	)	PUNCT
ejpam-5434	69	12	=	=	NOUN
ejpam-5434	69	13	∅	∅	NOUN
ejpam-5434	69	14	and	and	CCONJ
ejpam-5434	69	15	(	(	PUNCT
ejpam-5434	69	16	iii	iii	NOUN
ejpam-5434	69	17	)	)	PUNCT
ejpam-5434	69	18	mic	mic	ADJ
ejpam-5434	69	19	-	-	PUNCT
ejpam-5434	69	20	pfr(a	pfr(a	NOUN
ejpam-5434	69	21	)	)	PUNCT
ejpam-5434	69	22	=	=	SYM
ejpam-5434	69	23	mic	mic	ADJ
ejpam-5434	69	24	-	-	PUNCT
ejpam-5434	69	25	pa∗	pa∗	NOUN
ejpam-5434	69	26	∩	∩	ADJ
ejpam-5434	69	27	mic	mic	ADJ
ejpam-5434	69	28	-	-	PUNCT
ejpam-5434	69	29	p(u	p(u	ADJ
ejpam-5434	69	30	−a)∗.	−a)∗.	PROPN
ejpam-5434	69	31	proof	proof	NOUN
ejpam-5434	69	32	:	:	PUNCT
ejpam-5434	69	33	by	by	ADP
ejpam-5434	69	34	definition	definition	NOUN
ejpam-5434	69	35	of	of	ADP
ejpam-5434	69	36	mic	mic	ADJ
ejpam-5434	69	37	-	-	PUNCT
ejpam-5434	69	38	pfr(a	pfr(a	NOUN
ejpam-5434	69	39	)	)	PUNCT
ejpam-5434	69	40	,	,	PUNCT
ejpam-5434	69	41	we	we	PRON
ejpam-5434	69	42	have	have	AUX
ejpam-5434	69	43	(	(	PUNCT
ejpam-5434	69	44	i	i	NOUN
ejpam-5434	69	45	)	)	PUNCT
ejpam-5434	69	46	mic	mic	ADJ
ejpam-5434	69	47	-	-	PUNCT
ejpam-5434	69	48	pa∗	pa∗	NOUN
ejpam-5434	69	49	∪	∪	ADJ
ejpam-5434	69	50	mic	mic	ADJ
ejpam-5434	69	51	-	-	PUNCT
ejpam-5434	69	52	pfr(a	pfr(a	NOUN
ejpam-5434	69	53	)	)	PUNCT
ejpam-5434	69	54	=	=	SYM
ejpam-5434	69	55	mic	mic	ADJ
ejpam-5434	69	56	-	-	PUNCT
ejpam-5434	69	57	pa∗	pa∗	NOUN
ejpam-5434	69	58	∪	∪	NOUN
ejpam-5434	69	59	(	(	PUNCT
ejpam-5434	69	60	mic	mic	ADJ
ejpam-5434	69	61	-	-	PUNCT
ejpam-5434	69	62	pa∗−	pa∗−	NOUN
ejpam-5434	69	63	mic	mic	ADJ
ejpam-5434	69	64	-	-	PUNCT
ejpam-5434	69	65	pa∗	pa∗	NOUN
ejpam-5434	69	66	)	)	PUNCT
ejpam-5434	69	67	=	=	SYM
ejpam-5434	69	68	mic	mic	ADJ
ejpam-5434	69	69	-	-	PUNCT
ejpam-5434	69	70	pa∗.	pa∗.	NOUN
ejpam-5434	69	71	(	(	PUNCT
ejpam-5434	69	72	ii	ii	NOUN
ejpam-5434	69	73	)	)	PUNCT
ejpam-5434	69	74	mic	mic	ADJ
ejpam-5434	69	75	-	-	PUNCT
ejpam-5434	69	76	pa∗	pa∗	NOUN
ejpam-5434	69	77	∩	∩	ADJ
ejpam-5434	69	78	mic	mic	NOUN
ejpam-5434	69	79	-	-	PUNCT
ejpam-5434	69	80	pfr(a	pfr(a	NOUN
ejpam-5434	69	81	)	)	PUNCT
ejpam-5434	69	82	=	=	SYM
ejpam-5434	69	83	mic	mic	ADJ
ejpam-5434	69	84	-	-	PUNCT
ejpam-5434	69	85	pa∗	pa∗	NOUN
ejpam-5434	69	86	∩	∩	NOUN
ejpam-5434	69	87	(	(	PUNCT
ejpam-5434	69	88	mic	mic	ADJ
ejpam-5434	69	89	-	-	PUNCT
ejpam-5434	69	90	pa∗−	pa∗−	NOUN
ejpam-5434	69	91	mic	mic	ADJ
ejpam-5434	69	92	-	-	PUNCT
ejpam-5434	69	93	pa∗	pa∗	NOUN
ejpam-5434	69	94	)	)	PUNCT
ejpam-5434	70	1	=	=	PUNCT
ejpam-5434	70	2	∅.	∅.	PRON
ejpam-5434	70	3	(	(	PUNCT
ejpam-5434	70	4	iii	iii	NOUN
ejpam-5434	70	5	)	)	PUNCT
ejpam-5434	70	6	mic	mic	ADJ
ejpam-5434	70	7	-	-	PUNCT
ejpam-5434	70	8	pfr(a	pfr(a	NOUN
ejpam-5434	70	9	)	)	PUNCT
ejpam-5434	70	10	=	=	SYM
ejpam-5434	71	1	mic	mic	ADJ
ejpam-5434	71	2	-	-	PUNCT
ejpam-5434	71	3	pa∗−mic	pa∗−mic	ADJ
ejpam-5434	71	4	-	-	PUNCT
ejpam-5434	71	5	pa∗	pa∗	NOUN
ejpam-5434	71	6	=	=	SYM
ejpam-5434	71	7	mic	mic	ADJ
ejpam-5434	71	8	-	-	PUNCT
ejpam-5434	71	9	pa∗	pa∗	NOUN
ejpam-5434	71	10	∩	∩	NOUN
ejpam-5434	71	11	(	(	PUNCT
ejpam-5434	71	12	u−mic	u−mic	ADJ
ejpam-5434	71	13	-	-	PUNCT
ejpam-5434	71	14	pa∗	pa∗	NOUN
ejpam-5434	71	15	)	)	PUNCT
ejpam-5434	72	1	=	=	SYM
ejpam-5434	72	2	mic	mic	ADJ
ejpam-5434	72	3	-	-	PUNCT
ejpam-5434	72	4	pa∗	pa∗	NOUN
ejpam-5434	72	5	∩	∩	NOUN
ejpam-5434	72	6	micp(u	micp(u	ADJ
ejpam-5434	72	7	−a)∗	−a)∗	PROPN
ejpam-5434	72	8	by	by	ADP
ejpam-5434	72	9	lemma	lemma	PROPN
ejpam-5434	72	10	3.8(1	3.8(1	NUM
ejpam-5434	72	11	)	)	PUNCT
ejpam-5434	73	1	[	[	X
ejpam-5434	73	2	7	7	NUM
ejpam-5434	73	3	]	]	PUNCT
ejpam-5434	73	4	.	.	PUNCT
ejpam-5434	74	1	lemma	lemma	PROPN
ejpam-5434	74	2	2	2	NUM
ejpam-5434	74	3	.	.	X
ejpam-5434	74	4	mic	mic	ADJ
ejpam-5434	74	5	-	-	PUNCT
ejpam-5434	74	6	pfr(a	pfr(a	NOUN
ejpam-5434	74	7	)	)	PUNCT
ejpam-5434	74	8	is	be	AUX
ejpam-5434	74	9	micro	micro	ADJ
ejpam-5434	74	10	pre	pre	ADJ
ejpam-5434	74	11	-	-	ADJ
ejpam-5434	74	12	closed	closed	ADJ
ejpam-5434	74	13	.	.	PUNCT
ejpam-5434	75	1	proof	proof	NOUN
ejpam-5434	75	2	:	:	PUNCT
ejpam-5434	75	3	by	by	ADP
ejpam-5434	75	4	lemma	lemma	PROPN
ejpam-5434	75	5	1	1	NUM
ejpam-5434	75	6	,	,	PUNCT
ejpam-5434	75	7	mic	mic	ADJ
ejpam-5434	75	8	-	-	PUNCT
ejpam-5434	75	9	pfr(a	pfr(a	NOUN
ejpam-5434	75	10	)	)	PUNCT
ejpam-5434	75	11	=	=	SYM
ejpam-5434	75	12	mic	mic	ADJ
ejpam-5434	75	13	-	-	PUNCT
ejpam-5434	75	14	pa∗	pa∗	NOUN
ejpam-5434	75	15	∩	∩	ADJ
ejpam-5434	75	16	mic	mic	NOUN
ejpam-5434	75	17	-	-	PUNCT
ejpam-5434	75	18	p(u−a)∗	p(u−a)∗	NOUN
ejpam-5434	75	19	,	,	PUNCT
ejpam-5434	75	20	which	which	PRON
ejpam-5434	75	21	is	be	AUX
ejpam-5434	75	22	micro	micro	ADJ
ejpam-5434	75	23	pre	pre	ADJ
ejpam-5434	75	24	-	-	VERB
ejpam-5434	75	25	closed	closed	ADJ
ejpam-5434	75	26	by	by	ADP
ejpam-5434	75	27	corollary	corollary	ADJ
ejpam-5434	75	28	3.9	3.9	NUM
ejpam-5434	76	1	[	[	X
ejpam-5434	76	2	7	7	NUM
ejpam-5434	76	3	]	]	PUNCT
ejpam-5434	76	4	.	.	PUNCT
ejpam-5434	77	1	s.	s.	PROPN
ejpam-5434	77	2	stanley	stanley	PROPN
ejpam-5434	77	3	roshan	roshan	PROPN
ejpam-5434	77	4	et	et	PROPN
ejpam-5434	77	5	al	al	PROPN
ejpam-5434	77	6	.	.	PUNCT
ejpam-5434	77	7	/	/	SYM
ejpam-5434	77	8	eur	eur	PROPN
ejpam-5434	77	9	.	.	PUNCT
ejpam-5434	78	1	j.	j.	PROPN
ejpam-5434	78	2	pure	pure	PROPN
ejpam-5434	78	3	appl	appl	PROPN
ejpam-5434	78	4	.	.	PROPN
ejpam-5434	78	5	math	math	PROPN
ejpam-5434	78	6	,	,	PUNCT
ejpam-5434	78	7	17	17	NUM
ejpam-5434	78	8	(	(	PUNCT
ejpam-5434	78	9	4	4	NUM
ejpam-5434	78	10	)	)	PUNCT
ejpam-5434	78	11	(	(	PUNCT
ejpam-5434	78	12	2024	2024	NUM
ejpam-5434	78	13	)	)	PUNCT
ejpam-5434	78	14	,	,	PUNCT
ejpam-5434	78	15	3156	3156	NUM
ejpam-5434	78	16	-	-	SYM
ejpam-5434	78	17	3166	3166	NUM
ejpam-5434	78	18	3159	3159	NUM
ejpam-5434	78	19	definition	definition	NOUN
ejpam-5434	78	20	13	13	NUM
ejpam-5434	78	21	.	.	PUNCT
ejpam-5434	79	1	a	a	DET
ejpam-5434	79	2	subset	subset	NOUN
ejpam-5434	79	3	a	a	PRON
ejpam-5434	79	4	⊂	⊂	PROPN
ejpam-5434	79	5	u	u	NOUN
ejpam-5434	79	6	is	be	AUX
ejpam-5434	79	7	called	call	VERB
ejpam-5434	79	8	micro	micro	ADJ
ejpam-5434	79	9	pre	pre	NOUN
ejpam-5434	79	10	-	-	ADJ
ejpam-5434	79	11	regular	regular	ADJ
ejpam-5434	79	12	if	if	SCONJ
ejpam-5434	79	13	it	it	PRON
ejpam-5434	79	14	is	be	AUX
ejpam-5434	79	15	both	both	PRON
ejpam-5434	79	16	micro	micro	ADJ
ejpam-5434	79	17	pre	pre	ADJ
ejpam-5434	79	18	-	-	ADJ
ejpam-5434	79	19	open	open	ADJ
ejpam-5434	79	20	and	and	CCONJ
ejpam-5434	79	21	micro	micro	ADJ
ejpam-5434	79	22	pre	pre	ADJ
ejpam-5434	79	23	-	-	ADJ
ejpam-5434	79	24	closed	closed	ADJ
ejpam-5434	79	25	set	set	NOUN
ejpam-5434	79	26	.	.	PUNCT
ejpam-5434	80	1	the	the	DET
ejpam-5434	80	2	family	family	NOUN
ejpam-5434	80	3	of	of	ADP
ejpam-5434	80	4	all	all	DET
ejpam-5434	80	5	micro	micro	ADJ
ejpam-5434	80	6	pre	pre	ADJ
ejpam-5434	80	7	-	-	ADJ
ejpam-5434	80	8	regular	regular	ADJ
ejpam-5434	80	9	sets	set	NOUN
ejpam-5434	80	10	of	of	ADP
ejpam-5434	80	11	u	u	NOUN
ejpam-5434	80	12	is	be	AUX
ejpam-5434	80	13	denoted	denote	VERB
ejpam-5434	80	14	by	by	ADP
ejpam-5434	80	15	mic	mic	ADJ
ejpam-5434	80	16	-	-	PUNCT
ejpam-5434	80	17	pr(u	pr(u	NUM
ejpam-5434	80	18	)	)	PUNCT
ejpam-5434	80	19	.	.	PUNCT
ejpam-5434	81	1	micro	micro	PROPN
ejpam-5434	81	2	pre	pre	ADJ
ejpam-5434	81	3	-	-	ADJ
ejpam-5434	81	4	closed	closed	ADJ
ejpam-5434	81	5	is	be	AUX
ejpam-5434	81	6	denoted	denote	VERB
ejpam-5434	81	7	by	by	ADP
ejpam-5434	81	8	mic	mic	ADJ
ejpam-5434	81	9	-	-	PUNCT
ejpam-5434	81	10	pf(u	pf(u	NUM
ejpam-5434	81	11	)	)	PUNCT
ejpam-5434	81	12	.	.	PUNCT
ejpam-5434	82	1	theorem	theorem	NOUN
ejpam-5434	82	2	1	1	NUM
ejpam-5434	82	3	.	.	PUNCT
ejpam-5434	82	4	mic	mic	ADJ
ejpam-5434	82	5	-	-	PUNCT
ejpam-5434	82	6	pfr(a	pfr(a	NOUN
ejpam-5434	82	7	)	)	PUNCT
ejpam-5434	82	8	=	=	PUNCT
ejpam-5434	82	9	∅	∅	NOUN
ejpam-5434	82	10	iff	iff	VERB
ejpam-5434	82	11	a	a	DET
ejpam-5434	82	12	∈	∈	PROPN
ejpam-5434	82	13	mic	mic	NOUN
ejpam-5434	82	14	-	-	PUNCT
ejpam-5434	82	15	pr(u	pr(u	NUM
ejpam-5434	82	16	)	)	PUNCT
ejpam-5434	82	17	.	.	PUNCT
ejpam-5434	83	1	proof	proof	NOUN
ejpam-5434	83	2	:	:	PUNCT
ejpam-5434	83	3	let	let	VERB
ejpam-5434	83	4	a	a	DET
ejpam-5434	83	5	∈	∈	ADJ
ejpam-5434	83	6	mic	mic	NOUN
ejpam-5434	83	7	-	-	PUNCT
ejpam-5434	83	8	pr(u	pr(u	NUM
ejpam-5434	83	9	)	)	PUNCT
ejpam-5434	83	10	.	.	PUNCT
ejpam-5434	84	1	then	then	ADV
ejpam-5434	84	2	a	a	DET
ejpam-5434	84	3	∈	∈	NOUN
ejpam-5434	84	4	mic	mic	ADJ
ejpam-5434	84	5	-	-	PUNCT
ejpam-5434	84	6	po(u	po(u	NOUN
ejpam-5434	84	7	)	)	PUNCT
ejpam-5434	84	8	and	and	CCONJ
ejpam-5434	84	9	a	a	DET
ejpam-5434	84	10	∈	∈	NOUN
ejpam-5434	84	11	mic	mic	NOUN
ejpam-5434	84	12	-	-	PUNCT
ejpam-5434	84	13	pf(u	pf(u	NUM
ejpam-5434	84	14	)	)	PUNCT
ejpam-5434	84	15	.	.	PUNCT
ejpam-5434	85	1	now	now	ADV
ejpam-5434	85	2	,	,	PUNCT
ejpam-5434	85	3	using	use	VERB
ejpam-5434	85	4	results	result	NOUN
ejpam-5434	85	5	of	of	ADP
ejpam-5434	85	6	lemma	lemma	PROPN
ejpam-5434	85	7	3.7	3.7	NUM
ejpam-5434	85	8	[	[	X
ejpam-5434	85	9	7	7	NUM
ejpam-5434	85	10	]	]	PUNCT
ejpam-5434	85	11	and	and	CCONJ
ejpam-5434	85	12	theorem	theorem	VERB
ejpam-5434	85	13	3.16	3.16	NUM
ejpam-5434	85	14	[	[	X
ejpam-5434	85	15	7	7	X
ejpam-5434	85	16	]	]	PUNCT
ejpam-5434	85	17	it	it	PRON
ejpam-5434	85	18	follows	follow	VERB
ejpam-5434	85	19	that	that	SCONJ
ejpam-5434	85	20	mic	mic	ADJ
ejpam-5434	85	21	-	-	PUNCT
ejpam-5434	85	22	pfr(a	pfr(a	NOUN
ejpam-5434	85	23	)	)	PUNCT
ejpam-5434	85	24	=	=	NOUN
ejpam-5434	85	25	∅.	∅.	VERB
ejpam-5434	85	26	conversely	conversely	ADV
ejpam-5434	85	27	,	,	PUNCT
ejpam-5434	85	28	let	let	VERB
ejpam-5434	85	29	mic	mic	ADJ
ejpam-5434	85	30	-	-	PUNCT
ejpam-5434	85	31	pfr(a	pfr(a	NOUN
ejpam-5434	85	32	)	)	PUNCT
ejpam-5434	85	33	=	=	PUNCT
ejpam-5434	86	1	∅.	∅.	NOUN
ejpam-5434	86	2	then	then	ADV
ejpam-5434	86	3	we	we	PRON
ejpam-5434	86	4	show	show	VERB
ejpam-5434	86	5	that	that	SCONJ
ejpam-5434	86	6	a	a	DET
ejpam-5434	86	7	∈	∈	ADJ
ejpam-5434	86	8	mic	mic	NOUN
ejpam-5434	86	9	-	-	PUNCT
ejpam-5434	86	10	pr(u	pr(u	NUM
ejpam-5434	86	11	)	)	PUNCT
ejpam-5434	86	12	.	.	PUNCT
ejpam-5434	87	1	since	since	SCONJ
ejpam-5434	87	2	by	by	ADP
ejpam-5434	87	3	hypothesis	hypothesis	NOUN
ejpam-5434	87	4	,	,	PUNCT
ejpam-5434	87	5	mic	mic	ADJ
ejpam-5434	87	6	-	-	PUNCT
ejpam-5434	87	7	pa∗	pa∗	NOUN
ejpam-5434	87	8	−	−	PROPN
ejpam-5434	87	9	mic	mic	ADJ
ejpam-5434	87	10	-	-	PUNCT
ejpam-5434	87	11	pa∗	pa∗	NOUN
ejpam-5434	87	12	=	=	NOUN
ejpam-5434	87	13	∅.	∅.	NOUN
ejpam-5434	87	14	we	we	PRON
ejpam-5434	87	15	have	have	VERB
ejpam-5434	87	16	mic	mic	ADJ
ejpam-5434	87	17	-	-	PUNCT
ejpam-5434	87	18	pa∗	pa∗	NOUN
ejpam-5434	87	19	=	=	SYM
ejpam-5434	87	20	mic	mic	ADJ
ejpam-5434	87	21	-	-	PUNCT
ejpam-5434	87	22	pa∗.	pa∗.	NOUN
ejpam-5434	87	23	but	but	CCONJ
ejpam-5434	87	24	,	,	PUNCT
ejpam-5434	87	25	mic	mic	ADJ
ejpam-5434	87	26	-	-	PUNCT
ejpam-5434	87	27	pa∗	pa∗	NOUN
ejpam-5434	87	28	⊂	⊂	PROPN
ejpam-5434	87	29	a	a	DET
ejpam-5434	87	30	⊂	⊂	X
ejpam-5434	87	31	mic	mic	ADJ
ejpam-5434	87	32	-	-	PUNCT
ejpam-5434	87	33	pa∗.	pa∗.	NOUN
ejpam-5434	87	34	therefore	therefore	ADV
ejpam-5434	87	35	,	,	PUNCT
ejpam-5434	87	36	it	it	PRON
ejpam-5434	87	37	follows	follow	VERB
ejpam-5434	87	38	that	that	SCONJ
ejpam-5434	87	39	a	a	DET
ejpam-5434	87	40	=	=	PUNCT
ejpam-5434	87	41	mic	mic	ADJ
ejpam-5434	87	42	-	-	PUNCT
ejpam-5434	87	43	pa∗	pa∗	NOUN
ejpam-5434	87	44	=	=	SYM
ejpam-5434	87	45	mic	mic	ADJ
ejpam-5434	87	46	-	-	PUNCT
ejpam-5434	87	47	pa∗	pa∗	NOUN
ejpam-5434	87	48	which	which	PRON
ejpam-5434	87	49	means	mean	VERB
ejpam-5434	87	50	a	a	DET
ejpam-5434	87	51	∈	∈	ADJ
ejpam-5434	87	52	mic	mic	NOUN
ejpam-5434	87	53	-	-	PUNCT
ejpam-5434	87	54	pr(u	pr(u	NUM
ejpam-5434	87	55	)	)	PUNCT
ejpam-5434	87	56	.	.	PUNCT
ejpam-5434	88	1	theorem	theorem	NOUN
ejpam-5434	88	2	2	2	NUM
ejpam-5434	88	3	.	.	PUNCT
ejpam-5434	88	4	let	let	VERB
ejpam-5434	88	5	a	a	DET
ejpam-5434	88	6	be	be	AUX
ejpam-5434	88	7	subset	subset	VERB
ejpam-5434	88	8	of	of	ADP
ejpam-5434	88	9	u.	u.	NOUN
ejpam-5434	88	10	then	then	ADV
ejpam-5434	88	11	,	,	PUNCT
ejpam-5434	88	12	the	the	DET
ejpam-5434	88	13	following	follow	VERB
ejpam-5434	88	14	holds	hold	VERB
ejpam-5434	88	15	.	.	PUNCT
ejpam-5434	89	1	(	(	PUNCT
ejpam-5434	89	2	i	i	NOUN
ejpam-5434	89	3	)	)	PUNCT
ejpam-5434	89	4	mic	mic	ADJ
ejpam-5434	89	5	-	-	PUNCT
ejpam-5434	89	6	pfr(a	pfr(a	NOUN
ejpam-5434	89	7	)	)	PUNCT
ejpam-5434	89	8	=	=	SYM
ejpam-5434	89	9	mic	mic	ADJ
ejpam-5434	89	10	-	-	PUNCT
ejpam-5434	89	11	pfr(u	pfr(u	NOUN
ejpam-5434	89	12	−a	−a	NOUN
ejpam-5434	89	13	)	)	PUNCT
ejpam-5434	89	14	.	.	PUNCT
ejpam-5434	90	1	(	(	PUNCT
ejpam-5434	90	2	ii	ii	NOUN
ejpam-5434	90	3	)	)	PUNCT
ejpam-5434	90	4	a	a	DET
ejpam-5434	90	5	∈	∈	NOUN
ejpam-5434	90	6	mic	mic	ADJ
ejpam-5434	90	7	-	-	PUNCT
ejpam-5434	90	8	po(u	po(u	ADJ
ejpam-5434	90	9	)	)	PUNCT
ejpam-5434	90	10	iff	iff	PROPN
ejpam-5434	90	11	mic	mic	PROPN
ejpam-5434	90	12	-	-	PUNCT
ejpam-5434	90	13	pfr(a	pfr(a	NOUN
ejpam-5434	90	14	)	)	PUNCT
ejpam-5434	90	15	⊆	⊆	NUM
ejpam-5434	90	16	u	u	NOUN
ejpam-5434	90	17	−a	−a	NOUN
ejpam-5434	90	18	.	.	PUNCT
ejpam-5434	91	1	i.e.	i.e.	X
ejpam-5434	91	2	,	,	PUNCT
ejpam-5434	91	3	a	a	DET
ejpam-5434	91	4	∩	∩	ADJ
ejpam-5434	91	5	mic	mic	NOUN
ejpam-5434	91	6	-	-	PUNCT
ejpam-5434	91	7	pfr(a	pfr(a	NOUN
ejpam-5434	91	8	)	)	PUNCT
ejpam-5434	91	9	=	=	PUNCT
ejpam-5434	91	10	∅.	∅.	PRON
ejpam-5434	91	11	(	(	PUNCT
ejpam-5434	91	12	iii	iii	NOUN
ejpam-5434	91	13	)	)	PUNCT
ejpam-5434	91	14	a	a	DET
ejpam-5434	91	15	∈	∈	NOUN
ejpam-5434	91	16	mic	mic	NOUN
ejpam-5434	91	17	-	-	PUNCT
ejpam-5434	91	18	pf(u	pf(u	NUM
ejpam-5434	91	19	)	)	PUNCT
ejpam-5434	91	20	iff	iff	PROPN
ejpam-5434	91	21	mic	mic	PROPN
ejpam-5434	91	22	-	-	PUNCT
ejpam-5434	91	23	pfr(a	pfr(a	NOUN
ejpam-5434	91	24	)	)	PUNCT
ejpam-5434	91	25	⊆	⊆	NUM
ejpam-5434	91	26	a.	a.	NOUN
ejpam-5434	91	27	proof	proof	NOUN
ejpam-5434	91	28	:	:	PUNCT
ejpam-5434	91	29	(	(	PUNCT
ejpam-5434	91	30	i	i	NOUN
ejpam-5434	91	31	)	)	PUNCT
ejpam-5434	91	32	we	we	PRON
ejpam-5434	91	33	have	have	VERB
ejpam-5434	91	34	,	,	PUNCT
ejpam-5434	91	35	mic	mic	ADJ
ejpam-5434	91	36	-	-	PUNCT
ejpam-5434	91	37	pfr(u	pfr(u	NOUN
ejpam-5434	91	38	−a	−a	NOUN
ejpam-5434	91	39	)	)	PUNCT
ejpam-5434	91	40	=	=	PUNCT
ejpam-5434	91	41	(	(	PUNCT
ejpam-5434	91	42	u−mic	u−mic	ADJ
ejpam-5434	91	43	-	-	PUNCT
ejpam-5434	91	44	pa)∗	pa)∗	PROPN
ejpam-5434	91	45	∩	∩	NOUN
ejpam-5434	91	46	(	(	PUNCT
ejpam-5434	91	47	u	u	NOUN
ejpam-5434	91	48	−	−	PROPN
ejpam-5434	91	49	(	(	PUNCT
ejpam-5434	91	50	u−mic	u−mic	ADJ
ejpam-5434	91	51	-	-	PUNCT
ejpam-5434	91	52	pa))∗	pa))∗	NOUN
ejpam-5434	91	53	=	=	NOUN
ejpam-5434	91	54	(	(	PUNCT
ejpam-5434	91	55	u−mic	u−mic	ADJ
ejpam-5434	91	56	-	-	PUNCT
ejpam-5434	91	57	pa)∗	pa)∗	PROPN
ejpam-5434	91	58	∩	∩	ADJ
ejpam-5434	91	59	mic	mic	ADJ
ejpam-5434	91	60	-	-	PUNCT
ejpam-5434	91	61	pa∗	pa∗	NOUN
ejpam-5434	91	62	=	=	SYM
ejpam-5434	91	63	mic	mic	ADJ
ejpam-5434	91	64	-	-	PUNCT
ejpam-5434	91	65	pfr(a	pfr(a	NOUN
ejpam-5434	91	66	)	)	PUNCT
ejpam-5434	91	67	by	by	ADP
ejpam-5434	91	68	lemma	lemma	PROPN
ejpam-5434	91	69	1(3	1(3	NUM
ejpam-5434	91	70	)	)	PUNCT
ejpam-5434	91	71	.	.	PUNCT
ejpam-5434	92	1	(	(	PUNCT
ejpam-5434	92	2	ii	ii	NOUN
ejpam-5434	92	3	)	)	PUNCT
ejpam-5434	92	4	assume	assume	VERB
ejpam-5434	92	5	a	a	DET
ejpam-5434	92	6	∈	∈	NOUN
ejpam-5434	92	7	mic	mic	NOUN
ejpam-5434	92	8	-	-	PUNCT
ejpam-5434	92	9	po(u	po(u	ADJ
ejpam-5434	92	10	)	)	PUNCT
ejpam-5434	92	11	.	.	PUNCT
ejpam-5434	93	1	by	by	ADP
ejpam-5434	93	2	definition	definition	NOUN
ejpam-5434	93	3	,	,	PUNCT
ejpam-5434	93	4	we	we	PRON
ejpam-5434	93	5	have	have	VERB
ejpam-5434	93	6	mic	mic	ADJ
ejpam-5434	93	7	-	-	PUNCT
ejpam-5434	93	8	pfr(a	pfr(a	NOUN
ejpam-5434	93	9	)	)	PUNCT
ejpam-5434	93	10	=	=	SYM
ejpam-5434	93	11	mic	mic	ADJ
ejpam-5434	93	12	-	-	PUNCT
ejpam-5434	93	13	pa∗−mic	pa∗−mic	ADJ
ejpam-5434	93	14	-	-	PUNCT
ejpam-5434	93	15	pa∗	pa∗	NOUN
ejpam-5434	93	16	=	=	SYM
ejpam-5434	93	17	mic	mic	ADJ
ejpam-5434	93	18	-	-	PUNCT
ejpam-5434	93	19	pa∗	pa∗	NOUN
ejpam-5434	93	20	−	−	PROPN
ejpam-5434	93	21	a.	a.	NOUN
ejpam-5434	93	22	since	since	SCONJ
ejpam-5434	93	23	a	a	DET
ejpam-5434	93	24	∈	∈	NOUN
ejpam-5434	93	25	mic	mic	NOUN
ejpam-5434	93	26	-	-	PUNCT
ejpam-5434	93	27	po(u	po(u	ADJ
ejpam-5434	93	28	)	)	PUNCT
ejpam-5434	93	29	.	.	PUNCT
ejpam-5434	94	1	then	then	ADV
ejpam-5434	94	2	,	,	PUNCT
ejpam-5434	94	3	a	a	DET
ejpam-5434	94	4	∩	∩	ADJ
ejpam-5434	94	5	mic	mic	NOUN
ejpam-5434	94	6	-	-	PUNCT
ejpam-5434	94	7	pfr(a	pfr(a	NOUN
ejpam-5434	94	8	)	)	PUNCT
ejpam-5434	94	9	=	=	SYM
ejpam-5434	95	1	a	a	DET
ejpam-5434	95	2	∩	∩	NOUN
ejpam-5434	95	3	(	(	PUNCT
ejpam-5434	95	4	micpa∗	micpa∗	VERB
ejpam-5434	95	5	−	−	PROPN
ejpam-5434	95	6	a	a	X
ejpam-5434	95	7	)	)	PUNCT
ejpam-5434	95	8	=	=	SYM
ejpam-5434	95	9	mic	mic	ADJ
ejpam-5434	95	10	-	-	PUNCT
ejpam-5434	95	11	pa∗	pa∗	NOUN
ejpam-5434	95	12	∩	∩	NOUN
ejpam-5434	95	13	(	(	PUNCT
ejpam-5434	95	14	u	u	NOUN
ejpam-5434	95	15	−	−	PROPN
ejpam-5434	95	16	a	a	X
ejpam-5434	95	17	)	)	PUNCT
ejpam-5434	95	18	∩	∩	NOUN
ejpam-5434	95	19	a	a	DET
ejpam-5434	95	20	=	=	PUNCT
ejpam-5434	95	21	∅.	∅.	VERB
ejpam-5434	95	22	conversely	conversely	ADV
ejpam-5434	95	23	,	,	PUNCT
ejpam-5434	95	24	if	if	SCONJ
ejpam-5434	95	25	a	a	DET
ejpam-5434	95	26	∩	∩	ADJ
ejpam-5434	95	27	mic	mic	NOUN
ejpam-5434	95	28	-	-	PUNCT
ejpam-5434	95	29	pfr(a	pfr(a	NOUN
ejpam-5434	95	30	)	)	PUNCT
ejpam-5434	95	31	=	=	PUNCT
ejpam-5434	95	32	∅.	∅.	NOUN
ejpam-5434	95	33	then	then	ADV
ejpam-5434	95	34	,	,	PUNCT
ejpam-5434	95	35	a	a	DET
ejpam-5434	95	36	∩	∩	ADJ
ejpam-5434	95	37	mic	mic	ADJ
ejpam-5434	95	38	-	-	PUNCT
ejpam-5434	95	39	pa∗	pa∗	NOUN
ejpam-5434	95	40	∩	∩	NOUN
ejpam-5434	95	41	(	(	PUNCT
ejpam-5434	95	42	u−mic	u−mic	ADJ
ejpam-5434	95	43	-	-	PUNCT
ejpam-5434	95	44	pa∗	pa∗	NOUN
ejpam-5434	95	45	)	)	PUNCT
ejpam-5434	96	1	=	=	NOUN
ejpam-5434	96	2	∅	∅	NOUN
ejpam-5434	96	3	implies	imply	VERB
ejpam-5434	96	4	a	a	DET
ejpam-5434	96	5	∩	∩	NOUN
ejpam-5434	96	6	(	(	PUNCT
ejpam-5434	96	7	u	u	NOUN
ejpam-5434	96	8	−	−	PROPN
ejpam-5434	96	9	mic	mic	ADJ
ejpam-5434	96	10	-	-	PUNCT
ejpam-5434	96	11	pa∗	pa∗	NOUN
ejpam-5434	96	12	)	)	PUNCT
ejpam-5434	97	1	=	=	NOUN
ejpam-5434	97	2	∅	∅	NOUN
ejpam-5434	97	3	as	as	ADP
ejpam-5434	97	4	a	a	DET
ejpam-5434	97	5	⊂	⊂	X
ejpam-5434	97	6	u	u	NOUN
ejpam-5434	97	7	−	−	PROPN
ejpam-5434	97	8	(	(	PUNCT
ejpam-5434	97	9	u−mic	u−mic	ADJ
ejpam-5434	97	10	-	-	PUNCT
ejpam-5434	97	11	pa∗	pa∗	NOUN
ejpam-5434	97	12	)	)	PUNCT
ejpam-5434	97	13	=	=	SYM
ejpam-5434	97	14	mic	mic	ADJ
ejpam-5434	97	15	-	-	PUNCT
ejpam-5434	97	16	pa∗	pa∗	NOUN
ejpam-5434	97	17	,	,	PUNCT
ejpam-5434	97	18	but	but	CCONJ
ejpam-5434	97	19	on	on	ADP
ejpam-5434	97	20	the	the	DET
ejpam-5434	97	21	other	other	ADJ
ejpam-5434	97	22	hand	hand	NOUN
ejpam-5434	97	23	mic	mic	ADJ
ejpam-5434	97	24	-	-	PUNCT
ejpam-5434	97	25	pa∗	pa∗	NOUN
ejpam-5434	97	26	⊂	⊂	NOUN
ejpam-5434	97	27	a.	a.	NOUN
ejpam-5434	98	1	it	it	PRON
ejpam-5434	98	2	follows	follow	VERB
ejpam-5434	98	3	that	that	SCONJ
ejpam-5434	98	4	a	a	DET
ejpam-5434	98	5	=	=	PUNCT
ejpam-5434	98	6	mic	mic	ADJ
ejpam-5434	98	7	-	-	PUNCT
ejpam-5434	98	8	pa∗	pa∗	NOUN
ejpam-5434	98	9	,	,	PUNCT
ejpam-5434	98	10	which	which	PRON
ejpam-5434	98	11	implies	imply	VERB
ejpam-5434	98	12	a	a	DET
ejpam-5434	98	13	∈	∈	ADJ
ejpam-5434	98	14	mic	mic	ADJ
ejpam-5434	98	15	-	-	PUNCT
ejpam-5434	98	16	po(u	po(u	ADJ
ejpam-5434	98	17	)	)	PUNCT
ejpam-5434	98	18	.	.	PUNCT
ejpam-5434	99	1	(	(	PUNCT
ejpam-5434	99	2	iii	iii	X
ejpam-5434	99	3	)	)	PUNCT
ejpam-5434	99	4	assume	assume	VERB
ejpam-5434	99	5	a	a	DET
ejpam-5434	99	6	∈	∈	NOUN
ejpam-5434	99	7	mic	mic	NOUN
ejpam-5434	99	8	-	-	PUNCT
ejpam-5434	99	9	pf(u	pf(u	NUM
ejpam-5434	99	10	)	)	PUNCT
ejpam-5434	99	11	.	.	PUNCT
ejpam-5434	100	1	then	then	ADV
ejpam-5434	100	2	,	,	PUNCT
ejpam-5434	100	3	we	we	PRON
ejpam-5434	100	4	have	have	VERB
ejpam-5434	100	5	u	u	NOUN
ejpam-5434	100	6	−	−	PROPN
ejpam-5434	100	7	a	a	DET
ejpam-5434	100	8	∈	∈	NOUN
ejpam-5434	100	9	mic	mic	NOUN
ejpam-5434	100	10	-	-	PUNCT
ejpam-5434	100	11	po(u	po(u	ADJ
ejpam-5434	100	12	)	)	PUNCT
ejpam-5434	100	13	.	.	PUNCT
ejpam-5434	101	1	then	then	ADV
ejpam-5434	101	2	by	by	ADP
ejpam-5434	101	3	(	(	PUNCT
ejpam-5434	101	4	2	2	NUM
ejpam-5434	101	5	)	)	PUNCT
ejpam-5434	101	6	,	,	PUNCT
ejpam-5434	101	7	micpfr(u	micpfr(u	PROPN
ejpam-5434	101	8	−	−	PROPN
ejpam-5434	101	9	a	a	PRON
ejpam-5434	101	10	)	)	PUNCT
ejpam-5434	101	11	∩	∩	NOUN
ejpam-5434	101	12	(	(	PUNCT
ejpam-5434	101	13	u	u	NOUN
ejpam-5434	101	14	−	−	PROPN
ejpam-5434	101	15	a	a	NOUN
ejpam-5434	101	16	)	)	PUNCT
ejpam-5434	101	17	=	=	PUNCT
ejpam-5434	101	18	∅.	∅.	NOUN
ejpam-5434	101	19	but	but	CCONJ
ejpam-5434	101	20	,	,	PUNCT
ejpam-5434	101	21	by	by	ADP
ejpam-5434	101	22	(	(	PUNCT
ejpam-5434	101	23	1	1	NUM
ejpam-5434	101	24	)	)	PUNCT
ejpam-5434	101	25	,	,	PUNCT
ejpam-5434	101	26	mic	mic	ADJ
ejpam-5434	101	27	-	-	PUNCT
ejpam-5434	101	28	pfr	pfr	NOUN
ejpam-5434	101	29	(	(	PUNCT
ejpam-5434	101	30	u	u	NOUN
ejpam-5434	101	31	−	−	PROPN
ejpam-5434	101	32	a	a	NOUN
ejpam-5434	101	33	)	)	PUNCT
ejpam-5434	101	34	=	=	SYM
ejpam-5434	101	35	mic	mic	ADJ
ejpam-5434	101	36	-	-	PUNCT
ejpam-5434	101	37	pfr(a	pfr(a	NOUN
ejpam-5434	101	38	)	)	PUNCT
ejpam-5434	101	39	.	.	PUNCT
ejpam-5434	102	1	hence	hence	ADV
ejpam-5434	102	2	mic	mic	ADV
ejpam-5434	102	3	-	-	PUNCT
ejpam-5434	102	4	pfr(a	pfr(a	NOUN
ejpam-5434	102	5	)	)	PUNCT
ejpam-5434	102	6	∩	∩	NOUN
ejpam-5434	102	7	(	(	PUNCT
ejpam-5434	102	8	u	u	NOUN
ejpam-5434	102	9	−	−	PROPN
ejpam-5434	102	10	a	a	NOUN
ejpam-5434	102	11	)	)	PUNCT
ejpam-5434	102	12	=	=	PUNCT
ejpam-5434	102	13	∅.	∅.	ADP
ejpam-5434	102	14	this	this	PRON
ejpam-5434	102	15	shows	show	VERB
ejpam-5434	102	16	that	that	SCONJ
ejpam-5434	102	17	mic	mic	ADJ
ejpam-5434	102	18	-	-	PUNCT
ejpam-5434	102	19	pfr(a	pfr(a	NOUN
ejpam-5434	102	20	)	)	PUNCT
ejpam-5434	102	21	⊂	⊂	PROPN
ejpam-5434	102	22	a.	a.	NOUN
ejpam-5434	102	23	conversely	conversely	ADV
ejpam-5434	102	24	,	,	PUNCT
ejpam-5434	102	25	if	if	SCONJ
ejpam-5434	102	26	micpfr(a	micpfr(a	NUM
ejpam-5434	102	27	)	)	PUNCT
ejpam-5434	102	28	⊂	⊂	PROPN
ejpam-5434	102	29	a	a	DET
ejpam-5434	102	30	,	,	PUNCT
ejpam-5434	102	31	then	then	ADV
ejpam-5434	102	32	mic	mic	ADJ
ejpam-5434	102	33	-	-	PUNCT
ejpam-5434	102	34	pa∗	pa∗	NOUN
ejpam-5434	102	35	−	−	PROPN
ejpam-5434	102	36	mic	mic	ADJ
ejpam-5434	102	37	-	-	PUNCT
ejpam-5434	102	38	pa∗	pa∗	NOUN
ejpam-5434	102	39	⊂	⊂	PROPN
ejpam-5434	102	40	a	a	X
ejpam-5434	102	41	,	,	PUNCT
ejpam-5434	102	42	which	which	PRON
ejpam-5434	102	43	implies	imply	VERB
ejpam-5434	102	44	mic	mic	ADJ
ejpam-5434	102	45	-	-	PUNCT
ejpam-5434	102	46	pa∗	pa∗	NOUN
ejpam-5434	102	47	∪	∪	NOUN
ejpam-5434	102	48	(	(	PUNCT
ejpam-5434	102	49	mic	mic	ADJ
ejpam-5434	102	50	-	-	PUNCT
ejpam-5434	102	51	pa∗	pa∗	NOUN
ejpam-5434	102	52	−	−	PROPN
ejpam-5434	102	53	mic	mic	ADJ
ejpam-5434	102	54	-	-	PUNCT
ejpam-5434	102	55	pa∗	pa∗	NOUN
ejpam-5434	102	56	)	)	PUNCT
ejpam-5434	103	1	⊂	⊂	PROPN
ejpam-5434	103	2	a	a	DET
ejpam-5434	103	3	∪	∪	ADJ
ejpam-5434	103	4	mic	mic	ADJ
ejpam-5434	103	5	-	-	PUNCT
ejpam-5434	103	6	pa∗	pa∗	NOUN
ejpam-5434	103	7	=	=	SYM
ejpam-5434	103	8	a	a	NOUN
ejpam-5434	103	9	,	,	PUNCT
ejpam-5434	103	10	which	which	PRON
ejpam-5434	103	11	implies	imply	VERB
ejpam-5434	103	12	mic	mic	ADJ
ejpam-5434	103	13	-	-	PUNCT
ejpam-5434	103	14	pa∗	pa∗	NOUN
ejpam-5434	103	15	⊂	⊂	PROPN
ejpam-5434	103	16	a	a	X
ejpam-5434	103	17	by	by	ADP
ejpam-5434	103	18	lemma	lemma	PROPN
ejpam-5434	103	19	1(1	1(1	NUM
ejpam-5434	103	20	)	)	PUNCT
ejpam-5434	103	21	.	.	PUNCT
ejpam-5434	104	1	but	but	CCONJ
ejpam-5434	104	2	a	a	DET
ejpam-5434	104	3	⊂	⊂	PROPN
ejpam-5434	104	4	mic	mic	ADJ
ejpam-5434	104	5	-	-	PUNCT
ejpam-5434	104	6	pa∗.	pa∗.	NOUN
ejpam-5434	104	7	it	it	PRON
ejpam-5434	104	8	follows	follow	VERB
ejpam-5434	104	9	that	that	SCONJ
ejpam-5434	104	10	a	a	DET
ejpam-5434	104	11	=	=	PUNCT
ejpam-5434	104	12	mic	mic	ADJ
ejpam-5434	104	13	-	-	PUNCT
ejpam-5434	104	14	pa∗.	pa∗.	NOUN
ejpam-5434	104	15	hence	hence	ADV
ejpam-5434	104	16	a	a	DET
ejpam-5434	104	17	∈	∈	NOUN
ejpam-5434	104	18	mic	mic	NOUN
ejpam-5434	104	19	-	-	PUNCT
ejpam-5434	104	20	pf(u	pf(u	NUM
ejpam-5434	104	21	)	)	PUNCT
ejpam-5434	104	22	.	.	PUNCT
ejpam-5434	105	1	remark	remark	PROPN
ejpam-5434	105	2	1	1	NUM
ejpam-5434	105	3	.	.	PUNCT
ejpam-5434	106	1	let	let	VERB
ejpam-5434	106	2	a	a	PRON
ejpam-5434	106	3	and	and	CCONJ
ejpam-5434	106	4	b	b	NOUN
ejpam-5434	106	5	be	be	AUX
ejpam-5434	106	6	subsets	subset	NOUN
ejpam-5434	106	7	of	of	ADP
ejpam-5434	106	8	space	space	NOUN
ejpam-5434	107	1	u.	u.	PROPN
ejpam-5434	107	2	then	then	ADV
ejpam-5434	107	3	a	a	DET
ejpam-5434	107	4	⊂	⊂	PROPN
ejpam-5434	107	5	b	b	NOUN
ejpam-5434	107	6	does	do	AUX
ejpam-5434	107	7	not	not	PART
ejpam-5434	107	8	imply	imply	VERB
ejpam-5434	107	9	that	that	SCONJ
ejpam-5434	107	10	either	either	DET
ejpam-5434	107	11	micpfr(a	micpfr(a	NOUN
ejpam-5434	107	12	)	)	PUNCT
ejpam-5434	108	1	⊂	⊂	PROPN
ejpam-5434	108	2	mic	mic	ADJ
ejpam-5434	108	3	-	-	PUNCT
ejpam-5434	108	4	pfr(b	pfr(b	PROPN
ejpam-5434	108	5	)	)	PUNCT
ejpam-5434	108	6	or	or	CCONJ
ejpam-5434	108	7	mic	mic	ADJ
ejpam-5434	108	8	-	-	PUNCT
ejpam-5434	108	9	pfr(b	pfr(b	PROPN
ejpam-5434	108	10	)	)	PUNCT
ejpam-5434	109	1	⊂	⊂	PROPN
ejpam-5434	109	2	mic	mic	ADJ
ejpam-5434	109	3	-	-	PUNCT
ejpam-5434	109	4	pfr(a	pfr(a	NOUN
ejpam-5434	109	5	)	)	PUNCT
ejpam-5434	109	6	.	.	PUNCT
ejpam-5434	110	1	this	this	PRON
ejpam-5434	110	2	can	can	AUX
ejpam-5434	110	3	be	be	AUX
ejpam-5434	110	4	verified	verify	VERB
ejpam-5434	110	5	by	by	ADP
ejpam-5434	110	6	the	the	DET
ejpam-5434	110	7	following	following	NOUN
ejpam-5434	110	8	.	.	PUNCT
ejpam-5434	111	1	example	example	NOUN
ejpam-5434	112	1	2	2	NUM
ejpam-5434	112	2	.	.	PUNCT
ejpam-5434	112	3	let	let	VERB
ejpam-5434	112	4	u	u	PRON
ejpam-5434	112	5	=	=	X
ejpam-5434	112	6	{	{	PUNCT
ejpam-5434	112	7	a	a	PRON
ejpam-5434	112	8	,	,	PUNCT
ejpam-5434	112	9	b	b	NOUN
ejpam-5434	112	10	,	,	PUNCT
ejpam-5434	112	11	c	c	X
ejpam-5434	112	12	,	,	PUNCT
ejpam-5434	112	13	d	d	NOUN
ejpam-5434	112	14	}	}	PUNCT
ejpam-5434	112	15	,	,	PUNCT
ejpam-5434	112	16	u	u	NOUN
ejpam-5434	112	17	/	/	SYM
ejpam-5434	112	18	r	r	NOUN
ejpam-5434	112	19	=	=	PUNCT
ejpam-5434	112	20	{	{	PUNCT
ejpam-5434	112	21	{	{	PUNCT
ejpam-5434	112	22	a	a	PROPN
ejpam-5434	112	23	,	,	PUNCT
ejpam-5434	112	24	b	b	NOUN
ejpam-5434	112	25	}	}	PUNCT
ejpam-5434	112	26	,	,	PUNCT
ejpam-5434	112	27	{	{	PUNCT
ejpam-5434	112	28	c	c	X
ejpam-5434	112	29	,	,	PUNCT
ejpam-5434	112	30	d	d	NOUN
ejpam-5434	112	31	}	}	PUNCT
ejpam-5434	112	32	}	}	PUNCT
ejpam-5434	112	33	,	,	PUNCT
ejpam-5434	112	34	x	x	X
ejpam-5434	112	35	=	=	PRON
ejpam-5434	112	36	{	{	PUNCT
ejpam-5434	112	37	b	b	NOUN
ejpam-5434	112	38	,	,	PUNCT
ejpam-5434	112	39	c	c	NOUN
ejpam-5434	112	40	}	}	PUNCT
ejpam-5434	112	41	,	,	PUNCT
ejpam-5434	112	42	τr(x	τr(x	NUM
ejpam-5434	112	43	)	)	PUNCT
ejpam-5434	113	1	=	=	PRON
ejpam-5434	113	2	{	{	PUNCT
ejpam-5434	113	3	u	u	NOUN
ejpam-5434	113	4	,	,	PUNCT
ejpam-5434	113	5	∅	∅	NOUN
ejpam-5434	113	6	,	,	PUNCT
ejpam-5434	113	7	{	{	PUNCT
ejpam-5434	113	8	b	b	NOUN
ejpam-5434	113	9	,	,	PUNCT
ejpam-5434	113	10	c	c	NOUN
ejpam-5434	113	11	}	}	PUNCT
ejpam-5434	113	12	}	}	PUNCT
ejpam-5434	113	13	,	,	PUNCT
ejpam-5434	113	14	µ	µ	X
ejpam-5434	113	15	=	=	SYM
ejpam-5434	113	16	b	b	PROPN
ejpam-5434	113	17	and	and	CCONJ
ejpam-5434	113	18	µr(x	µr(x	NUM
ejpam-5434	113	19	)	)	PUNCT
ejpam-5434	114	1	=	=	SYM
ejpam-5434	114	2	{	{	PUNCT
ejpam-5434	114	3	u	u	NOUN
ejpam-5434	114	4	,	,	PUNCT
ejpam-5434	114	5	∅	∅	NOUN
ejpam-5434	114	6	,	,	PUNCT
ejpam-5434	114	7	{	{	PUNCT
ejpam-5434	114	8	b	b	NOUN
ejpam-5434	114	9	}	}	PUNCT
ejpam-5434	114	10	,	,	PUNCT
ejpam-5434	114	11	{	{	PUNCT
ejpam-5434	114	12	b	b	X
ejpam-5434	114	13	,	,	PUNCT
ejpam-5434	114	14	c	c	NOUN
ejpam-5434	114	15	}	}	PUNCT
ejpam-5434	114	16	}	}	PUNCT
ejpam-5434	114	17	.	.	PUNCT
ejpam-5434	115	1	mic	mic	ADJ
ejpam-5434	115	2	-	-	PUNCT
ejpam-5434	115	3	po(u	po(u	ADJ
ejpam-5434	115	4	)	)	PUNCT
ejpam-5434	115	5	=	=	PRON
ejpam-5434	115	6	{	{	PUNCT
ejpam-5434	115	7	u	u	NOUN
ejpam-5434	115	8	,	,	PUNCT
ejpam-5434	115	9	∅	∅	NOUN
ejpam-5434	115	10	,	,	PUNCT
ejpam-5434	115	11	{	{	PUNCT
ejpam-5434	115	12	b	b	NOUN
ejpam-5434	115	13	}	}	PUNCT
ejpam-5434	115	14	,	,	PUNCT
ejpam-5434	115	15	{	{	PUNCT
ejpam-5434	115	16	a	a	DET
ejpam-5434	115	17	,	,	PUNCT
ejpam-5434	115	18	b	b	NOUN
ejpam-5434	115	19	}	}	PUNCT
ejpam-5434	115	20	,	,	PUNCT
ejpam-5434	115	21	{	{	PUNCT
ejpam-5434	115	22	b	b	X
ejpam-5434	115	23	,	,	PUNCT
ejpam-5434	115	24	c	c	NOUN
ejpam-5434	115	25	}	}	PUNCT
ejpam-5434	115	26	,	,	PUNCT
ejpam-5434	115	27	{	{	PUNCT
ejpam-5434	115	28	b	b	X
ejpam-5434	115	29	,	,	PUNCT
ejpam-5434	115	30	d	d	NOUN
ejpam-5434	115	31	}	}	PUNCT
ejpam-5434	115	32	,	,	PUNCT
ejpam-5434	115	33	{	{	PUNCT
ejpam-5434	115	34	a	a	DET
ejpam-5434	115	35	,	,	PUNCT
ejpam-5434	115	36	b	b	NOUN
ejpam-5434	115	37	,	,	PUNCT
ejpam-5434	115	38	c	c	NOUN
ejpam-5434	115	39	}	}	PUNCT
ejpam-5434	115	40	,	,	PUNCT
ejpam-5434	115	41	{	{	PUNCT
ejpam-5434	115	42	b	b	X
ejpam-5434	115	43	,	,	PUNCT
ejpam-5434	115	44	c	c	NOUN
ejpam-5434	115	45	,	,	PUNCT
ejpam-5434	115	46	d	d	NOUN
ejpam-5434	115	47	}	}	PUNCT
ejpam-5434	115	48	,	,	PUNCT
ejpam-5434	115	49	{	{	PUNCT
ejpam-5434	115	50	a	a	DET
ejpam-5434	115	51	,	,	PUNCT
ejpam-5434	115	52	b	b	NOUN
ejpam-5434	115	53	,	,	PUNCT
ejpam-5434	115	54	d	d	NOUN
ejpam-5434	115	55	}	}	PUNCT
ejpam-5434	115	56	}	}	PUNCT
ejpam-5434	115	57	.	.	PUNCT
ejpam-5434	116	1	then	then	ADV
ejpam-5434	116	2	,	,	PUNCT
ejpam-5434	116	3	case(1	case(1	PROPN
ejpam-5434	116	4	):	):	PUNCT
ejpam-5434	116	5	take	take	VERB
ejpam-5434	116	6	a	a	DET
ejpam-5434	116	7	=	=	X
ejpam-5434	116	8	{	{	PUNCT
ejpam-5434	116	9	a	a	NOUN
ejpam-5434	116	10	}	}	PUNCT
ejpam-5434	116	11	and	and	CCONJ
ejpam-5434	116	12	b	b	X
ejpam-5434	116	13	=	=	NOUN
ejpam-5434	116	14	{	{	PUNCT
ejpam-5434	116	15	a	a	NOUN
ejpam-5434	116	16	,	,	PUNCT
ejpam-5434	116	17	c	c	NOUN
ejpam-5434	116	18	}	}	PUNCT
ejpam-5434	116	19	.	.	PUNCT
ejpam-5434	117	1	then	then	ADV
ejpam-5434	117	2	a	a	DET
ejpam-5434	117	3	⊂	⊂	PROPN
ejpam-5434	117	4	b.	b.	PROPN
ejpam-5434	117	5	also	also	ADV
ejpam-5434	117	6	mic	mic	ADJ
ejpam-5434	117	7	-	-	PUNCT
ejpam-5434	117	8	pa∗	pa∗	NOUN
ejpam-5434	117	9	=	=	PUNCT
ejpam-5434	117	10	{	{	PUNCT
ejpam-5434	117	11	a	a	NOUN
ejpam-5434	117	12	}	}	PUNCT
ejpam-5434	117	13	,	,	PUNCT
ejpam-5434	117	14	mic	mic	ADJ
ejpam-5434	117	15	-	-	PUNCT
ejpam-5434	117	16	pa∗	pa∗	NOUN
ejpam-5434	117	17	=	=	SYM
ejpam-5434	117	18	{	{	PUNCT
ejpam-5434	117	19	∅	∅	NOUN
ejpam-5434	117	20	}	}	PUNCT
ejpam-5434	117	21	and	and	CCONJ
ejpam-5434	117	22	mic	mic	ADJ
ejpam-5434	117	23	-	-	PUNCT
ejpam-5434	117	24	pfr(a	pfr(a	NOUN
ejpam-5434	117	25	)	)	PUNCT
ejpam-5434	117	26	=	=	PRON
ejpam-5434	117	27	{	{	PUNCT
ejpam-5434	117	28	a	a	NOUN
ejpam-5434	117	29	}	}	PUNCT
ejpam-5434	117	30	.	.	PUNCT
ejpam-5434	118	1	mic	mic	ADJ
ejpam-5434	118	2	-	-	PUNCT
ejpam-5434	118	3	pb∗	pb∗	NOUN
ejpam-5434	118	4	=	=	PUNCT
ejpam-5434	118	5	{	{	PUNCT
ejpam-5434	118	6	a	a	X
ejpam-5434	118	7	,	,	PUNCT
ejpam-5434	118	8	c	c	NOUN
ejpam-5434	118	9	}	}	PUNCT
ejpam-5434	118	10	,	,	PUNCT
ejpam-5434	118	11	mic	mic	ADJ
ejpam-5434	118	12	-	-	PUNCT
ejpam-5434	118	13	pb∗	pb∗	NOUN
ejpam-5434	118	14	=	=	SYM
ejpam-5434	118	15	{	{	PUNCT
ejpam-5434	118	16	∅	∅	NOUN
ejpam-5434	118	17	}	}	PUNCT
ejpam-5434	118	18	and	and	CCONJ
ejpam-5434	118	19	mic	mic	ADJ
ejpam-5434	118	20	-	-	PUNCT
ejpam-5434	118	21	pfr(b	pfr(b	PROPN
ejpam-5434	118	22	)	)	PUNCT
ejpam-5434	119	1	=	=	PRON
ejpam-5434	119	2	{	{	PUNCT
ejpam-5434	119	3	a	a	X
ejpam-5434	119	4	,	,	PUNCT
ejpam-5434	119	5	c	c	NOUN
ejpam-5434	119	6	}	}	PUNCT
ejpam-5434	119	7	.	.	PUNCT
ejpam-5434	120	1	this	this	PRON
ejpam-5434	120	2	shows	show	VERB
ejpam-5434	120	3	that	that	SCONJ
ejpam-5434	120	4	mic	mic	ADJ
ejpam-5434	120	5	-	-	PUNCT
ejpam-5434	120	6	pfr(a	pfr(a	NOUN
ejpam-5434	120	7	)	)	PUNCT
ejpam-5434	120	8	⊂	⊂	PROPN
ejpam-5434	120	9	mic	mic	ADJ
ejpam-5434	120	10	-	-	PUNCT
ejpam-5434	120	11	pfr(b	pfr(b	PROPN
ejpam-5434	120	12	)	)	PUNCT
ejpam-5434	120	13	.	.	PUNCT
ejpam-5434	121	1	s.	s.	PROPN
ejpam-5434	121	2	stanley	stanley	PROPN
ejpam-5434	121	3	roshan	roshan	PROPN
ejpam-5434	121	4	et	et	PROPN
ejpam-5434	121	5	al	al	PROPN
ejpam-5434	121	6	.	.	PUNCT
ejpam-5434	121	7	/	/	SYM
ejpam-5434	121	8	eur	eur	PROPN
ejpam-5434	121	9	.	.	PUNCT
ejpam-5434	122	1	j.	j.	PROPN
ejpam-5434	122	2	pure	pure	PROPN
ejpam-5434	122	3	appl	appl	PROPN
ejpam-5434	122	4	.	.	PROPN
ejpam-5434	122	5	math	math	PROPN
ejpam-5434	122	6	,	,	PUNCT
ejpam-5434	122	7	17	17	NUM
ejpam-5434	122	8	(	(	PUNCT
ejpam-5434	122	9	4	4	NUM
ejpam-5434	122	10	)	)	PUNCT
ejpam-5434	122	11	(	(	PUNCT
ejpam-5434	122	12	2024	2024	NUM
ejpam-5434	122	13	)	)	PUNCT
ejpam-5434	122	14	,	,	PUNCT
ejpam-5434	122	15	3156	3156	NUM
ejpam-5434	122	16	-	-	SYM
ejpam-5434	122	17	3166	3166	NUM
ejpam-5434	122	18	3160	3160	NUM
ejpam-5434	122	19	case(2	case(2	NOUN
ejpam-5434	122	20	):	):	PUNCT
ejpam-5434	122	21	take	take	VERB
ejpam-5434	122	22	a	a	DET
ejpam-5434	122	23	=	=	X
ejpam-5434	122	24	{	{	PUNCT
ejpam-5434	122	25	a	a	NOUN
ejpam-5434	122	26	}	}	PUNCT
ejpam-5434	122	27	and	and	CCONJ
ejpam-5434	122	28	b	b	X
ejpam-5434	122	29	=	=	NOUN
ejpam-5434	122	30	{	{	PUNCT
ejpam-5434	122	31	a	a	NOUN
ejpam-5434	122	32	,	,	PUNCT
ejpam-5434	122	33	c	c	NOUN
ejpam-5434	122	34	,	,	PUNCT
ejpam-5434	122	35	d	d	NOUN
ejpam-5434	122	36	}	}	PUNCT
ejpam-5434	122	37	.	.	PUNCT
ejpam-5434	123	1	also	also	ADV
ejpam-5434	123	2	mic	mic	ADJ
ejpam-5434	123	3	-	-	PUNCT
ejpam-5434	123	4	pa∗	pa∗	NOUN
ejpam-5434	123	5	=	=	PUNCT
ejpam-5434	123	6	{	{	PUNCT
ejpam-5434	123	7	a	a	NOUN
ejpam-5434	123	8	}	}	PUNCT
ejpam-5434	123	9	,	,	PUNCT
ejpam-5434	123	10	mic	mic	ADJ
ejpam-5434	123	11	-	-	PUNCT
ejpam-5434	123	12	pa∗	pa∗	NOUN
ejpam-5434	123	13	=	=	SYM
ejpam-5434	123	14	{	{	PUNCT
ejpam-5434	123	15	∅	∅	NOUN
ejpam-5434	123	16	}	}	PUNCT
ejpam-5434	123	17	and	and	CCONJ
ejpam-5434	123	18	mic	mic	ADJ
ejpam-5434	123	19	-	-	PUNCT
ejpam-5434	123	20	pfr(a	pfr(a	NOUN
ejpam-5434	123	21	)	)	PUNCT
ejpam-5434	123	22	=	=	PRON
ejpam-5434	123	23	{	{	PUNCT
ejpam-5434	123	24	a	a	X
ejpam-5434	123	25	}	}	PUNCT
ejpam-5434	123	26	.	.	PUNCT
ejpam-5434	124	1	let	let	VERB
ejpam-5434	124	2	mic	mic	ADJ
ejpam-5434	124	3	-	-	PUNCT
ejpam-5434	124	4	pb∗	pb∗	NOUN
ejpam-5434	124	5	=	=	SYM
ejpam-5434	124	6	{	{	PUNCT
ejpam-5434	124	7	c	c	NOUN
ejpam-5434	124	8	,	,	PUNCT
ejpam-5434	124	9	d	d	NOUN
ejpam-5434	124	10	,	,	PUNCT
ejpam-5434	124	11	a	a	PRON
ejpam-5434	124	12	}	}	PUNCT
ejpam-5434	124	13	,	,	PUNCT
ejpam-5434	124	14	mic	mic	ADJ
ejpam-5434	124	15	-	-	PUNCT
ejpam-5434	124	16	pb∗	pb∗	NOUN
ejpam-5434	124	17	=	=	SYM
ejpam-5434	124	18	{	{	PUNCT
ejpam-5434	124	19	∅	∅	NOUN
ejpam-5434	124	20	}	}	PUNCT
ejpam-5434	124	21	and	and	CCONJ
ejpam-5434	124	22	mic	mic	ADJ
ejpam-5434	124	23	-	-	PUNCT
ejpam-5434	124	24	pfr(b	pfr(b	PROPN
ejpam-5434	124	25	)	)	PUNCT
ejpam-5434	124	26	=	=	PRON
ejpam-5434	124	27	{	{	PUNCT
ejpam-5434	124	28	a	a	X
ejpam-5434	124	29	,	,	PUNCT
ejpam-5434	124	30	c	c	NOUN
ejpam-5434	124	31	,	,	PUNCT
ejpam-5434	124	32	d	d	NOUN
ejpam-5434	124	33	}	}	PUNCT
ejpam-5434	124	34	.	.	PUNCT
ejpam-5434	125	1	this	this	PRON
ejpam-5434	125	2	shows	show	VERB
ejpam-5434	125	3	that	that	SCONJ
ejpam-5434	125	4	mic	mic	ADJ
ejpam-5434	125	5	-	-	PUNCT
ejpam-5434	125	6	pfr(a	pfr(a	NOUN
ejpam-5434	125	7	)	)	PUNCT
ejpam-5434	125	8	⊂	⊂	PROPN
ejpam-5434	125	9	mic	mic	ADJ
ejpam-5434	125	10	-	-	PUNCT
ejpam-5434	125	11	pfr(b	pfr(b	PROPN
ejpam-5434	125	12	)	)	PUNCT
ejpam-5434	125	13	,	,	PUNCT
ejpam-5434	125	14	where	where	SCONJ
ejpam-5434	125	15	mic	mic	ADJ
ejpam-5434	125	16	-	-	PUNCT
ejpam-5434	125	17	pfr(b	pfr(b	NOUN
ejpam-5434	125	18	)	)	PUNCT
ejpam-5434	125	19	̸⊂	̸⊂	ADV
ejpam-5434	125	20	mic	mic	NOUN
ejpam-5434	125	21	-	-	PUNCT
ejpam-5434	125	22	pfr(a	pfr(a	NOUN
ejpam-5434	125	23	)	)	PUNCT
ejpam-5434	125	24	.	.	PUNCT
ejpam-5434	126	1	theorem	theorem	NOUN
ejpam-5434	126	2	3	3	NUM
ejpam-5434	126	3	.	.	PUNCT
ejpam-5434	127	1	if	if	SCONJ
ejpam-5434	127	2	a	a	DET
ejpam-5434	127	3	∈	∈	NOUN
ejpam-5434	127	4	mic	mic	ADJ
ejpam-5434	127	5	-	-	PUNCT
ejpam-5434	127	6	po(u	po(u	ADJ
ejpam-5434	127	7	)	)	PUNCT
ejpam-5434	127	8	∪	∪	ADP
ejpam-5434	127	9	mic	mic	NOUN
ejpam-5434	127	10	-	-	PUNCT
ejpam-5434	127	11	pf(u	pf(u	NUM
ejpam-5434	127	12	)	)	PUNCT
ejpam-5434	127	13	,	,	PUNCT
ejpam-5434	127	14	then	then	ADV
ejpam-5434	127	15	mic	mic	ADJ
ejpam-5434	127	16	-	-	PUNCT
ejpam-5434	127	17	pfr(a	pfr(a	NOUN
ejpam-5434	127	18	)	)	PUNCT
ejpam-5434	127	19	=	=	SYM
ejpam-5434	127	20	mic	mic	ADJ
ejpam-5434	127	21	-	-	PUNCT
ejpam-5434	127	22	pfr(mic	pfr(mic	ADJ
ejpam-5434	127	23	-	-	PUNCT
ejpam-5434	127	24	pfr(a	pfr(a	NOUN
ejpam-5434	127	25	)	)	PUNCT
ejpam-5434	127	26	)	)	PUNCT
ejpam-5434	127	27	.	.	PUNCT
ejpam-5434	128	1	proof	proof	NOUN
ejpam-5434	128	2	:	:	PUNCT
ejpam-5434	128	3	it	it	PRON
ejpam-5434	128	4	follows	follow	VERB
ejpam-5434	128	5	by	by	ADP
ejpam-5434	128	6	lemma	lemma	PROPN
ejpam-5434	128	7	1(3	1(3	NUM
ejpam-5434	128	8	)	)	PUNCT
ejpam-5434	128	9	,	,	PUNCT
ejpam-5434	128	10	lemma	lemma	PROPN
ejpam-5434	128	11	2	2	NUM
ejpam-5434	128	12	and	and	CCONJ
ejpam-5434	128	13	theorem	theorem	VERB
ejpam-5434	128	14	2	2	NUM
ejpam-5434	128	15	(	(	PUNCT
ejpam-5434	128	16	2	2	NUM
ejpam-5434	128	17	,	,	PUNCT
ejpam-5434	128	18	3	3	NUM
ejpam-5434	128	19	)	)	PUNCT
ejpam-5434	128	20	.	.	PUNCT
ejpam-5434	129	1	corollary	corollary	ADJ
ejpam-5434	129	2	1	1	NUM
ejpam-5434	129	3	.	.	PUNCT
ejpam-5434	130	1	for	for	ADP
ejpam-5434	130	2	every	every	DET
ejpam-5434	130	3	a	a	DET
ejpam-5434	130	4	⊂	⊂	PROPN
ejpam-5434	130	5	u	u	NOUN
ejpam-5434	130	6	,	,	PUNCT
ejpam-5434	130	7	mic	mic	ADJ
ejpam-5434	130	8	-	-	PUNCT
ejpam-5434	130	9	pfr(mic	pfr(mic	ADJ
ejpam-5434	130	10	-	-	PUNCT
ejpam-5434	130	11	pfr(mic	pfr(mic	ADJ
ejpam-5434	130	12	-	-	PUNCT
ejpam-5434	130	13	pfr(a	pfr(a	NOUN
ejpam-5434	130	14	)	)	PUNCT
ejpam-5434	130	15	)	)	PUNCT
ejpam-5434	130	16	)	)	PUNCT
ejpam-5434	131	1	=	=	SYM
ejpam-5434	131	2	mic	mic	ADJ
ejpam-5434	131	3	-	-	PUNCT
ejpam-5434	131	4	pfr(mic	pfr(mic	ADJ
ejpam-5434	131	5	-	-	PUNCT
ejpam-5434	131	6	pfr(a	pfr(a	NOUN
ejpam-5434	131	7	)	)	PUNCT
ejpam-5434	131	8	)	)	PUNCT
ejpam-5434	131	9	.	.	PUNCT
ejpam-5434	132	1	proof	proof	NOUN
ejpam-5434	132	2	:	:	PUNCT
ejpam-5434	132	3	it	it	PRON
ejpam-5434	132	4	is	be	AUX
ejpam-5434	132	5	obvious	obvious	ADJ
ejpam-5434	132	6	.	.	PUNCT
ejpam-5434	133	1	lemma	lemma	PROPN
ejpam-5434	133	2	3	3	NUM
ejpam-5434	133	3	.	.	PUNCT
ejpam-5434	134	1	a	a	DET
ejpam-5434	134	2	subset	subset	NOUN
ejpam-5434	134	3	a	a	PRON
ejpam-5434	134	4	of	of	ADP
ejpam-5434	134	5	u	u	NOUN
ejpam-5434	134	6	is	be	AUX
ejpam-5434	134	7	micro	micro	ADJ
ejpam-5434	134	8	pre	pre	ADJ
ejpam-5434	134	9	-	-	ADJ
ejpam-5434	134	10	closed	closed	ADJ
ejpam-5434	134	11	iff	iff	PROPN
ejpam-5434	134	12	a	a	DET
ejpam-5434	134	13	=	=	PUNCT
ejpam-5434	134	14	mic	mic	ADJ
ejpam-5434	134	15	-	-	PUNCT
ejpam-5434	134	16	pcl(a	pcl(a	NOUN
ejpam-5434	134	17	)	)	PUNCT
ejpam-5434	134	18	.	.	PUNCT
ejpam-5434	135	1	theorem	theorem	VERB
ejpam-5434	135	2	4	4	NUM
ejpam-5434	135	3	.	.	X
ejpam-5434	135	4	for	for	ADP
ejpam-5434	135	5	a	a	DET
ejpam-5434	135	6	subset	subset	NOUN
ejpam-5434	135	7	a	a	PRON
ejpam-5434	135	8	of	of	ADP
ejpam-5434	135	9	space	space	NOUN
ejpam-5434	135	10	u	u	NOUN
ejpam-5434	135	11	,	,	PUNCT
ejpam-5434	135	12	the	the	DET
ejpam-5434	135	13	following	follow	VERB
ejpam-5434	135	14	statements	statement	NOUN
ejpam-5434	135	15	hold	hold	VERB
ejpam-5434	135	16	(	(	PUNCT
ejpam-5434	135	17	i	i	NOUN
ejpam-5434	135	18	)	)	PUNCT
ejpam-5434	135	19	a	a	PRON
ejpam-5434	135	20	is	be	AUX
ejpam-5434	135	21	mic	mic	ADJ
ejpam-5434	135	22	-	-	PUNCT
ejpam-5434	135	23	po	po	NOUN
ejpam-5434	135	24	iff	iff	NOUN
ejpam-5434	135	25	mic	mic	PROPN
ejpam-5434	135	26	-	-	PUNCT
ejpam-5434	135	27	pfr(a	pfr(a	NOUN
ejpam-5434	135	28	)	)	PUNCT
ejpam-5434	135	29	=	=	SYM
ejpam-5434	135	30	mic	mic	NOUN
ejpam-5434	135	31	-	-	PUNCT
ejpam-5434	135	32	pd(a	pd(a	NOUN
ejpam-5434	135	33	)	)	PUNCT
ejpam-5434	135	34	.	.	PUNCT
ejpam-5434	136	1	(	(	PUNCT
ejpam-5434	136	2	ii	ii	NOUN
ejpam-5434	136	3	)	)	PUNCT
ejpam-5434	136	4	mic	mic	ADJ
ejpam-5434	136	5	-	-	PUNCT
ejpam-5434	136	6	pfr(mic	pfr(mic	ADJ
ejpam-5434	136	7	-	-	PUNCT
ejpam-5434	136	8	pfr(a	pfr(a	NOUN
ejpam-5434	136	9	)	)	PUNCT
ejpam-5434	136	10	)	)	PUNCT
ejpam-5434	137	1	⊆	⊆	X
ejpam-5434	137	2	mic	mic	ADJ
ejpam-5434	137	3	-	-	PUNCT
ejpam-5434	137	4	pfr(a	pfr(a	NOUN
ejpam-5434	137	5	)	)	PUNCT
ejpam-5434	137	6	.	.	PUNCT
ejpam-5434	138	1	(	(	PUNCT
ejpam-5434	138	2	iii	iii	X
ejpam-5434	138	3	)	)	PUNCT
ejpam-5434	138	4	mic	mic	ADJ
ejpam-5434	138	5	-	-	PUNCT
ejpam-5434	138	6	pfr(mic	pfr(mic	ADJ
ejpam-5434	138	7	-	-	PUNCT
ejpam-5434	138	8	pcl(a	pcl(a	NOUN
ejpam-5434	138	9	)	)	PUNCT
ejpam-5434	138	10	)	)	PUNCT
ejpam-5434	139	1	⊆	⊆	X
ejpam-5434	139	2	mic	mic	ADJ
ejpam-5434	139	3	-	-	PUNCT
ejpam-5434	139	4	pfr(a	pfr(a	NOUN
ejpam-5434	139	5	)	)	PUNCT
ejpam-5434	139	6	.	.	PUNCT
ejpam-5434	140	1	(	(	PUNCT
ejpam-5434	140	2	iv	iv	X
ejpam-5434	140	3	)	)	PUNCT
ejpam-5434	140	4	mic	mic	ADJ
ejpam-5434	140	5	-	-	PUNCT
ejpam-5434	140	6	pint(a	pint(a	NOUN
ejpam-5434	140	7	)	)	PUNCT
ejpam-5434	140	8	=	=	PUNCT
ejpam-5434	141	1	a	a	DET
ejpam-5434	141	2	−	−	PROPN
ejpam-5434	141	3	mic	mic	ADJ
ejpam-5434	141	4	-	-	PUNCT
ejpam-5434	141	5	pfr(a	pfr(a	NOUN
ejpam-5434	141	6	)	)	PUNCT
ejpam-5434	141	7	proof	proof	NOUN
ejpam-5434	141	8	:	:	PUNCT
ejpam-5434	141	9	(	(	PUNCT
ejpam-5434	141	10	i	i	NOUN
ejpam-5434	141	11	)	)	PUNCT
ejpam-5434	141	12	let	let	VERB
ejpam-5434	141	13	a	a	DET
ejpam-5434	141	14	be	be	AUX
ejpam-5434	141	15	micro	micro	ADJ
ejpam-5434	141	16	pre	pre	ADJ
ejpam-5434	141	17	-	-	ADJ
ejpam-5434	141	18	open	open	ADJ
ejpam-5434	141	19	then	then	ADV
ejpam-5434	141	20	mic	mic	ADJ
ejpam-5434	141	21	-	-	PUNCT
ejpam-5434	141	22	pint(a	pint(a	NOUN
ejpam-5434	141	23	)	)	PUNCT
ejpam-5434	141	24	=	=	SYM
ejpam-5434	141	25	a.	a.	NOUN
ejpam-5434	141	26	since	since	SCONJ
ejpam-5434	141	27	mic	mic	ADJ
ejpam-5434	141	28	-	-	PUNCT
ejpam-5434	141	29	pfr(a	pfr(a	NOUN
ejpam-5434	141	30	)	)	PUNCT
ejpam-5434	141	31	=	=	SYM
ejpam-5434	141	32	mic	mic	ADJ
ejpam-5434	141	33	-	-	PUNCT
ejpam-5434	141	34	pcl(a	pcl(a	NOUN
ejpam-5434	141	35	)	)	PUNCT
ejpam-5434	141	36	−	−	PROPN
ejpam-5434	141	37	mic	mic	ADJ
ejpam-5434	141	38	-	-	PUNCT
ejpam-5434	141	39	pint(a	pint(a	NOUN
ejpam-5434	141	40	)	)	PUNCT
ejpam-5434	141	41	=	=	SYM
ejpam-5434	141	42	mic	mic	ADJ
ejpam-5434	141	43	-	-	PUNCT
ejpam-5434	141	44	pcl(a)−a	pcl(a)−a	NOUN
ejpam-5434	141	45	.	.	PUNCT
ejpam-5434	141	46	by	by	ADP
ejpam-5434	141	47	lemma	lemma	PROPN
ejpam-5434	141	48	4.9	4.9	NUM
ejpam-5434	142	1	[	[	X
ejpam-5434	142	2	7	7	X
ejpam-5434	142	3	]	]	X
ejpam-5434	142	4	we	we	PRON
ejpam-5434	142	5	have	have	VERB
ejpam-5434	142	6	mic	mic	ADJ
ejpam-5434	142	7	-	-	PUNCT
ejpam-5434	142	8	pcl(a	pcl(a	NOUN
ejpam-5434	142	9	)	)	PUNCT
ejpam-5434	142	10	=	=	NOUN
ejpam-5434	142	11	a	a	DET
ejpam-5434	142	12	∪	∪	ADJ
ejpam-5434	142	13	mic	mic	NOUN
ejpam-5434	142	14	-	-	PUNCT
ejpam-5434	142	15	pd(a	pd(a	NOUN
ejpam-5434	142	16	)	)	PUNCT
ejpam-5434	142	17	.	.	PUNCT
ejpam-5434	143	1	therefore	therefore	ADV
ejpam-5434	143	2	mic	mic	ADJ
ejpam-5434	143	3	-	-	PUNCT
ejpam-5434	143	4	pfr(a	pfr(a	NOUN
ejpam-5434	143	5	)	)	PUNCT
ejpam-5434	143	6	=	=	PUNCT
ejpam-5434	144	1	[	[	X
ejpam-5434	144	2	a	a	DET
ejpam-5434	144	3	∪	∪	ADJ
ejpam-5434	144	4	mic	mic	ADJ
ejpam-5434	144	5	-	-	PUNCT
ejpam-5434	144	6	pd(a)]−	pd(a)]−	ADJ
ejpam-5434	144	7	a	a	DET
ejpam-5434	144	8	=	=	PUNCT
ejpam-5434	144	9	mic	mic	NOUN
ejpam-5434	144	10	-	-	PUNCT
ejpam-5434	144	11	pd(a	pd(a	NOUN
ejpam-5434	144	12	)	)	PUNCT
ejpam-5434	144	13	.	.	PUNCT
ejpam-5434	145	1	conversely	conversely	ADV
ejpam-5434	145	2	,	,	PUNCT
ejpam-5434	145	3	let	let	VERB
ejpam-5434	145	4	mic	mic	ADJ
ejpam-5434	145	5	-	-	PUNCT
ejpam-5434	145	6	pfr(a	pfr(a	NOUN
ejpam-5434	145	7	)	)	PUNCT
ejpam-5434	145	8	=	=	SYM
ejpam-5434	145	9	mic	mic	NOUN
ejpam-5434	145	10	-	-	PUNCT
ejpam-5434	145	11	pd(a	pd(a	NOUN
ejpam-5434	145	12	)	)	PUNCT
ejpam-5434	145	13	.	.	PUNCT
ejpam-5434	146	1	i.e.	i.e.	X
ejpam-5434	146	2	,	,	PUNCT
ejpam-5434	146	3	mic	mic	ADJ
ejpam-5434	146	4	-	-	PUNCT
ejpam-5434	146	5	pcl(a	pcl(a	NOUN
ejpam-5434	146	6	)	)	PUNCT
ejpam-5434	146	7	−	−	PROPN
ejpam-5434	146	8	mic	mic	ADJ
ejpam-5434	146	9	-	-	PUNCT
ejpam-5434	146	10	pint(a	pint(a	NOUN
ejpam-5434	146	11	)	)	PUNCT
ejpam-5434	146	12	=	=	PUNCT
ejpam-5434	147	1	[	[	X
ejpam-5434	147	2	a	a	DET
ejpam-5434	147	3	∪	∪	ADJ
ejpam-5434	147	4	mic	mic	NOUN
ejpam-5434	147	5	-	-	PUNCT
ejpam-5434	147	6	pd(a	pd(a	NOUN
ejpam-5434	147	7	)	)	PUNCT
ejpam-5434	147	8	]	]	X
ejpam-5434	147	9	mic	mic	ADJ
ejpam-5434	147	10	-	-	PUNCT
ejpam-5434	147	11	pint(a	pint(a	NOUN
ejpam-5434	147	12	)	)	PUNCT
ejpam-5434	147	13	=	=	SYM
ejpam-5434	147	14	mic	mic	ADJ
ejpam-5434	147	15	-	-	PUNCT
ejpam-5434	147	16	pd(a	pd(a	NOUN
ejpam-5434	147	17	)	)	PUNCT
ejpam-5434	147	18	⇒	⇒	VERB
ejpam-5434	147	19	a	a	DET
ejpam-5434	147	20	−	−	PROPN
ejpam-5434	147	21	mic	mic	ADJ
ejpam-5434	147	22	-	-	PUNCT
ejpam-5434	147	23	pint(a	pint(a	NOUN
ejpam-5434	147	24	)	)	PUNCT
ejpam-5434	148	1	=	=	NOUN
ejpam-5434	148	2	∅	∅	NOUN
ejpam-5434	148	3	implies	imply	VERB
ejpam-5434	148	4	a	a	DET
ejpam-5434	148	5	⊂	⊂	PROPN
ejpam-5434	148	6	mic	mic	ADJ
ejpam-5434	148	7	-	-	PUNCT
ejpam-5434	148	8	pint(a	pint(a	NOUN
ejpam-5434	148	9	)	)	PUNCT
ejpam-5434	148	10	−→	−→	NOUN
ejpam-5434	148	11	(	(	PUNCT
ejpam-5434	148	12	1	1	NUM
ejpam-5434	148	13	)	)	PUNCT
ejpam-5434	148	14	and	and	CCONJ
ejpam-5434	148	15	mic	mic	ADJ
ejpam-5434	148	16	-	-	PUNCT
ejpam-5434	148	17	pint(a	pint(a	NOUN
ejpam-5434	148	18	)	)	PUNCT
ejpam-5434	148	19	⊂	⊂	PROPN
ejpam-5434	148	20	a	a	DET
ejpam-5434	148	21	−→	−→	NOUN
ejpam-5434	148	22	(	(	PUNCT
ejpam-5434	148	23	2	2	NUM
ejpam-5434	148	24	)	)	PUNCT
ejpam-5434	148	25	.	.	PUNCT
ejpam-5434	149	1	therefore	therefore	ADV
ejpam-5434	149	2	from	from	ADP
ejpam-5434	149	3	(	(	PUNCT
ejpam-5434	149	4	1	1	NUM
ejpam-5434	149	5	)	)	PUNCT
ejpam-5434	149	6	and	and	CCONJ
ejpam-5434	149	7	(	(	PUNCT
ejpam-5434	149	8	2	2	X
ejpam-5434	149	9	)	)	PUNCT
ejpam-5434	149	10	we	we	PRON
ejpam-5434	149	11	have	have	VERB
ejpam-5434	149	12	mic	mic	ADJ
ejpam-5434	149	13	-	-	PUNCT
ejpam-5434	149	14	pint(a	pint(a	NOUN
ejpam-5434	149	15	)	)	PUNCT
ejpam-5434	149	16	=	=	PUNCT
ejpam-5434	150	1	a	a	PRON
ejpam-5434	150	2	is	be	AUX
ejpam-5434	150	3	micro	micro	ADJ
ejpam-5434	150	4	pre	pre	ADJ
ejpam-5434	150	5	-	-	ADJ
ejpam-5434	150	6	open	open	ADJ
ejpam-5434	150	7	.	.	PUNCT
ejpam-5434	151	1	(	(	PUNCT
ejpam-5434	151	2	ii	ii	NOUN
ejpam-5434	151	3	)	)	PUNCT
ejpam-5434	151	4	now	now	ADV
ejpam-5434	151	5	mic	mic	ADJ
ejpam-5434	151	6	-	-	PUNCT
ejpam-5434	151	7	pfr(mic	pfr(mic	ADJ
ejpam-5434	151	8	-	-	PUNCT
ejpam-5434	151	9	pfr(a	pfr(a	NOUN
ejpam-5434	151	10	)	)	PUNCT
ejpam-5434	151	11	)	)	PUNCT
ejpam-5434	152	1	⊆	⊆	NUM
ejpam-5434	152	2	mic	mic	ADJ
ejpam-5434	152	3	-	-	PUNCT
ejpam-5434	152	4	pcl(mic	pcl(mic	NOUN
ejpam-5434	152	5	-	-	PUNCT
ejpam-5434	152	6	pfr(a	pfr(a	NOUN
ejpam-5434	152	7	)	)	PUNCT
ejpam-5434	152	8	)	)	PUNCT
ejpam-5434	152	9	∩	∩	ADJ
ejpam-5434	152	10	mic	mic	ADJ
ejpam-5434	152	11	-	-	PUNCT
ejpam-5434	152	12	pcl(u	pcl(u	NOUN
ejpam-5434	152	13	−	−	NOUN
ejpam-5434	152	14	mic	mic	ADJ
ejpam-5434	152	15	-	-	PUNCT
ejpam-5434	152	16	pfr(a	pfr(a	NOUN
ejpam-5434	152	17	)	)	PUNCT
ejpam-5434	152	18	)	)	PUNCT
ejpam-5434	152	19	⇒	⇒	VERB
ejpam-5434	152	20	mic	mic	ADJ
ejpam-5434	152	21	-	-	PUNCT
ejpam-5434	152	22	pfr(mic	pfr(mic	ADJ
ejpam-5434	152	23	-	-	PUNCT
ejpam-5434	152	24	pfr(a	pfr(a	NOUN
ejpam-5434	152	25	)	)	PUNCT
ejpam-5434	152	26	)	)	PUNCT
ejpam-5434	153	1	⊆	⊆	NUM
ejpam-5434	153	2	mic	mic	ADJ
ejpam-5434	153	3	-	-	PUNCT
ejpam-5434	153	4	pcl(mic	pcl(mic	NOUN
ejpam-5434	153	5	-	-	PUNCT
ejpam-5434	153	6	pfr(a	pfr(a	NOUN
ejpam-5434	153	7	)	)	PUNCT
ejpam-5434	153	8	)	)	PUNCT
ejpam-5434	154	1	⊆	⊆	X
ejpam-5434	154	2	mic	mic	ADJ
ejpam-5434	154	3	-	-	PUNCT
ejpam-5434	154	4	pfr(a	pfr(a	NOUN
ejpam-5434	154	5	)	)	PUNCT
ejpam-5434	154	6	.	.	PUNCT
ejpam-5434	155	1	(	(	PUNCT
ejpam-5434	155	2	iii	iii	X
ejpam-5434	155	3	)	)	PUNCT
ejpam-5434	155	4	mic	mic	ADJ
ejpam-5434	155	5	-	-	PUNCT
ejpam-5434	155	6	pfr(mic	pfr(mic	ADJ
ejpam-5434	155	7	-	-	PUNCT
ejpam-5434	155	8	pcl(a	pcl(a	NOUN
ejpam-5434	155	9	)	)	PUNCT
ejpam-5434	155	10	)	)	PUNCT
ejpam-5434	156	1	⊆	⊆	NUM
ejpam-5434	156	2	mic	mic	ADJ
ejpam-5434	156	3	-	-	PUNCT
ejpam-5434	156	4	pcl(mic	pcl(mic	NOUN
ejpam-5434	156	5	-	-	PUNCT
ejpam-5434	156	6	pcl(a	pcl(a	NOUN
ejpam-5434	156	7	)	)	PUNCT
ejpam-5434	156	8	)	)	PUNCT
ejpam-5434	157	1	−	−	ADP
ejpam-5434	157	2	mic	mic	ADJ
ejpam-5434	157	3	-	-	PUNCT
ejpam-5434	157	4	pint(mic	pint(mic	ADJ
ejpam-5434	157	5	-	-	PUNCT
ejpam-5434	157	6	pcl(a	pcl(a	NOUN
ejpam-5434	157	7	)	)	PUNCT
ejpam-5434	157	8	)	)	PUNCT
ejpam-5434	158	1	⊆	⊆	X
ejpam-5434	158	2	mic	mic	ADJ
ejpam-5434	158	3	-	-	PUNCT
ejpam-5434	158	4	pcl(a	pcl(a	NOUN
ejpam-5434	158	5	)	)	PUNCT
ejpam-5434	158	6	−	−	PROPN
ejpam-5434	158	7	mic	mic	ADJ
ejpam-5434	158	8	-	-	PUNCT
ejpam-5434	158	9	pint(a	pint(a	NOUN
ejpam-5434	158	10	)	)	PUNCT
ejpam-5434	158	11	⊆	⊆	NUM
ejpam-5434	158	12	mic	mic	ADJ
ejpam-5434	158	13	-	-	PUNCT
ejpam-5434	158	14	pfr(a	pfr(a	NOUN
ejpam-5434	158	15	)	)	PUNCT
ejpam-5434	158	16	(	(	PUNCT
ejpam-5434	158	17	iv	iv	X
ejpam-5434	158	18	)	)	PUNCT
ejpam-5434	158	19	it	it	PRON
ejpam-5434	158	20	is	be	AUX
ejpam-5434	158	21	obvious	obvious	ADJ
ejpam-5434	158	22	from	from	ADP
ejpam-5434	158	23	the	the	DET
ejpam-5434	158	24	definition	definition	NOUN
ejpam-5434	158	25	of	of	ADP
ejpam-5434	158	26	micro	micro	ADJ
ejpam-5434	158	27	pre	pre	NOUN
ejpam-5434	158	28	-	-	ADJ
ejpam-5434	158	29	interior	interior	ADJ
ejpam-5434	158	30	and	and	CCONJ
ejpam-5434	158	31	micro	micro	ADJ
ejpam-5434	158	32	pre	pre	NOUN
ejpam-5434	158	33	-	-	NOUN
ejpam-5434	158	34	frontier	frontier	NOUN
ejpam-5434	158	35	.	.	PUNCT
ejpam-5434	159	1	3	3	X
ejpam-5434	159	2	.	.	X
ejpam-5434	159	3	micro	micro	ADJ
ejpam-5434	159	4	pre	pre	NOUN
ejpam-5434	159	5	-	-	ADJ
ejpam-5434	159	6	exterior	exterior	ADJ
ejpam-5434	159	7	in	in	ADP
ejpam-5434	159	8	this	this	DET
ejpam-5434	159	9	section	section	NOUN
ejpam-5434	159	10	,	,	PUNCT
ejpam-5434	159	11	we	we	PRON
ejpam-5434	159	12	define	define	VERB
ejpam-5434	159	13	and	and	CCONJ
ejpam-5434	159	14	study	study	VERB
ejpam-5434	159	15	the	the	DET
ejpam-5434	159	16	notions	notion	NOUN
ejpam-5434	159	17	of	of	ADP
ejpam-5434	159	18	micro	micro	ADJ
ejpam-5434	159	19	pre	pre	NOUN
ejpam-5434	159	20	-	-	ADJ
ejpam-5434	159	21	exterior	exterior	ADJ
ejpam-5434	159	22	and	and	CCONJ
ejpam-5434	159	23	obtain	obtain	VERB
ejpam-5434	159	24	its	its	PRON
ejpam-5434	159	25	basic	basic	ADJ
ejpam-5434	159	26	properties	property	NOUN
ejpam-5434	159	27	.	.	PUNCT
ejpam-5434	160	1	definition	definition	NOUN
ejpam-5434	160	2	14	14	NUM
ejpam-5434	160	3	.	.	PUNCT
ejpam-5434	161	1	a	a	DET
ejpam-5434	161	2	point	point	NOUN
ejpam-5434	161	3	x	x	X
ejpam-5434	161	4	∈	∈	NOUN
ejpam-5434	161	5	u	u	NOUN
ejpam-5434	161	6	is	be	AUX
ejpam-5434	161	7	called	call	VERB
ejpam-5434	161	8	micro	micro	ADJ
ejpam-5434	161	9	pre	pre	ADJ
ejpam-5434	161	10	-	-	ADJ
ejpam-5434	161	11	exterior	exterior	ADJ
ejpam-5434	161	12	point	point	NOUN
ejpam-5434	161	13	of	of	ADP
ejpam-5434	161	14	a	a	DET
ejpam-5434	161	15	subset	subset	NOUN
ejpam-5434	161	16	a	a	PRON
ejpam-5434	161	17	of	of	ADP
ejpam-5434	161	18	u	u	NOUN
ejpam-5434	161	19	if	if	SCONJ
ejpam-5434	161	20	x	x	PRON
ejpam-5434	161	21	is	be	AUX
ejpam-5434	161	22	micro	micro	ADJ
ejpam-5434	161	23	pre	pre	ADJ
ejpam-5434	161	24	-	-	ADJ
ejpam-5434	161	25	interior	interior	ADJ
ejpam-5434	161	26	point	point	NOUN
ejpam-5434	161	27	of	of	ADP
ejpam-5434	161	28	(	(	PUNCT
ejpam-5434	161	29	u	u	NOUN
ejpam-5434	161	30	−	−	PROPN
ejpam-5434	161	31	a	a	NOUN
ejpam-5434	161	32	)	)	PUNCT
ejpam-5434	161	33	and	and	CCONJ
ejpam-5434	161	34	set	set	VERB
ejpam-5434	161	35	of	of	ADP
ejpam-5434	161	36	all	all	DET
ejpam-5434	161	37	micro	micro	ADJ
ejpam-5434	161	38	pre	pre	ADJ
ejpam-5434	161	39	-	-	ADJ
ejpam-5434	161	40	exterior	exterior	ADJ
ejpam-5434	161	41	points	point	NOUN
ejpam-5434	161	42	of	of	ADP
ejpam-5434	161	43	a	a	PRON
ejpam-5434	161	44	is	be	AUX
ejpam-5434	161	45	called	call	VERB
ejpam-5434	161	46	micro	micro	ADJ
ejpam-5434	161	47	pre	pre	NOUN
ejpam-5434	161	48	-	-	ADJ
ejpam-5434	161	49	exterior	exterior	ADJ
ejpam-5434	161	50	of	of	ADP
ejpam-5434	161	51	a	a	PRON
ejpam-5434	161	52	and	and	CCONJ
ejpam-5434	161	53	denoted	denote	VERB
ejpam-5434	161	54	by	by	ADP
ejpam-5434	161	55	mic	mic	ADJ
ejpam-5434	161	56	-	-	PUNCT
ejpam-5434	161	57	pext(a	pext(a	NOUN
ejpam-5434	161	58	)	)	PUNCT
ejpam-5434	161	59	.	.	PUNCT
ejpam-5434	162	1	therefore	therefore	ADV
ejpam-5434	162	2	mic	mic	ADJ
ejpam-5434	162	3	-	-	PUNCT
ejpam-5434	162	4	pext(a	pext(a	NOUN
ejpam-5434	162	5	)	)	PUNCT
ejpam-5434	162	6	=	=	SYM
ejpam-5434	162	7	mic	mic	ADJ
ejpam-5434	162	8	-	-	PUNCT
ejpam-5434	162	9	pint(u	pint(u	NOUN
ejpam-5434	162	10	−a	−a	NOUN
ejpam-5434	162	11	)	)	PUNCT
ejpam-5434	162	12	.	.	PUNCT
ejpam-5434	163	1	s.	s.	PROPN
ejpam-5434	163	2	stanley	stanley	PROPN
ejpam-5434	163	3	roshan	roshan	PROPN
ejpam-5434	163	4	et	et	PROPN
ejpam-5434	163	5	al	al	PROPN
ejpam-5434	163	6	.	.	PUNCT
ejpam-5434	163	7	/	/	SYM
ejpam-5434	163	8	eur	eur	PROPN
ejpam-5434	163	9	.	.	PUNCT
ejpam-5434	164	1	j.	j.	PROPN
ejpam-5434	164	2	pure	pure	PROPN
ejpam-5434	164	3	appl	appl	PROPN
ejpam-5434	164	4	.	.	PROPN
ejpam-5434	164	5	math	math	PROPN
ejpam-5434	164	6	,	,	PUNCT
ejpam-5434	164	7	17	17	NUM
ejpam-5434	164	8	(	(	PUNCT
ejpam-5434	164	9	4	4	NUM
ejpam-5434	164	10	)	)	PUNCT
ejpam-5434	164	11	(	(	PUNCT
ejpam-5434	164	12	2024	2024	NUM
ejpam-5434	164	13	)	)	PUNCT
ejpam-5434	164	14	,	,	PUNCT
ejpam-5434	164	15	3156	3156	NUM
ejpam-5434	164	16	-	-	SYM
ejpam-5434	164	17	3166	3166	NUM
ejpam-5434	164	18	3161	3161	NUM
ejpam-5434	164	19	theorem	theorem	NOUN
ejpam-5434	164	20	5	5	NUM
ejpam-5434	164	21	.	.	X
ejpam-5434	164	22	for	for	ADP
ejpam-5434	164	23	a	a	DET
ejpam-5434	164	24	subset	subset	NOUN
ejpam-5434	164	25	a	a	PRON
ejpam-5434	164	26	of	of	ADP
ejpam-5434	164	27	a	a	DET
ejpam-5434	164	28	space	space	NOUN
ejpam-5434	164	29	u	u	NOUN
ejpam-5434	164	30	the	the	DET
ejpam-5434	164	31	following	follow	VERB
ejpam-5434	164	32	statements	statement	NOUN
ejpam-5434	164	33	hold	hold	VERB
ejpam-5434	164	34	(	(	PUNCT
ejpam-5434	164	35	i	i	NOUN
ejpam-5434	164	36	)	)	PUNCT
ejpam-5434	164	37	mic	mic	ADJ
ejpam-5434	164	38	-	-	PUNCT
ejpam-5434	164	39	ext(a	ext(a	NOUN
ejpam-5434	164	40	)	)	PUNCT
ejpam-5434	164	41	⊆	⊆	NUM
ejpam-5434	164	42	mic	mic	ADJ
ejpam-5434	164	43	-	-	PUNCT
ejpam-5434	164	44	pext(a	pext(a	NOUN
ejpam-5434	164	45	)	)	PUNCT
ejpam-5434	164	46	.	.	PUNCT
ejpam-5434	165	1	(	(	PUNCT
ejpam-5434	165	2	ii	ii	NOUN
ejpam-5434	165	3	)	)	PUNCT
ejpam-5434	165	4	mic	mic	ADJ
ejpam-5434	165	5	-	-	PUNCT
ejpam-5434	165	6	pext(a	pext(a	NOUN
ejpam-5434	165	7	)	)	PUNCT
ejpam-5434	166	1	⊂	⊂	PROPN
ejpam-5434	166	2	mic	mic	ADJ
ejpam-5434	166	3	-	-	PUNCT
ejpam-5434	166	4	po(u	po(u	ADJ
ejpam-5434	166	5	)	)	PUNCT
ejpam-5434	166	6	.	.	PUNCT
ejpam-5434	167	1	(	(	PUNCT
ejpam-5434	167	2	iii	iii	X
ejpam-5434	167	3	)	)	PUNCT
ejpam-5434	167	4	mic	mic	ADJ
ejpam-5434	167	5	-	-	PUNCT
ejpam-5434	167	6	pext(a	pext(a	NOUN
ejpam-5434	167	7	)	)	PUNCT
ejpam-5434	168	1	=	=	SYM
ejpam-5434	168	2	u−mic	u−mic	ADJ
ejpam-5434	168	3	-	-	PUNCT
ejpam-5434	168	4	pcl(a	pcl(a	NOUN
ejpam-5434	168	5	)	)	PUNCT
ejpam-5434	168	6	.	.	PUNCT
ejpam-5434	169	1	(	(	PUNCT
ejpam-5434	169	2	iv	iv	X
ejpam-5434	169	3	)	)	PUNCT
ejpam-5434	169	4	mic	mic	ADJ
ejpam-5434	169	5	-	-	PUNCT
ejpam-5434	169	6	pext(mic	pext(mic	ADJ
ejpam-5434	169	7	-	-	PUNCT
ejpam-5434	169	8	pext(a	pext(a	NOUN
ejpam-5434	169	9	)	)	PUNCT
ejpam-5434	169	10	)	)	PUNCT
ejpam-5434	170	1	=	=	SYM
ejpam-5434	170	2	mic	mic	ADJ
ejpam-5434	170	3	-	-	PUNCT
ejpam-5434	170	4	pint(mic	pint(mic	ADJ
ejpam-5434	170	5	-	-	PUNCT
ejpam-5434	170	6	pcl(a	pcl(a	NOUN
ejpam-5434	170	7	)	)	PUNCT
ejpam-5434	170	8	)	)	PUNCT
ejpam-5434	170	9	.	.	PUNCT
ejpam-5434	171	1	(	(	PUNCT
ejpam-5434	171	2	v	v	NOUN
ejpam-5434	171	3	)	)	PUNCT
ejpam-5434	171	4	if	if	SCONJ
ejpam-5434	171	5	a	a	DET
ejpam-5434	171	6	⊂	⊂	PROPN
ejpam-5434	171	7	b	b	PROPN
ejpam-5434	171	8	then	then	ADV
ejpam-5434	171	9	mic	mic	ADJ
ejpam-5434	171	10	-	-	PUNCT
ejpam-5434	171	11	pext(b	pext(b	NOUN
ejpam-5434	171	12	)	)	PUNCT
ejpam-5434	171	13	⊆	⊆	NUM
ejpam-5434	171	14	mic	mic	ADJ
ejpam-5434	171	15	-	-	PUNCT
ejpam-5434	171	16	pext(a	pext(a	NOUN
ejpam-5434	171	17	)	)	PUNCT
ejpam-5434	171	18	.	.	PUNCT
ejpam-5434	172	1	(	(	PUNCT
ejpam-5434	172	2	vi	vi	NOUN
ejpam-5434	172	3	)	)	PUNCT
ejpam-5434	172	4	mic	mic	ADJ
ejpam-5434	172	5	-	-	PUNCT
ejpam-5434	172	6	pext(a	pext(a	NOUN
ejpam-5434	172	7	∪	∪	NOUN
ejpam-5434	172	8	b	b	NOUN
ejpam-5434	172	9	)	)	PUNCT
ejpam-5434	172	10	⊆	⊆	NUM
ejpam-5434	172	11	mic	mic	ADJ
ejpam-5434	172	12	-	-	PUNCT
ejpam-5434	172	13	pext(a	pext(a	NOUN
ejpam-5434	172	14	)	)	PUNCT
ejpam-5434	172	15	∪	∪	ADP
ejpam-5434	172	16	mic	mic	ADJ
ejpam-5434	172	17	-	-	PUNCT
ejpam-5434	172	18	pext(b	pext(b	NOUN
ejpam-5434	172	19	)	)	PUNCT
ejpam-5434	172	20	.	.	PUNCT
ejpam-5434	173	1	(	(	PUNCT
ejpam-5434	173	2	vii	vii	PROPN
ejpam-5434	173	3	)	)	PUNCT
ejpam-5434	173	4	mic	mic	ADJ
ejpam-5434	173	5	-	-	PUNCT
ejpam-5434	173	6	pext(a	pext(a	NOUN
ejpam-5434	173	7	)	)	PUNCT
ejpam-5434	173	8	∩	∩	ADJ
ejpam-5434	173	9	mic	mic	ADJ
ejpam-5434	173	10	-	-	PUNCT
ejpam-5434	173	11	pext(b	pext(b	NOUN
ejpam-5434	173	12	)	)	PUNCT
ejpam-5434	173	13	⊆	⊆	NUM
ejpam-5434	173	14	mic	mic	ADJ
ejpam-5434	173	15	-	-	PUNCT
ejpam-5434	173	16	pext(a	pext(a	NOUN
ejpam-5434	173	17	∩	∩	ADJ
ejpam-5434	173	18	b	b	NOUN
ejpam-5434	173	19	)	)	PUNCT
ejpam-5434	173	20	.	.	PUNCT
ejpam-5434	174	1	(	(	PUNCT
ejpam-5434	174	2	viii	viii	NOUN
ejpam-5434	174	3	)	)	PUNCT
ejpam-5434	174	4	mic	mic	ADJ
ejpam-5434	174	5	-	-	PUNCT
ejpam-5434	174	6	pext(u	pext(u	NOUN
ejpam-5434	174	7	)	)	PUNCT
ejpam-5434	174	8	=	=	NOUN
ejpam-5434	174	9	∅	∅	NOUN
ejpam-5434	174	10	and	and	CCONJ
ejpam-5434	174	11	mic	mic	ADJ
ejpam-5434	174	12	-	-	PUNCT
ejpam-5434	174	13	pext(∅	pext(∅	NOUN
ejpam-5434	174	14	)	)	PUNCT
ejpam-5434	174	15	=	=	VERB
ejpam-5434	175	1	u.	u.	NOUN
ejpam-5434	175	2	(	(	PUNCT
ejpam-5434	175	3	ix	ix	ADJ
ejpam-5434	175	4	)	)	PUNCT
ejpam-5434	175	5	mic	mic	ADJ
ejpam-5434	175	6	-	-	PUNCT
ejpam-5434	175	7	pext(a	pext(a	NOUN
ejpam-5434	175	8	)	)	PUNCT
ejpam-5434	175	9	=	=	SYM
ejpam-5434	175	10	mic	mic	ADJ
ejpam-5434	175	11	-	-	PUNCT
ejpam-5434	175	12	pext[u	pext[u	NOUN
ejpam-5434	175	13	−	−	NOUN
ejpam-5434	175	14	mic	mic	ADJ
ejpam-5434	175	15	-	-	PUNCT
ejpam-5434	175	16	pext(a	pext(a	NOUN
ejpam-5434	175	17	)	)	PUNCT
ejpam-5434	175	18	]	]	PUNCT
ejpam-5434	175	19	.	.	PUNCT
ejpam-5434	176	1	(	(	PUNCT
ejpam-5434	176	2	x	x	X
ejpam-5434	176	3	)	)	PUNCT
ejpam-5434	176	4	mic	mic	ADJ
ejpam-5434	176	5	-	-	PUNCT
ejpam-5434	176	6	pint(a	pint(a	NOUN
ejpam-5434	176	7	)	)	PUNCT
ejpam-5434	176	8	⊆	⊆	NUM
ejpam-5434	176	9	mic	mic	ADJ
ejpam-5434	176	10	-	-	PUNCT
ejpam-5434	176	11	pext[mic	pext[mic	ADJ
ejpam-5434	176	12	-	-	PUNCT
ejpam-5434	176	13	pext(a	pext(a	NOUN
ejpam-5434	176	14	)	)	PUNCT
ejpam-5434	176	15	]	]	PUNCT
ejpam-5434	176	16	.	.	PUNCT
ejpam-5434	177	1	(	(	PUNCT
ejpam-5434	177	2	xi	xi	NOUN
ejpam-5434	177	3	)	)	PUNCT
ejpam-5434	177	4	mic	mic	ADJ
ejpam-5434	177	5	-	-	PUNCT
ejpam-5434	177	6	pint(a	pint(a	NOUN
ejpam-5434	177	7	)	)	PUNCT
ejpam-5434	177	8	,	,	PUNCT
ejpam-5434	177	9	mic	mic	ADJ
ejpam-5434	177	10	-	-	PUNCT
ejpam-5434	177	11	pext(a	pext(a	NOUN
ejpam-5434	177	12	)	)	PUNCT
ejpam-5434	177	13	and	and	CCONJ
ejpam-5434	177	14	mic	mic	ADJ
ejpam-5434	177	15	-	-	PUNCT
ejpam-5434	177	16	pfr(a	pfr(a	NOUN
ejpam-5434	177	17	)	)	PUNCT
ejpam-5434	177	18	are	be	AUX
ejpam-5434	177	19	mutually	mutually	ADV
ejpam-5434	177	20	disjoint	disjoint	ADJ
ejpam-5434	177	21	and	and	CCONJ
ejpam-5434	177	22	u	u	X
ejpam-5434	177	23	=	=	SYM
ejpam-5434	177	24	micpint(a	micpint(a	PROPN
ejpam-5434	177	25	)	)	PUNCT
ejpam-5434	177	26	∪	∪	ADP
ejpam-5434	177	27	mic	mic	ADJ
ejpam-5434	177	28	-	-	PUNCT
ejpam-5434	177	29	pext(a	pext(a	NOUN
ejpam-5434	177	30	)	)	PUNCT
ejpam-5434	177	31	∪	∪	ADP
ejpam-5434	177	32	mic	mic	ADJ
ejpam-5434	177	33	-	-	PUNCT
ejpam-5434	177	34	pfr(a	pfr(a	NOUN
ejpam-5434	177	35	)	)	PUNCT
ejpam-5434	177	36	.	.	PUNCT
ejpam-5434	178	1	(	(	PUNCT
ejpam-5434	178	2	xii	xii	NOUN
ejpam-5434	178	3	)	)	PUNCT
ejpam-5434	178	4	a	a	DET
ejpam-5434	178	5	∩	∩	ADJ
ejpam-5434	178	6	mic	mic	ADJ
ejpam-5434	178	7	-	-	PUNCT
ejpam-5434	178	8	pext(a	pext(a	NOUN
ejpam-5434	178	9	)	)	PUNCT
ejpam-5434	178	10	=	=	PUNCT
ejpam-5434	178	11	∅.	∅.	PRON
ejpam-5434	178	12	proof	proof	NOUN
ejpam-5434	178	13	:	:	PUNCT
ejpam-5434	178	14	(	(	PUNCT
ejpam-5434	178	15	i	i	NOUN
ejpam-5434	178	16	)	)	PUNCT
ejpam-5434	178	17	let	let	VERB
ejpam-5434	178	18	x	x	X
ejpam-5434	178	19	∈	∈	PROPN
ejpam-5434	178	20	mic	mic	ADJ
ejpam-5434	178	21	-	-	PUNCT
ejpam-5434	178	22	ext(a	ext(a	NOUN
ejpam-5434	178	23	)	)	PUNCT
ejpam-5434	178	24	⇒	⇒	NOUN
ejpam-5434	178	25	x	x	SYM
ejpam-5434	178	26	∈	∈	PROPN
ejpam-5434	178	27	mic	mic	NOUN
ejpam-5434	178	28	-	-	PUNCT
ejpam-5434	178	29	int(u	int(u	NOUN
ejpam-5434	178	30	−	−	PROPN
ejpam-5434	178	31	a	a	X
ejpam-5434	178	32	)	)	PUNCT
ejpam-5434	178	33	.	.	PUNCT
ejpam-5434	179	1	there	there	PRON
ejpam-5434	179	2	exists	exist	VERB
ejpam-5434	179	3	g	g	PROPN
ejpam-5434	179	4	∈	∈	PROPN
ejpam-5434	179	5	µr(x	µr(x	NUM
ejpam-5434	179	6	)	)	PUNCT
ejpam-5434	179	7	such	such	ADJ
ejpam-5434	179	8	that	that	SCONJ
ejpam-5434	179	9	x	x	SYM
ejpam-5434	179	10	∈	∈	NOUN
ejpam-5434	179	11	g	g	ADP
ejpam-5434	179	12	⊆	⊆	NUM
ejpam-5434	179	13	(	(	PUNCT
ejpam-5434	179	14	u	u	NOUN
ejpam-5434	179	15	−a	−a	NOUN
ejpam-5434	179	16	)	)	PUNCT
ejpam-5434	179	17	.	.	PUNCT
ejpam-5434	180	1	also	also	ADV
ejpam-5434	180	2	g	g	PROPN
ejpam-5434	180	3	∈	∈	PROPN
ejpam-5434	180	4	mic	mic	ADJ
ejpam-5434	180	5	-	-	PUNCT
ejpam-5434	180	6	po(u	po(u	ADJ
ejpam-5434	180	7	,	,	PUNCT
ejpam-5434	180	8	x	x	NOUN
ejpam-5434	180	9	)	)	PUNCT
ejpam-5434	180	10	.	.	PUNCT
ejpam-5434	181	1	therefore	therefore	ADV
ejpam-5434	181	2	x	x	X
ejpam-5434	181	3	∈	∈	PROPN
ejpam-5434	181	4	g	g	ADP
ejpam-5434	181	5	⊆	⊆	NUM
ejpam-5434	181	6	(	(	PUNCT
ejpam-5434	181	7	u	u	NOUN
ejpam-5434	181	8	−a	−a	NOUN
ejpam-5434	181	9	)	)	PUNCT
ejpam-5434	181	10	for	for	ADP
ejpam-5434	181	11	mic	mic	ADJ
ejpam-5434	181	12	-	-	PUNCT
ejpam-5434	181	13	po	po	NOUN
ejpam-5434	181	14	set	set	VERB
ejpam-5434	181	15	g	g	PROPN
ejpam-5434	181	16	⇒	⇒	NOUN
ejpam-5434	181	17	(	(	PUNCT
ejpam-5434	181	18	u	u	NOUN
ejpam-5434	181	19	−	−	PROPN
ejpam-5434	181	20	a	a	NOUN
ejpam-5434	181	21	)	)	PUNCT
ejpam-5434	181	22	is	be	AUX
ejpam-5434	181	23	mic	mic	ADJ
ejpam-5434	181	24	-	-	PUNCT
ejpam-5434	181	25	pint	pint	NOUN
ejpam-5434	181	26	of	of	ADP
ejpam-5434	181	27	x	x	X
ejpam-5434	181	28	,	,	PUNCT
ejpam-5434	181	29	x	x	SYM
ejpam-5434	181	30	∈	∈	PROPN
ejpam-5434	181	31	mic	mic	NOUN
ejpam-5434	181	32	-	-	PUNCT
ejpam-5434	181	33	pint(u	pint(u	NOUN
ejpam-5434	181	34	−	−	NOUN
ejpam-5434	181	35	a)i.e	a)i.e	ADV
ejpam-5434	181	36	.	.	PUNCT
ejpam-5434	182	1	,	,	PUNCT
ejpam-5434	182	2	x	x	PUNCT
ejpam-5434	182	3	∈	∈	PROPN
ejpam-5434	182	4	mic	mic	ADJ
ejpam-5434	182	5	-	-	PUNCT
ejpam-5434	182	6	pext(a	pext(a	NOUN
ejpam-5434	182	7	)	)	PUNCT
ejpam-5434	182	8	.	.	PUNCT
ejpam-5434	183	1	hence	hence	ADV
ejpam-5434	183	2	mic	mic	ADJ
ejpam-5434	183	3	-	-	PUNCT
ejpam-5434	183	4	ext(a	ext(a	NOUN
ejpam-5434	183	5	)	)	PUNCT
ejpam-5434	183	6	⊆	⊆	NUM
ejpam-5434	183	7	mic	mic	ADJ
ejpam-5434	183	8	-	-	PUNCT
ejpam-5434	183	9	pext(a	pext(a	NOUN
ejpam-5434	183	10	)	)	PUNCT
ejpam-5434	183	11	.	.	PUNCT
ejpam-5434	184	1	(	(	PUNCT
ejpam-5434	184	2	ii	ii	NOUN
ejpam-5434	184	3	)	)	PUNCT
ejpam-5434	184	4	now	now	ADV
ejpam-5434	184	5	mic	mic	ADJ
ejpam-5434	184	6	-	-	PUNCT
ejpam-5434	184	7	pint[mic	pint[mic	ADJ
ejpam-5434	184	8	-	-	PUNCT
ejpam-5434	184	9	pext(a	pext(a	NOUN
ejpam-5434	184	10	)	)	PUNCT
ejpam-5434	184	11	]	]	PUNCT
ejpam-5434	185	1	=	=	SYM
ejpam-5434	185	2	mic	mic	ADJ
ejpam-5434	185	3	-	-	PUNCT
ejpam-5434	185	4	pint[mic	pint[mic	ADJ
ejpam-5434	185	5	-	-	PUNCT
ejpam-5434	185	6	pint(u	pint(u	NOUN
ejpam-5434	185	7	−	−	NOUN
ejpam-5434	185	8	a	a	NOUN
ejpam-5434	185	9	)	)	PUNCT
ejpam-5434	185	10	]	]	PUNCT
ejpam-5434	186	1	=	=	SYM
ejpam-5434	186	2	mic	mic	ADJ
ejpam-5434	186	3	-	-	PUNCT
ejpam-5434	186	4	pint(u	pint(u	NUM
ejpam-5434	186	5	−	−	NOUN
ejpam-5434	186	6	a	a	X
ejpam-5434	186	7	)	)	PUNCT
ejpam-5434	186	8	=	=	SYM
ejpam-5434	186	9	mic	mic	ADJ
ejpam-5434	186	10	-	-	PUNCT
ejpam-5434	186	11	pext(a	pext(a	NOUN
ejpam-5434	186	12	)	)	PUNCT
ejpam-5434	186	13	⇒	⇒	NOUN
ejpam-5434	186	14	is	be	AUX
ejpam-5434	186	15	contained	contain	VERB
ejpam-5434	186	16	in	in	ADP
ejpam-5434	186	17	mic	mic	ADJ
ejpam-5434	186	18	-	-	PUNCT
ejpam-5434	186	19	po(u	po(u	ADJ
ejpam-5434	186	20	)	)	PUNCT
ejpam-5434	186	21	.	.	PUNCT
ejpam-5434	187	1	(	(	PUNCT
ejpam-5434	187	2	iii	iii	X
ejpam-5434	187	3	)	)	PUNCT
ejpam-5434	187	4	mic	mic	ADJ
ejpam-5434	187	5	-	-	PUNCT
ejpam-5434	187	6	pext(a	pext(a	NOUN
ejpam-5434	187	7	)	)	PUNCT
ejpam-5434	187	8	=	=	SYM
ejpam-5434	187	9	mic	mic	ADJ
ejpam-5434	187	10	-	-	PUNCT
ejpam-5434	187	11	pint(u	pint(u	NOUN
ejpam-5434	187	12	−a	−a	NOUN
ejpam-5434	187	13	)	)	PUNCT
ejpam-5434	188	1	=	=	PUNCT
ejpam-5434	188	2	u−mic	u−mic	ADJ
ejpam-5434	188	3	-	-	PUNCT
ejpam-5434	188	4	pcl(a	pcl(a	NOUN
ejpam-5434	188	5	)	)	PUNCT
ejpam-5434	188	6	.	.	PUNCT
ejpam-5434	189	1	(	(	PUNCT
ejpam-5434	189	2	iv	iv	X
ejpam-5434	189	3	)	)	PUNCT
ejpam-5434	189	4	mic	mic	ADJ
ejpam-5434	189	5	-	-	PUNCT
ejpam-5434	189	6	pext[mic	pext[mic	ADJ
ejpam-5434	189	7	-	-	PUNCT
ejpam-5434	189	8	pext(a	pext(a	NOUN
ejpam-5434	189	9	)	)	PUNCT
ejpam-5434	189	10	]	]	PUNCT
ejpam-5434	190	1	=	=	SYM
ejpam-5434	190	2	mic	mic	ADJ
ejpam-5434	190	3	-	-	PUNCT
ejpam-5434	190	4	pext[u−mic	pext[u−mic	NOUN
ejpam-5434	190	5	-	-	PUNCT
ejpam-5434	190	6	cl(a	cl(a	NUM
ejpam-5434	190	7	)	)	PUNCT
ejpam-5434	190	8	]	]	PUNCT
ejpam-5434	190	9	by	by	ADP
ejpam-5434	190	10	(	(	PUNCT
ejpam-5434	190	11	3	3	NUM
ejpam-5434	190	12	)	)	PUNCT
ejpam-5434	190	13	,	,	PUNCT
ejpam-5434	190	14	mic	mic	ADJ
ejpam-5434	190	15	-	-	PUNCT
ejpam-5434	190	16	pext[u−mic	pext[u−mic	NOUN
ejpam-5434	190	17	-	-	PUNCT
ejpam-5434	190	18	cl(a	cl(a	NUM
ejpam-5434	190	19	)	)	PUNCT
ejpam-5434	190	20	]	]	PUNCT
ejpam-5434	191	1	=	=	SYM
ejpam-5434	191	2	mic	mic	ADJ
ejpam-5434	191	3	-	-	PUNCT
ejpam-5434	191	4	pint[u−[u−mic	pint[u−[u−mic	ADJ
ejpam-5434	191	5	-	-	PUNCT
ejpam-5434	191	6	pcl(a	pcl(a	NOUN
ejpam-5434	191	7	)	)	PUNCT
ejpam-5434	191	8	]	]	PUNCT
ejpam-5434	191	9	]	]	X
ejpam-5434	191	10	=	=	SYM
ejpam-5434	191	11	mic	mic	ADJ
ejpam-5434	191	12	-	-	PUNCT
ejpam-5434	191	13	pint[mic	pint[mic	ADJ
ejpam-5434	191	14	-	-	PUNCT
ejpam-5434	191	15	pcl(a	pcl(a	NOUN
ejpam-5434	191	16	)	)	PUNCT
ejpam-5434	191	17	]	]	PUNCT
ejpam-5434	191	18	.	.	PUNCT
ejpam-5434	192	1	(	(	PUNCT
ejpam-5434	192	2	v	v	NOUN
ejpam-5434	192	3	)	)	PUNCT
ejpam-5434	192	4	if	if	SCONJ
ejpam-5434	192	5	a	a	DET
ejpam-5434	192	6	⊂	⊂	PROPN
ejpam-5434	192	7	b	b	PROPN
ejpam-5434	192	8	then	then	ADV
ejpam-5434	192	9	(	(	PUNCT
ejpam-5434	192	10	u	u	NOUN
ejpam-5434	192	11	−	−	PROPN
ejpam-5434	192	12	b	b	PROPN
ejpam-5434	192	13	)	)	PUNCT
ejpam-5434	192	14	⊂	⊂	PROPN
ejpam-5434	192	15	(	(	PUNCT
ejpam-5434	192	16	u	u	NOUN
ejpam-5434	192	17	−	−	PROPN
ejpam-5434	192	18	a	a	NOUN
ejpam-5434	192	19	)	)	PUNCT
ejpam-5434	192	20	⇒	⇒	NOUN
ejpam-5434	192	21	mic	mic	NOUN
ejpam-5434	192	22	-	-	PUNCT
ejpam-5434	192	23	pint(u	pint(u	NUM
ejpam-5434	192	24	−	−	PROPN
ejpam-5434	192	25	b	b	X
ejpam-5434	192	26	)	)	PUNCT
ejpam-5434	192	27	⊆	⊆	NUM
ejpam-5434	192	28	mic	mic	NOUN
ejpam-5434	192	29	-	-	PUNCT
ejpam-5434	192	30	pint(u	pint(u	NOUN
ejpam-5434	192	31	−	−	NOUN
ejpam-5434	192	32	a	a	X
ejpam-5434	192	33	)	)	PUNCT
ejpam-5434	192	34	i.e.	i.e.	X
ejpam-5434	192	35	,	,	PUNCT
ejpam-5434	192	36	mic	mic	ADJ
ejpam-5434	192	37	-	-	PUNCT
ejpam-5434	192	38	pext(b	pext(b	NOUN
ejpam-5434	192	39	)	)	PUNCT
ejpam-5434	192	40	⊆	⊆	NUM
ejpam-5434	192	41	mic	mic	ADJ
ejpam-5434	192	42	-	-	PUNCT
ejpam-5434	192	43	pext(a	pext(a	NOUN
ejpam-5434	192	44	)	)	PUNCT
ejpam-5434	192	45	.	.	PUNCT
ejpam-5434	193	1	(	(	PUNCT
ejpam-5434	193	2	vi	vi	X
ejpam-5434	193	3	)	)	PUNCT
ejpam-5434	193	4	since	since	SCONJ
ejpam-5434	193	5	a	a	DET
ejpam-5434	193	6	⊂	⊂	X
ejpam-5434	193	7	(	(	PUNCT
ejpam-5434	193	8	a	a	DET
ejpam-5434	193	9	∪	∪	ADJ
ejpam-5434	193	10	b	b	NOUN
ejpam-5434	193	11	)	)	PUNCT
ejpam-5434	193	12	and	and	CCONJ
ejpam-5434	193	13	b	b	X
ejpam-5434	193	14	⊂	⊂	PROPN
ejpam-5434	193	15	(	(	PUNCT
ejpam-5434	193	16	a	a	DET
ejpam-5434	193	17	∪	∪	ADJ
ejpam-5434	193	18	b	b	NOUN
ejpam-5434	193	19	)	)	PUNCT
ejpam-5434	193	20	⇒	⇒	VERB
ejpam-5434	193	21	mic	mic	ADJ
ejpam-5434	193	22	-	-	PUNCT
ejpam-5434	193	23	pext(a	pext(a	NOUN
ejpam-5434	193	24	∪	∪	NOUN
ejpam-5434	193	25	b	b	NOUN
ejpam-5434	193	26	)	)	PUNCT
ejpam-5434	193	27	⊆	⊆	NUM
ejpam-5434	193	28	mic	mic	ADJ
ejpam-5434	193	29	-	-	PUNCT
ejpam-5434	193	30	pext(a	pext(a	NOUN
ejpam-5434	193	31	)	)	PUNCT
ejpam-5434	193	32	∪	∪	ADP
ejpam-5434	193	33	mic	mic	ADJ
ejpam-5434	193	34	-	-	PUNCT
ejpam-5434	193	35	pext(a	pext(a	NOUN
ejpam-5434	193	36	∪	∪	NOUN
ejpam-5434	193	37	b	b	NOUN
ejpam-5434	193	38	)	)	PUNCT
ejpam-5434	193	39	⊆	⊆	NUM
ejpam-5434	193	40	mic	mic	ADJ
ejpam-5434	193	41	-	-	PUNCT
ejpam-5434	193	42	pext(b	pext(b	NOUN
ejpam-5434	193	43	)	)	PUNCT
ejpam-5434	193	44	.	.	PUNCT
ejpam-5434	194	1	therefore	therefore	ADV
ejpam-5434	194	2	mic	mic	ADJ
ejpam-5434	194	3	-	-	PUNCT
ejpam-5434	194	4	pext(a	pext(a	NOUN
ejpam-5434	194	5	∪	∪	NOUN
ejpam-5434	194	6	b	b	NOUN
ejpam-5434	194	7	)	)	PUNCT
ejpam-5434	194	8	⊆	⊆	NUM
ejpam-5434	194	9	mic	mic	ADJ
ejpam-5434	194	10	-	-	PUNCT
ejpam-5434	194	11	pext(a	pext(a	NOUN
ejpam-5434	194	12	)	)	PUNCT
ejpam-5434	194	13	∪	∪	ADP
ejpam-5434	194	14	mic	mic	ADJ
ejpam-5434	194	15	-	-	PUNCT
ejpam-5434	194	16	pext(b	pext(b	NOUN
ejpam-5434	194	17	)	)	PUNCT
ejpam-5434	194	18	.	.	PUNCT
ejpam-5434	195	1	s.	s.	PROPN
ejpam-5434	195	2	stanley	stanley	PROPN
ejpam-5434	195	3	roshan	roshan	PROPN
ejpam-5434	195	4	et	et	PROPN
ejpam-5434	195	5	al	al	PROPN
ejpam-5434	195	6	.	.	PUNCT
ejpam-5434	195	7	/	/	SYM
ejpam-5434	195	8	eur	eur	PROPN
ejpam-5434	195	9	.	.	PUNCT
ejpam-5434	196	1	j.	j.	PROPN
ejpam-5434	196	2	pure	pure	PROPN
ejpam-5434	196	3	appl	appl	PROPN
ejpam-5434	196	4	.	.	PROPN
ejpam-5434	196	5	math	math	PROPN
ejpam-5434	196	6	,	,	PUNCT
ejpam-5434	196	7	17	17	NUM
ejpam-5434	196	8	(	(	PUNCT
ejpam-5434	196	9	4	4	NUM
ejpam-5434	196	10	)	)	PUNCT
ejpam-5434	196	11	(	(	PUNCT
ejpam-5434	196	12	2024	2024	NUM
ejpam-5434	196	13	)	)	PUNCT
ejpam-5434	196	14	,	,	PUNCT
ejpam-5434	196	15	3156	3156	NUM
ejpam-5434	196	16	-	-	SYM
ejpam-5434	196	17	3166	3166	NUM
ejpam-5434	196	18	3162	3162	NUM
ejpam-5434	196	19	(	(	PUNCT
ejpam-5434	196	20	vii	vii	PROPN
ejpam-5434	196	21	)	)	PUNCT
ejpam-5434	197	1	we	we	PRON
ejpam-5434	197	2	have	have	VERB
ejpam-5434	197	3	(	(	PUNCT
ejpam-5434	197	4	a	a	DET
ejpam-5434	197	5	∩	∩	ADJ
ejpam-5434	197	6	b	b	X
ejpam-5434	197	7	)	)	PUNCT
ejpam-5434	197	8	⊂	⊂	PROPN
ejpam-5434	197	9	a	a	X
ejpam-5434	197	10	,	,	PUNCT
ejpam-5434	197	11	(	(	PUNCT
ejpam-5434	197	12	a	a	DET
ejpam-5434	197	13	∩	∩	ADJ
ejpam-5434	197	14	b	b	X
ejpam-5434	197	15	)	)	PUNCT
ejpam-5434	197	16	⊂	⊂	PROPN
ejpam-5434	197	17	b.	b.	PROPN
ejpam-5434	197	18	⇒	⇒	PROPN
ejpam-5434	197	19	mic	mic	ADJ
ejpam-5434	197	20	-	-	PUNCT
ejpam-5434	197	21	pext(a	pext(a	NOUN
ejpam-5434	197	22	)	)	PUNCT
ejpam-5434	198	1	⊆	⊆	NUM
ejpam-5434	198	2	mic	mic	ADJ
ejpam-5434	198	3	-	-	PUNCT
ejpam-5434	198	4	pext(a	pext(a	NOUN
ejpam-5434	198	5	∩	∩	ADJ
ejpam-5434	198	6	b	b	NOUN
ejpam-5434	198	7	)	)	PUNCT
ejpam-5434	198	8	and	and	CCONJ
ejpam-5434	198	9	mic	mic	ADJ
ejpam-5434	198	10	-	-	PUNCT
ejpam-5434	198	11	pext(b	pext(b	NOUN
ejpam-5434	198	12	)	)	PUNCT
ejpam-5434	198	13	⊆	⊆	NUM
ejpam-5434	198	14	mic	mic	ADJ
ejpam-5434	198	15	-	-	PUNCT
ejpam-5434	198	16	pext(a	pext(a	NOUN
ejpam-5434	198	17	∩	∩	ADJ
ejpam-5434	198	18	b	b	NOUN
ejpam-5434	198	19	)	)	PUNCT
ejpam-5434	198	20	⇒	⇒	NOUN
ejpam-5434	198	21	micpext(a	micpext(a	PROPN
ejpam-5434	198	22	)	)	PUNCT
ejpam-5434	198	23	∩	∩	ADJ
ejpam-5434	198	24	mic	mic	NOUN
ejpam-5434	198	25	-	-	PUNCT
ejpam-5434	198	26	pext(b	pext(b	NOUN
ejpam-5434	198	27	)	)	PUNCT
ejpam-5434	198	28	⊆	⊆	NUM
ejpam-5434	198	29	mic	mic	ADJ
ejpam-5434	198	30	-	-	PUNCT
ejpam-5434	198	31	pext(a	pext(a	NOUN
ejpam-5434	198	32	∩	∩	ADJ
ejpam-5434	198	33	b	b	NOUN
ejpam-5434	198	34	)	)	PUNCT
ejpam-5434	198	35	.	.	PUNCT
ejpam-5434	199	1	(	(	PUNCT
ejpam-5434	199	2	viii	viii	NOUN
ejpam-5434	199	3	)	)	PUNCT
ejpam-5434	199	4	mic	mic	ADJ
ejpam-5434	199	5	-	-	PUNCT
ejpam-5434	199	6	pext(u	pext(u	NOUN
ejpam-5434	199	7	)	)	PUNCT
ejpam-5434	199	8	=	=	SYM
ejpam-5434	199	9	mic	mic	ADJ
ejpam-5434	199	10	-	-	PUNCT
ejpam-5434	199	11	pint(u	pint(u	NUM
ejpam-5434	199	12	−	−	NOUN
ejpam-5434	199	13	u	u	NOUN
ejpam-5434	199	14	)	)	PUNCT
ejpam-5434	199	15	=	=	SYM
ejpam-5434	199	16	mic	mic	ADJ
ejpam-5434	199	17	-	-	PUNCT
ejpam-5434	199	18	pint(∅	pint(∅	NOUN
ejpam-5434	199	19	)	)	PUNCT
ejpam-5434	199	20	=	=	SYM
ejpam-5434	199	21	∅	∅	NOUN
ejpam-5434	199	22	and	and	CCONJ
ejpam-5434	199	23	mic	mic	ADJ
ejpam-5434	199	24	-	-	PUNCT
ejpam-5434	199	25	pext(∅	pext(∅	NOUN
ejpam-5434	199	26	)	)	PUNCT
ejpam-5434	199	27	=	=	SYM
ejpam-5434	199	28	micpint(u−∅	micpint(u−∅	PROPN
ejpam-5434	199	29	)	)	PUNCT
ejpam-5434	199	30	=	=	SYM
ejpam-5434	199	31	mic	mic	ADJ
ejpam-5434	199	32	-	-	PUNCT
ejpam-5434	199	33	pint(u	pint(u	NOUN
ejpam-5434	199	34	)	)	PUNCT
ejpam-5434	199	35	=	=	VERB
ejpam-5434	200	1	u.	u.	NOUN
ejpam-5434	200	2	(	(	PUNCT
ejpam-5434	200	3	ix	ix	ADJ
ejpam-5434	200	4	)	)	PUNCT
ejpam-5434	200	5	mic	mic	ADJ
ejpam-5434	200	6	-	-	PUNCT
ejpam-5434	200	7	pext[u	pext[u	NOUN
ejpam-5434	200	8	−	−	NOUN
ejpam-5434	200	9	mic	mic	ADJ
ejpam-5434	200	10	-	-	PUNCT
ejpam-5434	200	11	pext(a	pext(a	NOUN
ejpam-5434	200	12	)	)	PUNCT
ejpam-5434	200	13	]	]	PUNCT
ejpam-5434	201	1	=	=	SYM
ejpam-5434	201	2	mic	mic	ADJ
ejpam-5434	201	3	-	-	PUNCT
ejpam-5434	201	4	pint[u−(u−	pint[u−(u−	NOUN
ejpam-5434	201	5	mic	mic	ADJ
ejpam-5434	201	6	-	-	PUNCT
ejpam-5434	201	7	pint(a	pint(a	NOUN
ejpam-5434	201	8	)	)	PUNCT
ejpam-5434	201	9	)	)	PUNCT
ejpam-5434	201	10	]	]	PUNCT
ejpam-5434	202	1	=	=	SYM
ejpam-5434	202	2	mic	mic	ADJ
ejpam-5434	202	3	-	-	PUNCT
ejpam-5434	202	4	pint(micpext((a	pint(micpext((a	NUM
ejpam-5434	202	5	)	)	PUNCT
ejpam-5434	202	6	)	)	PUNCT
ejpam-5434	203	1	=	=	SYM
ejpam-5434	203	2	mic	mic	ADJ
ejpam-5434	203	3	-	-	PUNCT
ejpam-5434	203	4	pint[mic	pint[mic	ADJ
ejpam-5434	203	5	-	-	PUNCT
ejpam-5434	203	6	pint(u	pint(u	NOUN
ejpam-5434	203	7	−a	−a	NOUN
ejpam-5434	203	8	)	)	PUNCT
ejpam-5434	203	9	]	]	PUNCT
ejpam-5434	204	1	=	=	SYM
ejpam-5434	204	2	mic	mic	ADJ
ejpam-5434	204	3	-	-	PUNCT
ejpam-5434	204	4	pint(u	pint(u	NOUN
ejpam-5434	204	5	−a	−a	NOUN
ejpam-5434	204	6	)	)	PUNCT
ejpam-5434	204	7	=	=	SYM
ejpam-5434	204	8	mic	mic	ADJ
ejpam-5434	204	9	-	-	PUNCT
ejpam-5434	204	10	pext(a	pext(a	NOUN
ejpam-5434	204	11	)	)	PUNCT
ejpam-5434	204	12	.	.	PUNCT
ejpam-5434	205	1	(	(	PUNCT
ejpam-5434	205	2	x	x	X
ejpam-5434	205	3	)	)	PUNCT
ejpam-5434	205	4	by	by	ADP
ejpam-5434	205	5	the	the	DET
ejpam-5434	205	6	definition	definition	NOUN
ejpam-5434	205	7	mic	mic	ADJ
ejpam-5434	205	8	-	-	PUNCT
ejpam-5434	205	9	pext(a	pext(a	NOUN
ejpam-5434	205	10	)	)	PUNCT
ejpam-5434	205	11	⊂	⊂	PROPN
ejpam-5434	205	12	(	(	PUNCT
ejpam-5434	205	13	u	u	NOUN
ejpam-5434	205	14	−	−	PROPN
ejpam-5434	205	15	a	a	NOUN
ejpam-5434	205	16	)	)	PUNCT
ejpam-5434	205	17	then	then	ADV
ejpam-5434	205	18	from	from	ADP
ejpam-5434	205	19	(	(	PUNCT
ejpam-5434	205	20	5	5	NUM
ejpam-5434	205	21	)	)	PUNCT
ejpam-5434	205	22	mic	mic	ADJ
ejpam-5434	205	23	-	-	PUNCT
ejpam-5434	205	24	pext(u	pext(u	NOUN
ejpam-5434	205	25	−	−	NOUN
ejpam-5434	205	26	a	a	X
ejpam-5434	205	27	)	)	PUNCT
ejpam-5434	205	28	⊂	⊂	PROPN
ejpam-5434	205	29	micpext[mic	micpext[mic	NOUN
ejpam-5434	205	30	-	-	PUNCT
ejpam-5434	205	31	pext(a	pext(a	NOUN
ejpam-5434	205	32	)	)	PUNCT
ejpam-5434	205	33	]	]	PUNCT
ejpam-5434	205	34	i.e.	i.e.	X
ejpam-5434	205	35	,	,	PUNCT
ejpam-5434	205	36	mic	mic	ADJ
ejpam-5434	205	37	-	-	PUNCT
ejpam-5434	205	38	pint(a	pint(a	NOUN
ejpam-5434	205	39	)	)	PUNCT
ejpam-5434	205	40	⊂	⊂	PROPN
ejpam-5434	205	41	mic	mic	ADJ
ejpam-5434	205	42	-	-	PUNCT
ejpam-5434	205	43	pext[mic	pext[mic	ADJ
ejpam-5434	205	44	-	-	PUNCT
ejpam-5434	205	45	pext(a	pext(a	NOUN
ejpam-5434	205	46	)	)	PUNCT
ejpam-5434	205	47	]	]	PUNCT
ejpam-5434	205	48	.	.	PUNCT
ejpam-5434	206	1	(	(	PUNCT
ejpam-5434	206	2	xi	xi	X
ejpam-5434	206	3	)	)	PUNCT
ejpam-5434	206	4	let	let	VERB
ejpam-5434	206	5	us	we	PRON
ejpam-5434	206	6	assume	assume	VERB
ejpam-5434	206	7	that	that	SCONJ
ejpam-5434	206	8	mic	mic	ADJ
ejpam-5434	206	9	-	-	PUNCT
ejpam-5434	206	10	pext(a	pext(a	NOUN
ejpam-5434	206	11	)	)	PUNCT
ejpam-5434	206	12	∩	∩	ADJ
ejpam-5434	206	13	mic	mic	ADJ
ejpam-5434	206	14	-	-	PUNCT
ejpam-5434	206	15	pint(a	pint(a	NOUN
ejpam-5434	206	16	)	)	PUNCT
ejpam-5434	206	17	̸=	̸=	PROPN
ejpam-5434	206	18	∅	∅	NOUN
ejpam-5434	206	19	therefore	therefore	ADV
ejpam-5434	206	20	there	there	PRON
ejpam-5434	206	21	exists	exist	VERB
ejpam-5434	206	22	x	x	X
ejpam-5434	206	23	∈	∈	PROPN
ejpam-5434	206	24	micpext(a	micpext(a	NOUN
ejpam-5434	206	25	)	)	PUNCT
ejpam-5434	206	26	∩	∩	ADJ
ejpam-5434	206	27	mic	mic	ADJ
ejpam-5434	206	28	-	-	PUNCT
ejpam-5434	206	29	pint(a	pint(a	NOUN
ejpam-5434	206	30	)	)	PUNCT
ejpam-5434	206	31	⇒	⇒	NOUN
ejpam-5434	206	32	x	x	SYM
ejpam-5434	206	33	∈	∈	PROPN
ejpam-5434	206	34	mic	mic	ADJ
ejpam-5434	206	35	-	-	PUNCT
ejpam-5434	206	36	pext(a	pext(a	NOUN
ejpam-5434	206	37	)	)	PUNCT
ejpam-5434	206	38	and	and	CCONJ
ejpam-5434	206	39	x	x	PUNCT
ejpam-5434	206	40	∈	∈	PROPN
ejpam-5434	206	41	mic	mic	ADJ
ejpam-5434	206	42	-	-	PUNCT
ejpam-5434	206	43	pint(a	pint(a	NOUN
ejpam-5434	206	44	)	)	PUNCT
ejpam-5434	206	45	⇒	⇒	NOUN
ejpam-5434	206	46	x	x	X
ejpam-5434	207	1	∈	∈	PROPN
ejpam-5434	207	2	(	(	PUNCT
ejpam-5434	207	3	u	u	NOUN
ejpam-5434	207	4	−	−	PROPN
ejpam-5434	207	5	a	a	NOUN
ejpam-5434	207	6	)	)	PUNCT
ejpam-5434	207	7	and	and	CCONJ
ejpam-5434	207	8	x	x	PUNCT
ejpam-5434	207	9	∈	∈	PROPN
ejpam-5434	207	10	a	a	DET
ejpam-5434	207	11	which	which	PRON
ejpam-5434	207	12	is	be	AUX
ejpam-5434	207	13	not	not	PART
ejpam-5434	207	14	possible	possible	ADJ
ejpam-5434	207	15	.	.	PUNCT
ejpam-5434	208	1	therefore	therefore	ADV
ejpam-5434	208	2	our	our	PRON
ejpam-5434	208	3	assumption	assumption	NOUN
ejpam-5434	208	4	is	be	AUX
ejpam-5434	208	5	wrong	wrong	ADJ
ejpam-5434	208	6	.	.	PUNCT
ejpam-5434	209	1	hence	hence	ADV
ejpam-5434	209	2	micpext(a	micpext(a	NOUN
ejpam-5434	209	3	)	)	PUNCT
ejpam-5434	209	4	∩	∩	ADJ
ejpam-5434	209	5	mic	mic	ADJ
ejpam-5434	209	6	-	-	PUNCT
ejpam-5434	209	7	pint(a	pint(a	NOUN
ejpam-5434	209	8	)	)	PUNCT
ejpam-5434	209	9	=	=	NOUN
ejpam-5434	209	10	∅	∅	NOUN
ejpam-5434	209	11	similarly	similarly	ADV
ejpam-5434	209	12	other	other	ADJ
ejpam-5434	209	13	two	two	NUM
ejpam-5434	209	14	results	result	NOUN
ejpam-5434	209	15	.	.	PUNCT
ejpam-5434	210	1	we	we	PRON
ejpam-5434	210	2	have	have	VERB
ejpam-5434	210	3	mic	mic	ADJ
ejpam-5434	210	4	-	-	PUNCT
ejpam-5434	210	5	pext(a	pext(a	NOUN
ejpam-5434	210	6	)	)	PUNCT
ejpam-5434	210	7	=	=	SYM
ejpam-5434	210	8	u−	u−	ADJ
ejpam-5434	210	9	mic	mic	NOUN
ejpam-5434	210	10	-	-	PUNCT
ejpam-5434	210	11	cl(a	cl(a	NUM
ejpam-5434	210	12	)	)	PUNCT
ejpam-5434	210	13	=	=	X
ejpam-5434	210	14	u−[mic	u−[mic	PROPN
ejpam-5434	210	15	-	-	PUNCT
ejpam-5434	210	16	pint(a	pint(a	NOUN
ejpam-5434	210	17	)	)	PUNCT
ejpam-5434	210	18	∪	∪	ADP
ejpam-5434	210	19	mic	mic	ADJ
ejpam-5434	210	20	-	-	PUNCT
ejpam-5434	210	21	pfr(a	pfr(a	NOUN
ejpam-5434	210	22	)	)	PUNCT
ejpam-5434	210	23	]	]	PUNCT
ejpam-5434	210	24	that	that	PRON
ejpam-5434	210	25	implies	imply	VERB
ejpam-5434	210	26	u	u	NOUN
ejpam-5434	210	27	=	=	NOUN
ejpam-5434	210	28	mic	mic	ADJ
ejpam-5434	210	29	-	-	PUNCT
ejpam-5434	210	30	pint(a	pint(a	NOUN
ejpam-5434	210	31	)	)	PUNCT
ejpam-5434	210	32	∪	∪	ADP
ejpam-5434	210	33	mic	mic	ADJ
ejpam-5434	210	34	-	-	PUNCT
ejpam-5434	210	35	pext(a	pext(a	NOUN
ejpam-5434	210	36	)	)	PUNCT
ejpam-5434	210	37	∪	∪	ADP
ejpam-5434	210	38	mic	mic	ADJ
ejpam-5434	210	39	-	-	PUNCT
ejpam-5434	210	40	pfr(a	pfr(a	NOUN
ejpam-5434	210	41	)	)	PUNCT
ejpam-5434	210	42	.	.	PUNCT
ejpam-5434	211	1	(	(	PUNCT
ejpam-5434	211	2	xii	xii	NOUN
ejpam-5434	211	3	)	)	PUNCT
ejpam-5434	211	4	obvious	obvious	ADJ
ejpam-5434	211	5	.	.	PUNCT
ejpam-5434	212	1	in	in	ADP
ejpam-5434	212	2	general	general	ADJ
ejpam-5434	212	3	,	,	PUNCT
ejpam-5434	212	4	the	the	DET
ejpam-5434	212	5	converse	converse	NOUN
ejpam-5434	212	6	of	of	ADP
ejpam-5434	212	7	(	(	PUNCT
ejpam-5434	212	8	6	6	NUM
ejpam-5434	212	9	)	)	PUNCT
ejpam-5434	212	10	and	and	CCONJ
ejpam-5434	212	11	(	(	PUNCT
ejpam-5434	212	12	7	7	X
ejpam-5434	212	13	)	)	PUNCT
ejpam-5434	212	14	are	be	AUX
ejpam-5434	212	15	not	not	PART
ejpam-5434	212	16	true	true	ADJ
ejpam-5434	212	17	i.e.	i.e.	X
ejpam-5434	212	18	,	,	PUNCT
ejpam-5434	212	19	mic	mic	ADJ
ejpam-5434	212	20	-	-	PUNCT
ejpam-5434	212	21	pext(a	pext(a	NOUN
ejpam-5434	212	22	)	)	PUNCT
ejpam-5434	212	23	∪	∪	ADP
ejpam-5434	212	24	mic	mic	ADJ
ejpam-5434	212	25	-	-	PUNCT
ejpam-5434	212	26	pext(b	pext(b	NOUN
ejpam-5434	212	27	)	)	PUNCT
ejpam-5434	212	28	̸⊂	̸⊂	ADV
ejpam-5434	212	29	mic	mic	ADJ
ejpam-5434	212	30	-	-	PUNCT
ejpam-5434	212	31	pext(a	pext(a	NOUN
ejpam-5434	212	32	∪	∪	NOUN
ejpam-5434	212	33	b	b	NOUN
ejpam-5434	212	34	)	)	PUNCT
ejpam-5434	212	35	and	and	CCONJ
ejpam-5434	212	36	mic	mic	ADJ
ejpam-5434	212	37	-	-	PUNCT
ejpam-5434	212	38	pext(a	pext(a	NOUN
ejpam-5434	212	39	∩	∩	ADJ
ejpam-5434	212	40	b	b	X
ejpam-5434	212	41	)	)	PUNCT
ejpam-5434	212	42	̸⊂	̸⊂	ADV
ejpam-5434	212	43	mic	mic	ADJ
ejpam-5434	212	44	-	-	PUNCT
ejpam-5434	212	45	pext(a	pext(a	NOUN
ejpam-5434	212	46	)	)	PUNCT
ejpam-5434	212	47	∩	∩	ADJ
ejpam-5434	212	48	mic	mic	NOUN
ejpam-5434	212	49	-	-	PUNCT
ejpam-5434	212	50	pext(b	pext(b	NOUN
ejpam-5434	212	51	)	)	PUNCT
ejpam-5434	212	52	.	.	PUNCT
ejpam-5434	213	1	example	example	NOUN
ejpam-5434	214	1	3	3	X
ejpam-5434	214	2	.	.	PUNCT
ejpam-5434	214	3	let	let	VERB
ejpam-5434	214	4	u	u	PRON
ejpam-5434	214	5	=	=	X
ejpam-5434	214	6	{	{	PUNCT
ejpam-5434	214	7	a	a	PRON
ejpam-5434	214	8	,	,	PUNCT
ejpam-5434	214	9	b	b	NOUN
ejpam-5434	214	10	,	,	PUNCT
ejpam-5434	214	11	c	c	NOUN
ejpam-5434	214	12	,	,	PUNCT
ejpam-5434	214	13	d	d	NOUN
ejpam-5434	214	14	}	}	PUNCT
ejpam-5434	214	15	,	,	PUNCT
ejpam-5434	214	16	u\r	u\r	X
ejpam-5434	214	17	=	=	PRON
ejpam-5434	214	18	{	{	PUNCT
ejpam-5434	214	19	{	{	PUNCT
ejpam-5434	214	20	a	a	PROPN
ejpam-5434	214	21	,	,	PUNCT
ejpam-5434	214	22	b	b	NOUN
ejpam-5434	214	23	}	}	PUNCT
ejpam-5434	214	24	,	,	PUNCT
ejpam-5434	214	25	{	{	PUNCT
ejpam-5434	214	26	c	c	X
ejpam-5434	214	27	,	,	PUNCT
ejpam-5434	214	28	d	d	NOUN
ejpam-5434	214	29	}	}	PUNCT
ejpam-5434	214	30	}	}	PUNCT
ejpam-5434	214	31	,	,	PUNCT
ejpam-5434	214	32	x	x	X
ejpam-5434	214	33	=	=	PRON
ejpam-5434	214	34	{	{	PUNCT
ejpam-5434	214	35	b	b	NOUN
ejpam-5434	214	36	,	,	PUNCT
ejpam-5434	214	37	c	c	NOUN
ejpam-5434	214	38	}	}	PUNCT
ejpam-5434	214	39	,	,	PUNCT
ejpam-5434	214	40	τr(x	τr(x	NUM
ejpam-5434	214	41	)	)	PUNCT
ejpam-5434	215	1	=	=	PRON
ejpam-5434	215	2	{	{	PUNCT
ejpam-5434	215	3	u	u	NOUN
ejpam-5434	215	4	,	,	PUNCT
ejpam-5434	215	5	∅	∅	NOUN
ejpam-5434	215	6	,	,	PUNCT
ejpam-5434	215	7	{	{	PUNCT
ejpam-5434	215	8	b	b	NOUN
ejpam-5434	215	9	,	,	PUNCT
ejpam-5434	215	10	c	c	NOUN
ejpam-5434	215	11	}	}	PUNCT
ejpam-5434	215	12	}	}	PUNCT
ejpam-5434	215	13	,	,	PUNCT
ejpam-5434	215	14	µ	µ	X
ejpam-5434	215	15	=	=	SYM
ejpam-5434	215	16	{	{	PUNCT
ejpam-5434	215	17	b	b	PROPN
ejpam-5434	215	18	,	,	PUNCT
ejpam-5434	215	19	d	d	NOUN
ejpam-5434	215	20	}	}	PUNCT
ejpam-5434	215	21	and	and	CCONJ
ejpam-5434	215	22	µr(x	µr(x	NUM
ejpam-5434	215	23	)	)	PUNCT
ejpam-5434	215	24	=	=	SYM
ejpam-5434	215	25	{	{	PUNCT
ejpam-5434	215	26	u	u	NOUN
ejpam-5434	215	27	,	,	PUNCT
ejpam-5434	215	28	∅	∅	NOUN
ejpam-5434	215	29	,	,	PUNCT
ejpam-5434	215	30	{	{	PUNCT
ejpam-5434	215	31	b	b	NOUN
ejpam-5434	215	32	}	}	PUNCT
ejpam-5434	215	33	,	,	PUNCT
ejpam-5434	215	34	{	{	PUNCT
ejpam-5434	215	35	b	b	X
ejpam-5434	215	36	,	,	PUNCT
ejpam-5434	215	37	c	c	NOUN
ejpam-5434	215	38	}	}	PUNCT
ejpam-5434	215	39	,	,	PUNCT
ejpam-5434	215	40	{	{	PUNCT
ejpam-5434	215	41	b	b	X
ejpam-5434	215	42	,	,	PUNCT
ejpam-5434	215	43	d	d	NOUN
ejpam-5434	215	44	}	}	PUNCT
ejpam-5434	215	45	,	,	PUNCT
ejpam-5434	215	46	{	{	PUNCT
ejpam-5434	215	47	b	b	X
ejpam-5434	215	48	,	,	PUNCT
ejpam-5434	215	49	c	c	NOUN
ejpam-5434	215	50	,	,	PUNCT
ejpam-5434	215	51	d	d	NOUN
ejpam-5434	215	52	}	}	PUNCT
ejpam-5434	215	53	}	}	PUNCT
ejpam-5434	215	54	.	.	PUNCT
ejpam-5434	216	1	mic	mic	ADJ
ejpam-5434	216	2	-	-	PUNCT
ejpam-5434	216	3	po(u	po(u	ADJ
ejpam-5434	216	4	)	)	PUNCT
ejpam-5434	216	5	=	=	PRON
ejpam-5434	216	6	{	{	PUNCT
ejpam-5434	216	7	u	u	NOUN
ejpam-5434	216	8	,	,	PUNCT
ejpam-5434	216	9	∅	∅	NOUN
ejpam-5434	216	10	,	,	PUNCT
ejpam-5434	216	11	{	{	PUNCT
ejpam-5434	216	12	b	b	NOUN
ejpam-5434	216	13	}	}	PUNCT
ejpam-5434	216	14	,	,	PUNCT
ejpam-5434	216	15	{	{	PUNCT
ejpam-5434	216	16	a	a	DET
ejpam-5434	216	17	,	,	PUNCT
ejpam-5434	216	18	b	b	NOUN
ejpam-5434	216	19	}	}	PUNCT
ejpam-5434	216	20	,	,	PUNCT
ejpam-5434	216	21	{	{	PUNCT
ejpam-5434	216	22	b	b	X
ejpam-5434	216	23	,	,	PUNCT
ejpam-5434	216	24	c	c	NOUN
ejpam-5434	216	25	}	}	PUNCT
ejpam-5434	216	26	,	,	PUNCT
ejpam-5434	216	27	{	{	PUNCT
ejpam-5434	216	28	b	b	X
ejpam-5434	216	29	,	,	PUNCT
ejpam-5434	216	30	d	d	NOUN
ejpam-5434	216	31	}	}	PUNCT
ejpam-5434	216	32	,	,	PUNCT
ejpam-5434	216	33	{	{	PUNCT
ejpam-5434	216	34	a	a	DET
ejpam-5434	216	35	,	,	PUNCT
ejpam-5434	216	36	b	b	NOUN
ejpam-5434	216	37	,	,	PUNCT
ejpam-5434	216	38	c	c	NOUN
ejpam-5434	216	39	}	}	PUNCT
ejpam-5434	216	40	,	,	PUNCT
ejpam-5434	216	41	{	{	PUNCT
ejpam-5434	216	42	b	b	X
ejpam-5434	216	43	,	,	PUNCT
ejpam-5434	216	44	c	c	NOUN
ejpam-5434	216	45	,	,	PUNCT
ejpam-5434	216	46	d	d	NOUN
ejpam-5434	216	47	}	}	PUNCT
ejpam-5434	216	48	,	,	PUNCT
ejpam-5434	216	49	{	{	PUNCT
ejpam-5434	216	50	a	a	DET
ejpam-5434	216	51	,	,	PUNCT
ejpam-5434	216	52	b	b	NOUN
ejpam-5434	216	53	,	,	PUNCT
ejpam-5434	216	54	d	d	NOUN
ejpam-5434	216	55	}	}	PUNCT
ejpam-5434	216	56	}	}	PUNCT
ejpam-5434	216	57	.	.	PUNCT
ejpam-5434	217	1	let	let	VERB
ejpam-5434	217	2	a	a	DET
ejpam-5434	217	3	=	=	X
ejpam-5434	217	4	{	{	PUNCT
ejpam-5434	217	5	c	c	NOUN
ejpam-5434	217	6	,	,	PUNCT
ejpam-5434	217	7	d	d	NOUN
ejpam-5434	217	8	,	,	PUNCT
ejpam-5434	217	9	a	a	PRON
ejpam-5434	217	10	}	}	PUNCT
ejpam-5434	217	11	and	and	CCONJ
ejpam-5434	217	12	b	b	X
ejpam-5434	217	13	=	=	SYM
ejpam-5434	217	14	{	{	PUNCT
ejpam-5434	217	15	c	c	NOUN
ejpam-5434	217	16	,	,	PUNCT
ejpam-5434	217	17	d	d	NOUN
ejpam-5434	217	18	}	}	PUNCT
ejpam-5434	217	19	.	.	PUNCT
ejpam-5434	218	1	then	then	ADV
ejpam-5434	218	2	mic	mic	ADJ
ejpam-5434	218	3	-	-	PUNCT
ejpam-5434	218	4	pext(a	pext(a	NOUN
ejpam-5434	218	5	)	)	PUNCT
ejpam-5434	218	6	=	=	PUNCT
ejpam-5434	218	7	{	{	PUNCT
ejpam-5434	218	8	b	b	NOUN
ejpam-5434	218	9	}	}	PUNCT
ejpam-5434	218	10	and	and	CCONJ
ejpam-5434	218	11	mic	mic	ADJ
ejpam-5434	218	12	-	-	PUNCT
ejpam-5434	218	13	pext(b	pext(b	NOUN
ejpam-5434	218	14	)	)	PUNCT
ejpam-5434	218	15	=	=	NOUN
ejpam-5434	218	16	{	{	PUNCT
ejpam-5434	218	17	a	a	DET
ejpam-5434	218	18	,	,	PUNCT
ejpam-5434	218	19	b	b	NOUN
ejpam-5434	218	20	}	}	PUNCT
ejpam-5434	218	21	.	.	PUNCT
ejpam-5434	219	1	mic	mic	ADJ
ejpam-5434	219	2	-	-	PUNCT
ejpam-5434	219	3	pext(a	pext(a	NOUN
ejpam-5434	219	4	∪	∪	NOUN
ejpam-5434	219	5	b	b	NOUN
ejpam-5434	219	6	)	)	PUNCT
ejpam-5434	219	7	=	=	PUNCT
ejpam-5434	219	8	{	{	PUNCT
ejpam-5434	219	9	b	b	NOUN
ejpam-5434	219	10	}	}	PUNCT
ejpam-5434	219	11	.	.	PUNCT
ejpam-5434	220	1	⇒	⇒	PROPN
ejpam-5434	220	2	mic	mic	ADJ
ejpam-5434	220	3	-	-	PUNCT
ejpam-5434	220	4	pext(a	pext(a	NOUN
ejpam-5434	220	5	)	)	PUNCT
ejpam-5434	220	6	∪	∪	ADP
ejpam-5434	220	7	mic	mic	ADJ
ejpam-5434	220	8	-	-	PUNCT
ejpam-5434	220	9	pext(b	pext(b	NOUN
ejpam-5434	220	10	)	)	PUNCT
ejpam-5434	220	11	̸⊂	̸⊂	ADV
ejpam-5434	220	12	mic	mic	ADJ
ejpam-5434	220	13	-	-	PUNCT
ejpam-5434	220	14	pext(a	pext(a	NOUN
ejpam-5434	220	15	∪	∪	NOUN
ejpam-5434	220	16	b	b	NOUN
ejpam-5434	220	17	)	)	PUNCT
ejpam-5434	220	18	and	and	CCONJ
ejpam-5434	220	19	mic	mic	ADJ
ejpam-5434	220	20	-	-	PUNCT
ejpam-5434	220	21	pext(a	pext(a	NOUN
ejpam-5434	220	22	∩	∩	ADJ
ejpam-5434	220	23	b	b	NOUN
ejpam-5434	220	24	)	)	PUNCT
ejpam-5434	220	25	=	=	NOUN
ejpam-5434	220	26	{	{	PUNCT
ejpam-5434	220	27	a	a	DET
ejpam-5434	220	28	,	,	PUNCT
ejpam-5434	220	29	b	b	NOUN
ejpam-5434	220	30	}	}	PUNCT
ejpam-5434	220	31	which	which	PRON
ejpam-5434	220	32	implies	imply	VERB
ejpam-5434	220	33	mic	mic	ADJ
ejpam-5434	220	34	-	-	PUNCT
ejpam-5434	220	35	pext(a	pext(a	NOUN
ejpam-5434	220	36	∩	∩	ADJ
ejpam-5434	220	37	b	b	X
ejpam-5434	220	38	)	)	PUNCT
ejpam-5434	220	39	̸⊂	̸⊂	ADV
ejpam-5434	220	40	mic	mic	ADJ
ejpam-5434	220	41	-	-	PUNCT
ejpam-5434	220	42	pext(a	pext(a	NOUN
ejpam-5434	220	43	)	)	PUNCT
ejpam-5434	220	44	∩	∩	ADJ
ejpam-5434	220	45	mic	mic	NOUN
ejpam-5434	220	46	-	-	PUNCT
ejpam-5434	220	47	pext(b	pext(b	NOUN
ejpam-5434	220	48	)	)	PUNCT
ejpam-5434	220	49	.	.	PUNCT
ejpam-5434	221	1	theorem	theorem	VERB
ejpam-5434	221	2	6	6	NUM
ejpam-5434	221	3	.	.	PUNCT
ejpam-5434	221	4	mic	mic	ADJ
ejpam-5434	221	5	-	-	PUNCT
ejpam-5434	221	6	pfr(a	pfr(a	NOUN
ejpam-5434	221	7	)	)	PUNCT
ejpam-5434	221	8	∩	∩	ADJ
ejpam-5434	221	9	mic	mic	ADJ
ejpam-5434	221	10	-	-	PUNCT
ejpam-5434	221	11	pext(a	pext(a	NOUN
ejpam-5434	221	12	)	)	PUNCT
ejpam-5434	221	13	=	=	PUNCT
ejpam-5434	221	14	∅.	∅.	PRON
ejpam-5434	221	15	proof	proof	NOUN
ejpam-5434	221	16	:	:	PUNCT
ejpam-5434	221	17	let	let	VERB
ejpam-5434	221	18	x	x	X
ejpam-5434	221	19	∈	∈	PROPN
ejpam-5434	221	20	mic	mic	ADJ
ejpam-5434	221	21	-	-	PUNCT
ejpam-5434	221	22	pfr(a	pfr(a	NOUN
ejpam-5434	221	23	)	)	PUNCT
ejpam-5434	221	24	i.e.	i.e.	X
ejpam-5434	221	25	,	,	PUNCT
ejpam-5434	221	26	x	x	SYM
ejpam-5434	221	27	∈	∈	PROPN
ejpam-5434	221	28	(	(	PUNCT
ejpam-5434	221	29	mic	mic	ADJ
ejpam-5434	221	30	-	-	PUNCT
ejpam-5434	221	31	pcl(a	pcl(a	NOUN
ejpam-5434	221	32	)	)	PUNCT
ejpam-5434	221	33	−	−	PROPN
ejpam-5434	221	34	mic	mic	ADJ
ejpam-5434	221	35	-	-	PUNCT
ejpam-5434	221	36	pint(a	pint(a	NOUN
ejpam-5434	221	37	)	)	PUNCT
ejpam-5434	221	38	)	)	PUNCT
ejpam-5434	221	39	.	.	PUNCT
ejpam-5434	222	1	if	if	SCONJ
ejpam-5434	222	2	x	x	SYM
ejpam-5434	222	3	∈	∈	PROPN
ejpam-5434	222	4	mic	mic	NOUN
ejpam-5434	222	5	-	-	PUNCT
ejpam-5434	222	6	pcl(a	pcl(a	NOUN
ejpam-5434	222	7	)	)	PUNCT
ejpam-5434	222	8	then	then	ADV
ejpam-5434	222	9	x	x	SYM
ejpam-5434	222	10	/∈	/∈	PUNCT
ejpam-5434	222	11	mic	mic	ADJ
ejpam-5434	222	12	-	-	PUNCT
ejpam-5434	222	13	pint(a	pint(a	NOUN
ejpam-5434	222	14	)	)	PUNCT
ejpam-5434	222	15	.	.	PUNCT
ejpam-5434	223	1	we	we	PRON
ejpam-5434	223	2	know	know	VERB
ejpam-5434	223	3	that	that	SCONJ
ejpam-5434	223	4	mic	mic	ADJ
ejpam-5434	223	5	-	-	PUNCT
ejpam-5434	223	6	pcl(a	pcl(a	NOUN
ejpam-5434	223	7	)	)	PUNCT
ejpam-5434	223	8	∩	∩	ADJ
ejpam-5434	223	9	mic	mic	NOUN
ejpam-5434	223	10	-	-	PUNCT
ejpam-5434	223	11	pint(u	pint(u	NUM
ejpam-5434	223	12	−	−	NOUN
ejpam-5434	223	13	a	a	X
ejpam-5434	223	14	)	)	PUNCT
ejpam-5434	223	15	=	=	PUNCT
ejpam-5434	223	16	∅.	∅.	VERB
ejpam-5434	223	17	therefore	therefore	ADV
ejpam-5434	223	18	x	x	NOUN
ejpam-5434	223	19	/∈	/∈	INTJ
ejpam-5434	223	20	mic	mic	ADJ
ejpam-5434	223	21	-	-	PUNCT
ejpam-5434	223	22	pint(u	pint(u	NUM
ejpam-5434	223	23	−	−	NOUN
ejpam-5434	223	24	a	a	PRON
ejpam-5434	223	25	)	)	PUNCT
ejpam-5434	223	26	implies	imply	VERB
ejpam-5434	223	27	x	x	X
ejpam-5434	223	28	/∈	/∈	PUNCT
ejpam-5434	223	29	mic	mic	ADJ
ejpam-5434	223	30	-	-	PUNCT
ejpam-5434	223	31	pext(a	pext(a	NOUN
ejpam-5434	223	32	)	)	PUNCT
ejpam-5434	223	33	.	.	PUNCT
ejpam-5434	224	1	hence	hence	ADV
ejpam-5434	224	2	mic	mic	ADV
ejpam-5434	224	3	-	-	PUNCT
ejpam-5434	224	4	pfr(a	pfr(a	NOUN
ejpam-5434	224	5	)	)	PUNCT
ejpam-5434	224	6	∩	∩	ADJ
ejpam-5434	224	7	mic	mic	ADJ
ejpam-5434	224	8	-	-	PUNCT
ejpam-5434	224	9	pext(a	pext(a	NOUN
ejpam-5434	224	10	)	)	PUNCT
ejpam-5434	224	11	=	=	PUNCT
ejpam-5434	224	12	∅.	∅.	PRON
ejpam-5434	224	13	4	4	NUM
ejpam-5434	224	14	.	.	PUNCT
ejpam-5434	224	15	micro	micro	ADJ
ejpam-5434	224	16	pre	pre	NOUN
ejpam-5434	224	17	-	-	NOUN
ejpam-5434	224	18	border	border	ADJ
ejpam-5434	224	19	in	in	ADP
ejpam-5434	224	20	this	this	DET
ejpam-5434	224	21	section	section	NOUN
ejpam-5434	224	22	,	,	PUNCT
ejpam-5434	224	23	we	we	PRON
ejpam-5434	224	24	define	define	VERB
ejpam-5434	224	25	and	and	CCONJ
ejpam-5434	224	26	study	study	VERB
ejpam-5434	224	27	the	the	DET
ejpam-5434	224	28	notions	notion	NOUN
ejpam-5434	224	29	of	of	ADP
ejpam-5434	224	30	micro	micro	ADJ
ejpam-5434	224	31	pre	pre	NOUN
ejpam-5434	224	32	-	-	NOUN
ejpam-5434	224	33	border	border	NOUN
ejpam-5434	224	34	and	and	CCONJ
ejpam-5434	224	35	obtain	obtain	VERB
ejpam-5434	224	36	its	its	PRON
ejpam-5434	224	37	basic	basic	ADJ
ejpam-5434	224	38	properties	property	NOUN
ejpam-5434	224	39	.	.	PUNCT
ejpam-5434	225	1	definition	definition	NOUN
ejpam-5434	225	2	15	15	NUM
ejpam-5434	225	3	.	.	PUNCT
ejpam-5434	226	1	let	let	VERB
ejpam-5434	226	2	a	a	DET
ejpam-5434	226	3	be	be	AUX
ejpam-5434	226	4	a	a	DET
ejpam-5434	226	5	subset	subset	NOUN
ejpam-5434	226	6	of	of	ADP
ejpam-5434	226	7	a	a	DET
ejpam-5434	226	8	space	space	NOUN
ejpam-5434	227	1	u.	u.	NOUN
ejpam-5434	228	1	then	then	ADV
ejpam-5434	228	2	the	the	DET
ejpam-5434	228	3	micro	micro	ADJ
ejpam-5434	228	4	pre	pre	NOUN
ejpam-5434	228	5	-	-	NOUN
ejpam-5434	228	6	border	border	NOUN
ejpam-5434	228	7	of	of	ADP
ejpam-5434	228	8	a	a	PRON
ejpam-5434	228	9	is	be	AUX
ejpam-5434	228	10	defined	define	VERB
ejpam-5434	228	11	as	as	ADP
ejpam-5434	228	12	mic	mic	ADJ
ejpam-5434	228	13	-	-	PUNCT
ejpam-5434	228	14	pbr(a	pbr(a	NOUN
ejpam-5434	228	15	)	)	PUNCT
ejpam-5434	228	16	=	=	NOUN
ejpam-5434	228	17	a	a	DET
ejpam-5434	228	18	−	−	PROPN
ejpam-5434	228	19	mic	mic	ADJ
ejpam-5434	228	20	-	-	PUNCT
ejpam-5434	228	21	pint(a	pint(a	NOUN
ejpam-5434	228	22	)	)	PUNCT
ejpam-5434	228	23	.	.	PUNCT
ejpam-5434	229	1	theorem	theorem	VERB
ejpam-5434	229	2	7	7	NUM
ejpam-5434	229	3	.	.	X
ejpam-5434	229	4	for	for	ADP
ejpam-5434	229	5	a	a	DET
ejpam-5434	229	6	subset	subset	NOUN
ejpam-5434	229	7	of	of	ADP
ejpam-5434	229	8	u	u	NOUN
ejpam-5434	229	9	,	,	PUNCT
ejpam-5434	229	10	the	the	DET
ejpam-5434	229	11	following	follow	VERB
ejpam-5434	229	12	statements	statement	NOUN
ejpam-5434	229	13	holds	hold	VERB
ejpam-5434	229	14	.	.	PUNCT
ejpam-5434	230	1	s.	s.	PROPN
ejpam-5434	230	2	stanley	stanley	PROPN
ejpam-5434	230	3	roshan	roshan	PROPN
ejpam-5434	230	4	et	et	PROPN
ejpam-5434	230	5	al	al	PROPN
ejpam-5434	230	6	.	.	PUNCT
ejpam-5434	230	7	/	/	SYM
ejpam-5434	230	8	eur	eur	PROPN
ejpam-5434	230	9	.	.	PUNCT
ejpam-5434	231	1	j.	j.	PROPN
ejpam-5434	231	2	pure	pure	PROPN
ejpam-5434	231	3	appl	appl	PROPN
ejpam-5434	231	4	.	.	PROPN
ejpam-5434	231	5	math	math	PROPN
ejpam-5434	231	6	,	,	PUNCT
ejpam-5434	231	7	17	17	NUM
ejpam-5434	231	8	(	(	PUNCT
ejpam-5434	231	9	4	4	NUM
ejpam-5434	231	10	)	)	PUNCT
ejpam-5434	231	11	(	(	PUNCT
ejpam-5434	231	12	2024	2024	NUM
ejpam-5434	231	13	)	)	PUNCT
ejpam-5434	231	14	,	,	PUNCT
ejpam-5434	231	15	3156	3156	NUM
ejpam-5434	231	16	-	-	SYM
ejpam-5434	231	17	3166	3166	NUM
ejpam-5434	231	18	3163	3163	NUM
ejpam-5434	231	19	(	(	PUNCT
ejpam-5434	231	20	i	i	NOUN
ejpam-5434	231	21	)	)	PUNCT
ejpam-5434	231	22	mic	mic	ADJ
ejpam-5434	231	23	-	-	PUNCT
ejpam-5434	231	24	pbr(a	pbr(a	NOUN
ejpam-5434	231	25	)	)	PUNCT
ejpam-5434	231	26	⊆	⊆	NUM
ejpam-5434	231	27	mic	mic	NOUN
ejpam-5434	231	28	-	-	PUNCT
ejpam-5434	231	29	br(a	br(a	NOUN
ejpam-5434	231	30	)	)	PUNCT
ejpam-5434	231	31	where	where	SCONJ
ejpam-5434	231	32	br(a	br(a	PUNCT
ejpam-5434	231	33	)	)	PUNCT
ejpam-5434	231	34	denote	denote	VERB
ejpam-5434	231	35	the	the	DET
ejpam-5434	231	36	border	border	NOUN
ejpam-5434	231	37	of	of	ADP
ejpam-5434	231	38	a.	a.	PROPN
ejpam-5434	231	39	(	(	PUNCT
ejpam-5434	231	40	ii	ii	PROPN
ejpam-5434	231	41	)	)	PUNCT
ejpam-5434	231	42	a	a	DET
ejpam-5434	231	43	=	=	SYM
ejpam-5434	231	44	mic	mic	ADJ
ejpam-5434	231	45	-	-	PUNCT
ejpam-5434	231	46	pint(a	pint(a	NOUN
ejpam-5434	231	47	)	)	PUNCT
ejpam-5434	231	48	∪	∪	ADP
ejpam-5434	231	49	mic	mic	ADJ
ejpam-5434	231	50	-	-	PUNCT
ejpam-5434	231	51	pbr(a	pbr(a	NOUN
ejpam-5434	231	52	)	)	PUNCT
ejpam-5434	231	53	.	.	PUNCT
ejpam-5434	232	1	(	(	PUNCT
ejpam-5434	232	2	iii	iii	X
ejpam-5434	232	3	)	)	PUNCT
ejpam-5434	232	4	mic	mic	ADJ
ejpam-5434	232	5	-	-	PUNCT
ejpam-5434	232	6	pint(a	pint(a	NOUN
ejpam-5434	232	7	)	)	PUNCT
ejpam-5434	232	8	∩	∩	ADJ
ejpam-5434	232	9	mic	mic	ADJ
ejpam-5434	232	10	-	-	PUNCT
ejpam-5434	232	11	pbr(a	pbr(a	NOUN
ejpam-5434	232	12	)	)	PUNCT
ejpam-5434	233	1	=	=	SYM
ejpam-5434	233	2	∅.	∅.	X
ejpam-5434	233	3	(	(	PUNCT
ejpam-5434	233	4	iv	iv	X
ejpam-5434	233	5	)	)	PUNCT
ejpam-5434	233	6	if	if	SCONJ
ejpam-5434	233	7	a	a	PRON
ejpam-5434	233	8	is	be	AUX
ejpam-5434	233	9	mic	mic	ADJ
ejpam-5434	233	10	-	-	PUNCT
ejpam-5434	233	11	po	po	NOUN
ejpam-5434	233	12	then	then	ADV
ejpam-5434	233	13	mic	mic	ADJ
ejpam-5434	233	14	-	-	PUNCT
ejpam-5434	233	15	pbr(a	pbr(a	NOUN
ejpam-5434	233	16	)	)	PUNCT
ejpam-5434	233	17	=	=	PUNCT
ejpam-5434	233	18	∅.	∅.	X
ejpam-5434	233	19	(	(	PUNCT
ejpam-5434	233	20	v	v	NOUN
ejpam-5434	233	21	)	)	PUNCT
ejpam-5434	233	22	mic	mic	ADJ
ejpam-5434	233	23	-	-	PUNCT
ejpam-5434	233	24	pint(mic	pint(mic	ADJ
ejpam-5434	233	25	-	-	PUNCT
ejpam-5434	233	26	pbr(a	pbr(a	NOUN
ejpam-5434	233	27	)	)	PUNCT
ejpam-5434	233	28	)	)	PUNCT
ejpam-5434	234	1	=	=	PUNCT
ejpam-5434	234	2	∅.	∅.	X
ejpam-5434	234	3	(	(	PUNCT
ejpam-5434	234	4	vi	vi	NOUN
ejpam-5434	234	5	)	)	PUNCT
ejpam-5434	234	6	mic	mic	ADJ
ejpam-5434	234	7	-	-	PUNCT
ejpam-5434	234	8	pbr(mic	pbr(mic	ADJ
ejpam-5434	234	9	-	-	PUNCT
ejpam-5434	234	10	pbr(a	pbr(a	NOUN
ejpam-5434	234	11	)	)	PUNCT
ejpam-5434	234	12	)	)	PUNCT
ejpam-5434	235	1	=	=	SYM
ejpam-5434	235	2	mic	mic	ADJ
ejpam-5434	235	3	-	-	PUNCT
ejpam-5434	235	4	pbr(a	pbr(a	NOUN
ejpam-5434	235	5	)	)	PUNCT
ejpam-5434	235	6	.	.	PUNCT
ejpam-5434	236	1	(	(	PUNCT
ejpam-5434	236	2	vii	vii	PROPN
ejpam-5434	236	3	)	)	PUNCT
ejpam-5434	236	4	mic	mic	ADJ
ejpam-5434	236	5	-	-	PUNCT
ejpam-5434	236	6	pbr(a	pbr(a	NOUN
ejpam-5434	236	7	)	)	PUNCT
ejpam-5434	236	8	=	=	NOUN
ejpam-5434	237	1	a	a	DET
ejpam-5434	237	2	∩	∩	ADJ
ejpam-5434	237	3	mic	mic	ADJ
ejpam-5434	237	4	-	-	PUNCT
ejpam-5434	237	5	pcl(u	pcl(u	NOUN
ejpam-5434	237	6	−a	−a	NOUN
ejpam-5434	237	7	)	)	PUNCT
ejpam-5434	237	8	.	.	PUNCT
ejpam-5434	238	1	proof	proof	NOUN
ejpam-5434	238	2	:	:	PUNCT
ejpam-5434	238	3	(	(	PUNCT
ejpam-5434	238	4	i	i	NOUN
ejpam-5434	238	5	)	)	PUNCT
ejpam-5434	238	6	obvious	obvious	ADJ
ejpam-5434	238	7	from	from	ADP
ejpam-5434	238	8	the	the	DET
ejpam-5434	238	9	definitions	definition	NOUN
ejpam-5434	238	10	of	of	ADP
ejpam-5434	238	11	micro	micro	ADJ
ejpam-5434	238	12	pre	pre	ADJ
ejpam-5434	238	13	-	-	ADJ
ejpam-5434	238	14	border	border	ADJ
ejpam-5434	238	15	and	and	CCONJ
ejpam-5434	238	16	micro	micro	ADJ
ejpam-5434	238	17	border	border	NOUN
ejpam-5434	238	18	of	of	ADP
ejpam-5434	238	19	a.	a.	PROPN
ejpam-5434	238	20	(	(	PUNCT
ejpam-5434	238	21	ii	ii	PROPN
ejpam-5434	238	22	)	)	PUNCT
ejpam-5434	238	23	obvious	obvious	ADJ
ejpam-5434	238	24	from	from	ADP
ejpam-5434	238	25	the	the	DET
ejpam-5434	238	26	definitions	definition	NOUN
ejpam-5434	238	27	of	of	ADP
ejpam-5434	238	28	micro	micro	ADJ
ejpam-5434	238	29	pre	pre	NOUN
ejpam-5434	238	30	-	-	NOUN
ejpam-5434	238	31	border	border	NOUN
ejpam-5434	238	32	of	of	ADP
ejpam-5434	238	33	a.	a.	NOUN
ejpam-5434	238	34	(	(	PUNCT
ejpam-5434	238	35	iii	iii	NOUN
ejpam-5434	238	36	)	)	PUNCT
ejpam-5434	238	37	obvious	obvious	ADJ
ejpam-5434	238	38	from	from	ADP
ejpam-5434	238	39	the	the	DET
ejpam-5434	238	40	definitions	definition	NOUN
ejpam-5434	238	41	of	of	ADP
ejpam-5434	238	42	micro	micro	ADJ
ejpam-5434	238	43	pre	pre	NOUN
ejpam-5434	238	44	-	-	NOUN
ejpam-5434	238	45	border	border	NOUN
ejpam-5434	238	46	of	of	ADP
ejpam-5434	238	47	a.	a.	NOUN
ejpam-5434	238	48	(	(	PUNCT
ejpam-5434	238	49	iv	iv	X
ejpam-5434	238	50	)	)	PUNCT
ejpam-5434	238	51	if	if	SCONJ
ejpam-5434	238	52	a	a	PRON
ejpam-5434	238	53	is	be	AUX
ejpam-5434	238	54	mic	mic	ADJ
ejpam-5434	238	55	-	-	PUNCT
ejpam-5434	238	56	po	po	NOUN
ejpam-5434	238	57	,	,	PUNCT
ejpam-5434	238	58	then	then	ADV
ejpam-5434	238	59	a	a	DET
ejpam-5434	238	60	=	=	PUNCT
ejpam-5434	238	61	mic	mic	ADJ
ejpam-5434	238	62	-	-	PUNCT
ejpam-5434	238	63	pint(a	pint(a	NOUN
ejpam-5434	238	64	)	)	PUNCT
ejpam-5434	238	65	.	.	PUNCT
ejpam-5434	239	1	hence	hence	ADV
ejpam-5434	239	2	the	the	DET
ejpam-5434	239	3	result	result	NOUN
ejpam-5434	239	4	follows	follow	VERB
ejpam-5434	239	5	.	.	PUNCT
ejpam-5434	240	1	(	(	PUNCT
ejpam-5434	240	2	v	v	NOUN
ejpam-5434	240	3	)	)	PUNCT
ejpam-5434	240	4	if	if	SCONJ
ejpam-5434	240	5	x	x	PROPN
ejpam-5434	240	6	∈	∈	PROPN
ejpam-5434	240	7	mic	mic	ADJ
ejpam-5434	240	8	-	-	PUNCT
ejpam-5434	240	9	pint(mic	pint(mic	ADJ
ejpam-5434	240	10	-	-	PUNCT
ejpam-5434	240	11	pbr(a	pbr(a	NOUN
ejpam-5434	240	12	)	)	PUNCT
ejpam-5434	240	13	)	)	PUNCT
ejpam-5434	240	14	,	,	PUNCT
ejpam-5434	240	15	then	then	ADV
ejpam-5434	240	16	x	x	X
ejpam-5434	240	17	∈	∈	PROPN
ejpam-5434	240	18	mic	mic	NOUN
ejpam-5434	240	19	-	-	PUNCT
ejpam-5434	240	20	pbr(a	pbr(a	NOUN
ejpam-5434	240	21	)	)	PUNCT
ejpam-5434	240	22	.	.	PUNCT
ejpam-5434	241	1	now	now	ADV
ejpam-5434	241	2	,	,	PUNCT
ejpam-5434	241	3	mic	mic	ADJ
ejpam-5434	241	4	-	-	PUNCT
ejpam-5434	241	5	pbr(a	pbr(a	NOUN
ejpam-5434	241	6	)	)	PUNCT
ejpam-5434	241	7	⊂	⊂	PROPN
ejpam-5434	241	8	a	a	PRON
ejpam-5434	241	9	implies	imply	VERB
ejpam-5434	241	10	mic	mic	ADJ
ejpam-5434	241	11	-	-	PUNCT
ejpam-5434	241	12	pint(mic	pint(mic	ADJ
ejpam-5434	241	13	-	-	PUNCT
ejpam-5434	241	14	pbr(a	pbr(a	NOUN
ejpam-5434	241	15	)	)	PUNCT
ejpam-5434	241	16	)	)	PUNCT
ejpam-5434	242	1	⊂	⊂	PROPN
ejpam-5434	242	2	mic	mic	ADJ
ejpam-5434	242	3	-	-	PUNCT
ejpam-5434	242	4	pint(a	pint(a	NOUN
ejpam-5434	242	5	)	)	PUNCT
ejpam-5434	242	6	.	.	PUNCT
ejpam-5434	243	1	hence	hence	ADV
ejpam-5434	243	2	x	x	SYM
ejpam-5434	243	3	∈	∈	PROPN
ejpam-5434	243	4	mic	mic	ADJ
ejpam-5434	243	5	-	-	PUNCT
ejpam-5434	243	6	pint(a	pint(a	NOUN
ejpam-5434	243	7	)	)	PUNCT
ejpam-5434	243	8	which	which	PRON
ejpam-5434	243	9	is	be	AUX
ejpam-5434	243	10	a	a	DET
ejpam-5434	243	11	contradiction	contradiction	NOUN
ejpam-5434	243	12	to	to	ADP
ejpam-5434	243	13	x	x	SYM
ejpam-5434	243	14	∈	∈	PROPN
ejpam-5434	243	15	mic	mic	ADJ
ejpam-5434	243	16	-	-	PUNCT
ejpam-5434	243	17	pbr(a	pbr(a	NOUN
ejpam-5434	243	18	)	)	PUNCT
ejpam-5434	243	19	.	.	PUNCT
ejpam-5434	244	1	thus	thus	ADV
ejpam-5434	244	2	mic	mic	ADJ
ejpam-5434	244	3	-	-	PUNCT
ejpam-5434	244	4	pint(mic	pint(mic	ADJ
ejpam-5434	244	5	-	-	PUNCT
ejpam-5434	244	6	pbr(a	pbr(a	NOUN
ejpam-5434	244	7	)	)	PUNCT
ejpam-5434	244	8	)	)	PUNCT
ejpam-5434	245	1	=	=	PUNCT
ejpam-5434	245	2	∅.	∅.	X
ejpam-5434	245	3	(	(	PUNCT
ejpam-5434	245	4	vi	vi	NOUN
ejpam-5434	245	5	)	)	PUNCT
ejpam-5434	245	6	mic	mic	ADJ
ejpam-5434	245	7	-	-	PUNCT
ejpam-5434	245	8	pbr(mic	pbr(mic	ADJ
ejpam-5434	245	9	-	-	PUNCT
ejpam-5434	245	10	pbr(a	pbr(a	NOUN
ejpam-5434	245	11	)	)	PUNCT
ejpam-5434	245	12	)	)	PUNCT
ejpam-5434	246	1	=	=	SYM
ejpam-5434	246	2	mic	mic	ADJ
ejpam-5434	246	3	-	-	PUNCT
ejpam-5434	246	4	pbr(a	pbr(a	ADJ
ejpam-5434	246	5	−	−	NOUN
ejpam-5434	246	6	mic	mic	ADJ
ejpam-5434	246	7	-	-	PUNCT
ejpam-5434	246	8	pint(a	pint(a	NOUN
ejpam-5434	246	9	)	)	PUNCT
ejpam-5434	246	10	)	)	PUNCT
ejpam-5434	247	1	=	=	PRON
ejpam-5434	247	2	(	(	PUNCT
ejpam-5434	247	3	a	a	DET
ejpam-5434	247	4	−	−	PROPN
ejpam-5434	247	5	mic	mic	ADJ
ejpam-5434	247	6	-	-	PUNCT
ejpam-5434	247	7	pint(a))−micpint(a	pint(a))−micpint(a	NOUN
ejpam-5434	247	8	−	−	NOUN
ejpam-5434	247	9	mic	mic	ADJ
ejpam-5434	247	10	-	-	PUNCT
ejpam-5434	247	11	pint(a	pint(a	NOUN
ejpam-5434	247	12	)	)	PUNCT
ejpam-5434	247	13	)	)	PUNCT
ejpam-5434	247	14	which	which	PRON
ejpam-5434	247	15	is	be	AUX
ejpam-5434	247	16	mic	mic	ADJ
ejpam-5434	247	17	-	-	PUNCT
ejpam-5434	247	18	pbr(a	pbr(a	NOUN
ejpam-5434	247	19	)	)	PUNCT
ejpam-5434	247	20	−	−	NOUN
ejpam-5434	247	21	∅	∅	NOUN
ejpam-5434	247	22	,	,	PUNCT
ejpam-5434	247	23	by	by	ADP
ejpam-5434	247	24	(	(	PUNCT
ejpam-5434	247	25	4	4	NUM
ejpam-5434	247	26	)	)	PUNCT
ejpam-5434	247	27	.	.	PUNCT
ejpam-5434	248	1	hence	hence	ADV
ejpam-5434	248	2	,	,	PUNCT
ejpam-5434	248	3	mic	mic	NOUN
ejpam-5434	248	4	-	-	PUNCT
ejpam-5434	248	5	pbr(micpbr(a	pbr(micpbr(a	NOUN
ejpam-5434	248	6	)	)	PUNCT
ejpam-5434	248	7	)	)	PUNCT
ejpam-5434	249	1	=	=	SYM
ejpam-5434	249	2	mic	mic	ADJ
ejpam-5434	249	3	-	-	PUNCT
ejpam-5434	249	4	pbr(a	pbr(a	NOUN
ejpam-5434	249	5	)	)	PUNCT
ejpam-5434	249	6	.	.	PUNCT
ejpam-5434	250	1	(	(	PUNCT
ejpam-5434	250	2	vii	vii	PROPN
ejpam-5434	250	3	)	)	PUNCT
ejpam-5434	250	4	mic	mic	ADJ
ejpam-5434	250	5	-	-	PUNCT
ejpam-5434	250	6	pbr(a	pbr(a	NOUN
ejpam-5434	250	7	)	)	PUNCT
ejpam-5434	250	8	=	=	NOUN
ejpam-5434	251	1	a	a	DET
ejpam-5434	251	2	−	−	PROPN
ejpam-5434	251	3	mic	mic	ADJ
ejpam-5434	251	4	-	-	PUNCT
ejpam-5434	251	5	pint(a	pint(a	NOUN
ejpam-5434	251	6	)	)	PUNCT
ejpam-5434	251	7	=	=	NOUN
ejpam-5434	251	8	a−(u−(mic	a−(u−(mic	ADJ
ejpam-5434	251	9	-	-	PUNCT
ejpam-5434	251	10	pcl(u−a	pcl(u−a	NOUN
ejpam-5434	251	11	)	)	PUNCT
ejpam-5434	251	12	)	)	PUNCT
ejpam-5434	251	13	)	)	PUNCT
ejpam-5434	252	1	=	=	PUNCT
ejpam-5434	252	2	a	a	DET
ejpam-5434	252	3	∩	∩	ADJ
ejpam-5434	252	4	mic	mic	ADJ
ejpam-5434	252	5	-	-	PUNCT
ejpam-5434	252	6	pcl(u−a	pcl(u−a	ADJ
ejpam-5434	252	7	)	)	PUNCT
ejpam-5434	252	8	.	.	PUNCT
ejpam-5434	253	1	theorem	theorem	VERB
ejpam-5434	253	2	8	8	NUM
ejpam-5434	253	3	.	.	PUNCT
ejpam-5434	254	1	for	for	ADP
ejpam-5434	254	2	a	a	DET
ejpam-5434	254	3	subset	subset	NOUN
ejpam-5434	254	4	of	of	ADP
ejpam-5434	254	5	u	u	NOUN
ejpam-5434	254	6	,	,	PUNCT
ejpam-5434	254	7	the	the	DET
ejpam-5434	254	8	following	follow	VERB
ejpam-5434	254	9	condition	condition	NOUN
ejpam-5434	254	10	hold	hold	NOUN
ejpam-5434	254	11	.	.	PUNCT
ejpam-5434	255	1	(	(	PUNCT
ejpam-5434	255	2	i	i	NOUN
ejpam-5434	255	3	)	)	PUNCT
ejpam-5434	255	4	mic	mic	ADJ
ejpam-5434	255	5	-	-	PUNCT
ejpam-5434	255	6	pbr(a	pbr(a	NOUN
ejpam-5434	255	7	)	)	PUNCT
ejpam-5434	255	8	⊆	⊆	NUM
ejpam-5434	255	9	mic	mic	ADJ
ejpam-5434	255	10	-	-	PUNCT
ejpam-5434	255	11	pfr(a	pfr(a	NOUN
ejpam-5434	255	12	)	)	PUNCT
ejpam-5434	255	13	.	.	PUNCT
ejpam-5434	256	1	(	(	PUNCT
ejpam-5434	256	2	ii	ii	NOUN
ejpam-5434	256	3	)	)	PUNCT
ejpam-5434	256	4	mic	mic	ADJ
ejpam-5434	256	5	-	-	PUNCT
ejpam-5434	256	6	pext(a	pext(a	NOUN
ejpam-5434	256	7	)	)	PUNCT
ejpam-5434	256	8	∩	∩	ADJ
ejpam-5434	256	9	mic	mic	ADJ
ejpam-5434	256	10	-	-	PUNCT
ejpam-5434	256	11	pbr(a	pbr(a	NOUN
ejpam-5434	256	12	)	)	PUNCT
ejpam-5434	256	13	=	=	PUNCT
ejpam-5434	256	14	∅.	∅.	NOUN
ejpam-5434	256	15	proof	proof	NOUN
ejpam-5434	256	16	:	:	PUNCT
ejpam-5434	256	17	(	(	PUNCT
ejpam-5434	256	18	i	i	NOUN
ejpam-5434	256	19	)	)	PUNCT
ejpam-5434	256	20	let	let	VERB
ejpam-5434	256	21	,	,	PUNCT
ejpam-5434	256	22	x	x	SYM
ejpam-5434	256	23	∈	∈	PROPN
ejpam-5434	256	24	mic	mic	ADJ
ejpam-5434	256	25	-	-	PUNCT
ejpam-5434	256	26	pbr(a	pbr(a	NOUN
ejpam-5434	256	27	)	)	PUNCT
ejpam-5434	256	28	i.e.	i.e.	X
ejpam-5434	256	29	,	,	PUNCT
ejpam-5434	256	30	x	x	SYM
ejpam-5434	256	31	∈	∈	VERB
ejpam-5434	256	32	a	a	DET
ejpam-5434	256	33	−	−	NOUN
ejpam-5434	256	34	mic	mic	ADJ
ejpam-5434	256	35	-	-	PUNCT
ejpam-5434	256	36	pint(a	pint(a	NOUN
ejpam-5434	256	37	)	)	PUNCT
ejpam-5434	256	38	.	.	PUNCT
ejpam-5434	257	1	by	by	ADP
ejpam-5434	257	2	theorem	theorem	NOUN
ejpam-5434	257	3	3.16	3.16	NUM
ejpam-5434	257	4	[	[	X
ejpam-5434	257	5	7	7	NUM
ejpam-5434	257	6	]	]	PUNCT
ejpam-5434	257	7	a	a	DET
ejpam-5434	257	8	=	=	PUNCT
ejpam-5434	257	9	mic	mic	ADJ
ejpam-5434	257	10	-	-	PUNCT
ejpam-5434	257	11	pint(a	pint(a	NOUN
ejpam-5434	257	12	)	)	PUNCT
ejpam-5434	257	13	if	if	SCONJ
ejpam-5434	257	14	a	a	PRON
ejpam-5434	257	15	is	be	AUX
ejpam-5434	257	16	mic	mic	ADJ
ejpam-5434	257	17	-	-	PUNCT
ejpam-5434	257	18	po	po	NOUN
ejpam-5434	257	19	.	.	PUNCT
ejpam-5434	258	1	if	if	SCONJ
ejpam-5434	258	2	a	a	PRON
ejpam-5434	258	3	is	be	AUX
ejpam-5434	258	4	not	not	PART
ejpam-5434	258	5	mic	mic	ADJ
ejpam-5434	258	6	-	-	PUNCT
ejpam-5434	258	7	po	po	NOUN
ejpam-5434	258	8	then	then	ADV
ejpam-5434	258	9	mic	mic	ADJ
ejpam-5434	258	10	-	-	PUNCT
ejpam-5434	258	11	pint(a	pint(a	NOUN
ejpam-5434	258	12	)	)	PUNCT
ejpam-5434	259	1	⊂	⊂	PROPN
ejpam-5434	259	2	a.	a.	NOUN
ejpam-5434	259	3	therefore	therefore	ADV
ejpam-5434	259	4	in	in	ADP
ejpam-5434	259	5	general	general	ADJ
ejpam-5434	259	6	mic	mic	ADJ
ejpam-5434	259	7	-	-	PUNCT
ejpam-5434	259	8	pint(a	pint(a	NOUN
ejpam-5434	259	9	)	)	PUNCT
ejpam-5434	259	10	⊆	⊆	NUM
ejpam-5434	259	11	a.	a.	NOUN
ejpam-5434	259	12	so	so	NOUN
ejpam-5434	259	13	x	x	SYM
ejpam-5434	259	14	∈	∈	PROPN
ejpam-5434	259	15	mic	mic	ADJ
ejpam-5434	259	16	-	-	PUNCT
ejpam-5434	259	17	pint(a	pint(a	NOUN
ejpam-5434	259	18	)	)	PUNCT
ejpam-5434	259	19	.	.	PUNCT
ejpam-5434	260	1	it	it	PRON
ejpam-5434	260	2	is	be	AUX
ejpam-5434	260	3	obvious	obvious	ADJ
ejpam-5434	260	4	that	that	SCONJ
ejpam-5434	260	5	if	if	SCONJ
ejpam-5434	260	6	x	x	PROPN
ejpam-5434	260	7	∈	∈	PROPN
ejpam-5434	260	8	mic	mic	ADJ
ejpam-5434	260	9	-	-	PUNCT
ejpam-5434	260	10	pint(a	pint(a	NOUN
ejpam-5434	260	11	)	)	PUNCT
ejpam-5434	260	12	then	then	ADV
ejpam-5434	260	13	x	x	X
ejpam-5434	260	14	/∈	/∈	PUNCT
ejpam-5434	260	15	mic	mic	ADJ
ejpam-5434	260	16	-	-	PUNCT
ejpam-5434	260	17	pcl(a	pcl(a	NOUN
ejpam-5434	260	18	)	)	PUNCT
ejpam-5434	260	19	.	.	PUNCT
ejpam-5434	261	1	therefore	therefore	ADV
ejpam-5434	261	2	x	x	X
ejpam-5434	261	3	∈	∈	PROPN
ejpam-5434	261	4	(	(	PUNCT
ejpam-5434	261	5	mic	mic	ADJ
ejpam-5434	261	6	-	-	PUNCT
ejpam-5434	261	7	pcl(a	pcl(a	NOUN
ejpam-5434	261	8	)	)	PUNCT
ejpam-5434	261	9	−	−	PROPN
ejpam-5434	261	10	mic	mic	ADJ
ejpam-5434	261	11	-	-	PUNCT
ejpam-5434	261	12	pint(a	pint(a	NOUN
ejpam-5434	261	13	)	)	PUNCT
ejpam-5434	261	14	)	)	PUNCT
ejpam-5434	261	15	implies	imply	VERB
ejpam-5434	261	16	x	x	PUNCT
ejpam-5434	261	17	∈	∈	PROPN
ejpam-5434	261	18	mic	mic	NOUN
ejpam-5434	261	19	-	-	PUNCT
ejpam-5434	261	20	pfr(a	pfr(a	NOUN
ejpam-5434	261	21	)	)	PUNCT
ejpam-5434	261	22	.	.	PUNCT
ejpam-5434	262	1	hence	hence	ADV
ejpam-5434	262	2	mic	mic	ADV
ejpam-5434	262	3	-	-	PUNCT
ejpam-5434	262	4	pbr(a	pbr(a	NOUN
ejpam-5434	262	5	)	)	PUNCT
ejpam-5434	262	6	⊆	⊆	NUM
ejpam-5434	262	7	mic	mic	ADJ
ejpam-5434	262	8	-	-	PUNCT
ejpam-5434	262	9	pfr(a	pfr(a	NOUN
ejpam-5434	262	10	)	)	PUNCT
ejpam-5434	262	11	.	.	PUNCT
ejpam-5434	263	1	(	(	PUNCT
ejpam-5434	263	2	ii	ii	X
ejpam-5434	263	3	)	)	PUNCT
ejpam-5434	263	4	let	let	VERB
ejpam-5434	263	5	x	x	X
ejpam-5434	263	6	∈	∈	PROPN
ejpam-5434	263	7	mic	mic	ADJ
ejpam-5434	263	8	-	-	PUNCT
ejpam-5434	263	9	pext(a	pext(a	NOUN
ejpam-5434	263	10	)	)	PUNCT
ejpam-5434	263	11	i.e.	i.e.	X
ejpam-5434	263	12	,	,	PUNCT
ejpam-5434	263	13	x	x	SYM
ejpam-5434	263	14	∈	∈	PROPN
ejpam-5434	263	15	mic	mic	NOUN
ejpam-5434	263	16	-	-	PUNCT
ejpam-5434	263	17	pint(u−a	pint(u−a	NOUN
ejpam-5434	263	18	)	)	PUNCT
ejpam-5434	263	19	where	where	SCONJ
ejpam-5434	263	20	x	x	SYM
ejpam-5434	263	21	∈	∈	PROPN
ejpam-5434	263	22	mic	mic	ADJ
ejpam-5434	263	23	-	-	PUNCT
ejpam-5434	263	24	pint(a	pint(a	NOUN
ejpam-5434	263	25	)	)	PUNCT
ejpam-5434	263	26	.	.	PUNCT
ejpam-5434	264	1	by	by	ADP
ejpam-5434	264	2	theorem	theorem	NOUN
ejpam-5434	264	3	3.16	3.16	NUM
ejpam-5434	264	4	[	[	X
ejpam-5434	264	5	7	7	NUM
ejpam-5434	264	6	]	]	PUNCT
ejpam-5434	264	7	a	a	DET
ejpam-5434	264	8	=	=	PUNCT
ejpam-5434	264	9	mic	mic	ADJ
ejpam-5434	264	10	-	-	PUNCT
ejpam-5434	264	11	pint(a	pint(a	NOUN
ejpam-5434	264	12	)	)	PUNCT
ejpam-5434	264	13	if	if	SCONJ
ejpam-5434	264	14	a	a	PRON
ejpam-5434	264	15	is	be	AUX
ejpam-5434	264	16	mic	mic	ADJ
ejpam-5434	264	17	-	-	PUNCT
ejpam-5434	264	18	po	po	NOUN
ejpam-5434	264	19	.	.	PUNCT
ejpam-5434	265	1	if	if	SCONJ
ejpam-5434	265	2	a	a	PRON
ejpam-5434	265	3	is	be	AUX
ejpam-5434	265	4	not	not	PART
ejpam-5434	265	5	mic	mic	ADJ
ejpam-5434	265	6	-	-	PUNCT
ejpam-5434	265	7	po	po	NOUN
ejpam-5434	265	8	then	then	ADV
ejpam-5434	265	9	mic	mic	ADJ
ejpam-5434	265	10	-	-	PUNCT
ejpam-5434	265	11	pint(a	pint(a	NOUN
ejpam-5434	265	12	)	)	PUNCT
ejpam-5434	266	1	⊂	⊂	PROPN
ejpam-5434	266	2	a.	a.	NOUN
ejpam-5434	266	3	therefore	therefore	ADV
ejpam-5434	266	4	in	in	ADP
ejpam-5434	266	5	general	general	ADJ
ejpam-5434	266	6	mic	mic	ADJ
ejpam-5434	266	7	-	-	PUNCT
ejpam-5434	266	8	pint(a	pint(a	NOUN
ejpam-5434	266	9	)	)	PUNCT
ejpam-5434	266	10	⊆	⊆	NUM
ejpam-5434	266	11	a.	a.	NOUN
ejpam-5434	266	12	therefore	therefore	ADV
ejpam-5434	267	1	x	x	X
ejpam-5434	267	2	/∈	/∈	PUNCT
ejpam-5434	268	1	a	a	DET
ejpam-5434	268	2	−	−	PROPN
ejpam-5434	268	3	mic	mic	ADJ
ejpam-5434	268	4	-	-	PUNCT
ejpam-5434	268	5	pint(a	pint(a	NOUN
ejpam-5434	268	6	)	)	PUNCT
ejpam-5434	268	7	implies	imply	VERB
ejpam-5434	268	8	x	x	X
ejpam-5434	268	9	/∈	/∈	INTJ
ejpam-5434	268	10	mic	mic	ADJ
ejpam-5434	268	11	-	-	PUNCT
ejpam-5434	268	12	pbr(a	pbr(a	NOUN
ejpam-5434	268	13	)	)	PUNCT
ejpam-5434	268	14	.	.	PUNCT
ejpam-5434	269	1	hence	hence	ADV
ejpam-5434	269	2	mic	mic	ADJ
ejpam-5434	269	3	-	-	PUNCT
ejpam-5434	269	4	pext(a	pext(a	NOUN
ejpam-5434	269	5	)	)	PUNCT
ejpam-5434	269	6	∩	∩	ADJ
ejpam-5434	269	7	mic	mic	ADJ
ejpam-5434	269	8	-	-	PUNCT
ejpam-5434	269	9	pbr(a	pbr(a	NOUN
ejpam-5434	269	10	)	)	PUNCT
ejpam-5434	269	11	=	=	PUNCT
ejpam-5434	269	12	∅.	∅.	PROPN
ejpam-5434	269	13	s.	s.	PROPN
ejpam-5434	269	14	stanley	stanley	PROPN
ejpam-5434	269	15	roshan	roshan	PROPN
ejpam-5434	269	16	et	et	PROPN
ejpam-5434	269	17	al	al	PROPN
ejpam-5434	269	18	.	.	PUNCT
ejpam-5434	269	19	/	/	SYM
ejpam-5434	269	20	eur	eur	PROPN
ejpam-5434	269	21	.	.	PUNCT
ejpam-5434	270	1	j.	j.	PROPN
ejpam-5434	270	2	pure	pure	PROPN
ejpam-5434	270	3	appl	appl	PROPN
ejpam-5434	270	4	.	.	PROPN
ejpam-5434	270	5	math	math	PROPN
ejpam-5434	270	6	,	,	PUNCT
ejpam-5434	270	7	17	17	NUM
ejpam-5434	270	8	(	(	PUNCT
ejpam-5434	270	9	4	4	NUM
ejpam-5434	270	10	)	)	PUNCT
ejpam-5434	270	11	(	(	PUNCT
ejpam-5434	270	12	2024	2024	NUM
ejpam-5434	270	13	)	)	PUNCT
ejpam-5434	270	14	,	,	PUNCT
ejpam-5434	270	15	3156	3156	NUM
ejpam-5434	270	16	-	-	SYM
ejpam-5434	270	17	3166	3166	NUM
ejpam-5434	270	18	3164	3164	NUM
ejpam-5434	270	19	5	5	NUM
ejpam-5434	270	20	.	.	PUNCT
ejpam-5434	270	21	micro	micro	PROPN
ejpam-5434	270	22	pre	pre	NOUN
ejpam-5434	270	23	-	-	NOUN
ejpam-5434	270	24	kernel	kernel	NOUN
ejpam-5434	270	25	in	in	ADP
ejpam-5434	270	26	this	this	DET
ejpam-5434	270	27	section	section	NOUN
ejpam-5434	270	28	,	,	PUNCT
ejpam-5434	270	29	we	we	PRON
ejpam-5434	270	30	define	define	VERB
ejpam-5434	270	31	and	and	CCONJ
ejpam-5434	270	32	study	study	VERB
ejpam-5434	270	33	the	the	DET
ejpam-5434	270	34	notions	notion	NOUN
ejpam-5434	270	35	of	of	ADP
ejpam-5434	270	36	micro	micro	ADJ
ejpam-5434	270	37	pre	pre	NOUN
ejpam-5434	270	38	-	-	NOUN
ejpam-5434	270	39	kernel	kernel	NOUN
ejpam-5434	270	40	and	and	CCONJ
ejpam-5434	270	41	obtain	obtain	VERB
ejpam-5434	270	42	its	its	PRON
ejpam-5434	270	43	basic	basic	ADJ
ejpam-5434	270	44	properties	property	NOUN
ejpam-5434	270	45	.	.	PUNCT
ejpam-5434	271	1	definition	definition	NOUN
ejpam-5434	271	2	16	16	NUM
ejpam-5434	271	3	.	.	PUNCT
ejpam-5434	272	1	for	for	ADP
ejpam-5434	272	2	any	any	PRON
ejpam-5434	272	3	a	a	PRON
ejpam-5434	272	4	⊂	⊂	PROPN
ejpam-5434	272	5	u	u	NOUN
ejpam-5434	272	6	,	,	PUNCT
ejpam-5434	272	7	mic	mic	ADJ
ejpam-5434	272	8	-	-	PUNCT
ejpam-5434	272	9	pker(a	pker(a	NOUN
ejpam-5434	272	10	)	)	PUNCT
ejpam-5434	272	11	is	be	AUX
ejpam-5434	272	12	defined	define	VERB
ejpam-5434	272	13	as	as	ADP
ejpam-5434	272	14	the	the	DET
ejpam-5434	272	15	intersection	intersection	NOUN
ejpam-5434	272	16	of	of	ADP
ejpam-5434	272	17	all	all	DET
ejpam-5434	272	18	micro	micro	ADJ
ejpam-5434	272	19	pre	pre	ADJ
ejpam-5434	272	20	-	-	ADJ
ejpam-5434	272	21	open	open	ADJ
ejpam-5434	272	22	sets	set	NOUN
ejpam-5434	272	23	containing	contain	VERB
ejpam-5434	272	24	a.	a.	NOUN
ejpam-5434	272	25	in	in	ADP
ejpam-5434	272	26	notation	notation	NOUN
ejpam-5434	272	27	,	,	PUNCT
ejpam-5434	272	28	mic	mic	ADJ
ejpam-5434	272	29	-	-	PUNCT
ejpam-5434	272	30	pker(a	pker(a	NOUN
ejpam-5434	272	31	)	)	PUNCT
ejpam-5434	273	1	=	=	SYM
ejpam-5434	273	2	⋂	⋂	PROPN
ejpam-5434	273	3	{	{	PUNCT
ejpam-5434	273	4	m	m	PROPN
ejpam-5434	273	5	/	/	SYM
ejpam-5434	273	6	a	a	DET
ejpam-5434	273	7	⊂	⊂	PROPN
ejpam-5434	273	8	m	m	PROPN
ejpam-5434	273	9	,	,	PUNCT
ejpam-5434	273	10	m	m	PROPN
ejpam-5434	273	11	∈	∈	ADJ
ejpam-5434	273	12	mic	mic	ADJ
ejpam-5434	273	13	-	-	PUNCT
ejpam-5434	273	14	po	po	NOUN
ejpam-5434	273	15	}	}	PUNCT
ejpam-5434	273	16	.	.	PUNCT
ejpam-5434	274	1	lemma	lemma	PROPN
ejpam-5434	274	2	4	4	NUM
ejpam-5434	274	3	.	.	X
ejpam-5434	275	1	for	for	ADP
ejpam-5434	275	2	subsets	subset	NOUN
ejpam-5434	275	3	a	a	PRON
ejpam-5434	275	4	,	,	PUNCT
ejpam-5434	275	5	b	b	NOUN
ejpam-5434	275	6	and	and	CCONJ
ejpam-5434	275	7	ai(i	ai(i	SYM
ejpam-5434	275	8	∈	∈	PROPN
ejpam-5434	276	1	i	i	PRON
ejpam-5434	276	2	,	,	PUNCT
ejpam-5434	276	3	where	where	SCONJ
ejpam-5434	276	4	i	i	PRON
ejpam-5434	276	5	is	be	AUX
ejpam-5434	276	6	an	an	DET
ejpam-5434	276	7	index	index	NOUN
ejpam-5434	276	8	set	set	NOUN
ejpam-5434	276	9	)	)	PUNCT
ejpam-5434	276	10	of	of	ADP
ejpam-5434	276	11	a	a	DET
ejpam-5434	276	12	micro	micro	ADJ
ejpam-5434	276	13	topological	topological	ADJ
ejpam-5434	276	14	space	space	NOUN
ejpam-5434	276	15	(	(	PUNCT
ejpam-5434	276	16	u	u	NOUN
ejpam-5434	276	17	,	,	PUNCT
ejpam-5434	276	18	µr(x	µr(x	X
ejpam-5434	276	19	)	)	PUNCT
ejpam-5434	276	20	)	)	PUNCT
ejpam-5434	276	21	,	,	PUNCT
ejpam-5434	276	22	the	the	DET
ejpam-5434	276	23	following	follow	VERB
ejpam-5434	276	24	holds	hold	VERB
ejpam-5434	276	25	.	.	PUNCT
ejpam-5434	277	1	(	(	PUNCT
ejpam-5434	277	2	i	i	NOUN
ejpam-5434	277	3	)	)	PUNCT
ejpam-5434	277	4	a	a	DET
ejpam-5434	277	5	⊆	⊆	NUM
ejpam-5434	277	6	mic	mic	ADJ
ejpam-5434	277	7	-	-	PUNCT
ejpam-5434	277	8	pker(a	pker(a	NOUN
ejpam-5434	277	9	)	)	PUNCT
ejpam-5434	277	10	.	.	PUNCT
ejpam-5434	278	1	(	(	PUNCT
ejpam-5434	278	2	ii	ii	NOUN
ejpam-5434	278	3	)	)	PUNCT
ejpam-5434	278	4	if	if	SCONJ
ejpam-5434	278	5	a	a	DET
ejpam-5434	278	6	⊂	⊂	PROPN
ejpam-5434	278	7	b	b	PROPN
ejpam-5434	278	8	,	,	PUNCT
ejpam-5434	278	9	then	then	ADV
ejpam-5434	278	10	mic	mic	ADJ
ejpam-5434	278	11	-	-	PUNCT
ejpam-5434	278	12	pker(a	pker(a	NOUN
ejpam-5434	278	13	)	)	PUNCT
ejpam-5434	278	14	⊂	⊂	PROPN
ejpam-5434	278	15	mic	mic	ADJ
ejpam-5434	278	16	-	-	PUNCT
ejpam-5434	278	17	pker(b	pker(b	NOUN
ejpam-5434	278	18	)	)	PUNCT
ejpam-5434	278	19	.	.	PUNCT
ejpam-5434	279	1	(	(	PUNCT
ejpam-5434	279	2	iii	iii	X
ejpam-5434	279	3	)	)	PUNCT
ejpam-5434	279	4	mic	mic	ADJ
ejpam-5434	279	5	-	-	PUNCT
ejpam-5434	279	6	pker(mic	pker(mic	NOUN
ejpam-5434	279	7	-	-	PUNCT
ejpam-5434	279	8	pker(a	pker(a	NOUN
ejpam-5434	279	9	)	)	PUNCT
ejpam-5434	279	10	)	)	PUNCT
ejpam-5434	280	1	=	=	SYM
ejpam-5434	280	2	mic	mic	ADJ
ejpam-5434	280	3	-	-	PUNCT
ejpam-5434	280	4	pker(a	pker(a	NOUN
ejpam-5434	280	5	)	)	PUNCT
ejpam-5434	280	6	.	.	PUNCT
ejpam-5434	281	1	(	(	PUNCT
ejpam-5434	281	2	iv	iv	X
ejpam-5434	281	3	)	)	PUNCT
ejpam-5434	281	4	mic	mic	ADJ
ejpam-5434	281	5	-	-	PUNCT
ejpam-5434	281	6	pker	pker	NOUN
ejpam-5434	281	7	(	(	PUNCT
ejpam-5434	281	8	⋃	⋃	NOUN
ejpam-5434	281	9	ai/	ai/	ADJ
ejpam-5434	282	1	i	i	PRON
ejpam-5434	282	2	∈	∈	PROPN
ejpam-5434	282	3	i	i	X
ejpam-5434	282	4	)	)	PUNCT
ejpam-5434	282	5	⊆	⊆	NUM
ejpam-5434	282	6	⋃	⋃	NOUN
ejpam-5434	282	7	{	{	PUNCT
ejpam-5434	282	8	mic	mic	ADJ
ejpam-5434	282	9	-	-	PUNCT
ejpam-5434	282	10	pker	pker	NOUN
ejpam-5434	282	11	(	(	PUNCT
ejpam-5434	282	12	ai)/	ai)/	NOUN
ejpam-5434	283	1	i	i	PRON
ejpam-5434	283	2	∈	∈	PROPN
ejpam-5434	283	3	i	i	PRON
ejpam-5434	283	4	}	}	PUNCT
ejpam-5434	283	5	.	.	PUNCT
ejpam-5434	284	1	(	(	PUNCT
ejpam-5434	284	2	v	v	NOUN
ejpam-5434	284	3	)	)	PUNCT
ejpam-5434	284	4	mic	mic	ADJ
ejpam-5434	284	5	-	-	PUNCT
ejpam-5434	284	6	pker	pker	NOUN
ejpam-5434	284	7	(	(	PUNCT
ejpam-5434	284	8	⋂	⋂	PROPN
ejpam-5434	284	9	ai/	ai/	ADJ
ejpam-5434	285	1	i	i	PRON
ejpam-5434	285	2	∈	∈	PROPN
ejpam-5434	285	3	i	i	PRON
ejpam-5434	285	4	)	)	PUNCT
ejpam-5434	285	5	⊆	⊆	PROPN
ejpam-5434	285	6	⋂	⋂	PROPN
ejpam-5434	285	7	{	{	PUNCT
ejpam-5434	285	8	mic	mic	ADJ
ejpam-5434	285	9	-	-	PUNCT
ejpam-5434	285	10	pker	pker	NOUN
ejpam-5434	285	11	(	(	PUNCT
ejpam-5434	285	12	ai)/	ai)/	NOUN
ejpam-5434	285	13	i	i	PRON
ejpam-5434	285	14	∈	∈	VERB
ejpam-5434	286	1	i	i	X
ejpam-5434	286	2	}	}	PUNCT
ejpam-5434	286	3	.	.	PUNCT
ejpam-5434	287	1	proof	proof	NOUN
ejpam-5434	287	2	:	:	PUNCT
ejpam-5434	287	3	(	(	PUNCT
ejpam-5434	287	4	i	i	NOUN
ejpam-5434	287	5	)	)	PUNCT
ejpam-5434	287	6	it	it	PRON
ejpam-5434	287	7	follows	follow	VERB
ejpam-5434	287	8	by	by	ADP
ejpam-5434	287	9	the	the	DET
ejpam-5434	287	10	definition	definition	NOUN
ejpam-5434	287	11	of	of	ADP
ejpam-5434	287	12	mic	mic	ADJ
ejpam-5434	287	13	-	-	PUNCT
ejpam-5434	287	14	pker(a	pker(a	NOUN
ejpam-5434	287	15	)	)	PUNCT
ejpam-5434	287	16	.	.	PUNCT
ejpam-5434	288	1	(	(	PUNCT
ejpam-5434	288	2	ii	ii	NOUN
ejpam-5434	288	3	)	)	PUNCT
ejpam-5434	288	4	suppose	suppose	VERB
ejpam-5434	288	5	x	x	SYM
ejpam-5434	288	6	/∈	/∈	INTJ
ejpam-5434	288	7	mic	mic	ADJ
ejpam-5434	288	8	-	-	PUNCT
ejpam-5434	288	9	pker(b	pker(b	NOUN
ejpam-5434	288	10	)	)	PUNCT
ejpam-5434	288	11	,	,	PUNCT
ejpam-5434	288	12	then	then	ADV
ejpam-5434	288	13	there	there	PRON
ejpam-5434	288	14	exists	exist	VERB
ejpam-5434	288	15	a	a	DET
ejpam-5434	288	16	subset	subset	NOUN
ejpam-5434	288	17	s	s	X
ejpam-5434	288	18	∈	∈	PROPN
ejpam-5434	288	19	mic	mic	ADJ
ejpam-5434	288	20	-	-	PUNCT
ejpam-5434	288	21	po	po	NOUN
ejpam-5434	288	22	such	such	ADJ
ejpam-5434	288	23	that	that	PRON
ejpam-5434	288	24	b	b	X
ejpam-5434	288	25	⊂	⊂	X
ejpam-5434	288	26	s	s	X
ejpam-5434	288	27	with	with	ADP
ejpam-5434	288	28	x	x	PROPN
ejpam-5434	288	29	/∈	/∈	PROPN
ejpam-5434	288	30	s.	s.	PROPN
ejpam-5434	288	31	since	since	SCONJ
ejpam-5434	288	32	a	a	DET
ejpam-5434	288	33	⊂	⊂	PROPN
ejpam-5434	288	34	b	b	PROPN
ejpam-5434	288	35	,	,	PUNCT
ejpam-5434	288	36	x	x	PROPN
ejpam-5434	288	37	/∈	/∈	PUNCT
ejpam-5434	288	38	mic	mic	ADJ
ejpam-5434	288	39	-	-	PUNCT
ejpam-5434	288	40	pker(a	pker(a	NOUN
ejpam-5434	288	41	)	)	PUNCT
ejpam-5434	288	42	.	.	PUNCT
ejpam-5434	289	1	thus	thus	ADV
ejpam-5434	289	2	mic	mic	ADJ
ejpam-5434	289	3	-	-	PUNCT
ejpam-5434	289	4	pker(a	pker(a	NOUN
ejpam-5434	289	5	)	)	PUNCT
ejpam-5434	289	6	⊂	⊂	PROPN
ejpam-5434	289	7	mic	mic	ADJ
ejpam-5434	289	8	-	-	PUNCT
ejpam-5434	289	9	pker(b	pker(b	NOUN
ejpam-5434	289	10	)	)	PUNCT
ejpam-5434	289	11	.	.	PUNCT
ejpam-5434	290	1	(	(	PUNCT
ejpam-5434	290	2	iii	iii	NOUN
ejpam-5434	290	3	)	)	PUNCT
ejpam-5434	290	4	follows	follow	VERB
ejpam-5434	290	5	from	from	ADP
ejpam-5434	290	6	(	(	PUNCT
ejpam-5434	290	7	1	1	NUM
ejpam-5434	290	8	)	)	PUNCT
ejpam-5434	290	9	and	and	CCONJ
ejpam-5434	290	10	definition	definition	NOUN
ejpam-5434	290	11	of	of	ADP
ejpam-5434	290	12	mic	mic	ADJ
ejpam-5434	290	13	-	-	PUNCT
ejpam-5434	290	14	pker(a	pker(a	NOUN
ejpam-5434	290	15	)	)	PUNCT
ejpam-5434	290	16	.	.	PUNCT
ejpam-5434	291	1	(	(	PUNCT
ejpam-5434	291	2	iv	iv	X
ejpam-5434	291	3	)	)	PUNCT
ejpam-5434	291	4	for	for	ADP
ejpam-5434	291	5	each	each	DET
ejpam-5434	291	6	i	i	PRON
ejpam-5434	291	7	∈	∈	PROPN
ejpam-5434	292	1	i	i	PRON
ejpam-5434	292	2	,	,	PUNCT
ejpam-5434	292	3	mic	mic	ADJ
ejpam-5434	292	4	-	-	PUNCT
ejpam-5434	292	5	pker	pker	NOUN
ejpam-5434	292	6	(	(	PUNCT
ejpam-5434	292	7	ai	ai	PROPN
ejpam-5434	292	8	)	)	PUNCT
ejpam-5434	292	9	⊆	⊆	NUM
ejpam-5434	292	10	mic	mic	ADJ
ejpam-5434	292	11	-	-	PUNCT
ejpam-5434	292	12	pker	pker	NOUN
ejpam-5434	292	13	(	(	PUNCT
ejpam-5434	292	14	⋃	⋃	PROPN
ejpam-5434	292	15	i∈i	i∈i	ADJ
ejpam-5434	292	16	ai	ai	NOUN
ejpam-5434	292	17	)	)	PUNCT
ejpam-5434	292	18	.	.	PUNCT
ejpam-5434	293	1	therefore	therefore	ADV
ejpam-5434	293	2	we	we	PRON
ejpam-5434	293	3	have	have	VERB
ejpam-5434	293	4	⋃	⋃	NOUN
ejpam-5434	293	5	i∈i{micpker(ai	i∈i{micpker(ai	NOUN
ejpam-5434	293	6	)	)	PUNCT
ejpam-5434	293	7	}	}	PUNCT
ejpam-5434	293	8	⊆	⊆	NUM
ejpam-5434	293	9	mic	mic	ADJ
ejpam-5434	293	10	-	-	PUNCT
ejpam-5434	293	11	pker	pker	NOUN
ejpam-5434	293	12	(	(	PUNCT
ejpam-5434	293	13	⋃	⋃	ADP
ejpam-5434	293	14	i∈i	i∈i	ADJ
ejpam-5434	293	15	ai	ai	NOUN
ejpam-5434	293	16	)	)	PUNCT
ejpam-5434	293	17	.	.	PUNCT
ejpam-5434	294	1	(	(	PUNCT
ejpam-5434	294	2	v	v	NOUN
ejpam-5434	294	3	)	)	PUNCT
ejpam-5434	294	4	suppose	suppose	VERB
ejpam-5434	294	5	that	that	SCONJ
ejpam-5434	294	6	x	x	PROPN
ejpam-5434	294	7	/∈	/∈	PROPN
ejpam-5434	295	1	⋂	⋂	PROPN
ejpam-5434	295	2	{	{	PUNCT
ejpam-5434	295	3	mic	mic	ADJ
ejpam-5434	295	4	-	-	PUNCT
ejpam-5434	295	5	pker(ai	pker(ai	NOUN
ejpam-5434	295	6	/	/	SYM
ejpam-5434	295	7	i	i	PROPN
ejpam-5434	295	8	∈	∈	PROPN
ejpam-5434	296	1	i	i	NOUN
ejpam-5434	296	2	)	)	PUNCT
ejpam-5434	296	3	}	}	PUNCT
ejpam-5434	296	4	then	then	ADV
ejpam-5434	296	5	there	there	PRON
ejpam-5434	296	6	exists	exist	VERB
ejpam-5434	296	7	an	an	DET
ejpam-5434	296	8	i0	i0	PROPN
ejpam-5434	296	9	∈	∈	PROPN
ejpam-5434	297	1	i	i	PRON
ejpam-5434	297	2	,	,	PUNCT
ejpam-5434	297	3	such	such	ADJ
ejpam-5434	297	4	that	that	SCONJ
ejpam-5434	297	5	x	x	SYM
ejpam-5434	297	6	/∈	/∈	INTJ
ejpam-5434	297	7	mic	mic	ADJ
ejpam-5434	297	8	-	-	PUNCT
ejpam-5434	297	9	pker(ai0	pker(ai0	ADJ
ejpam-5434	297	10	)	)	PUNCT
ejpam-5434	297	11	and	and	CCONJ
ejpam-5434	297	12	there	there	PRON
ejpam-5434	297	13	exists	exist	VERB
ejpam-5434	297	14	a	a	DET
ejpam-5434	297	15	micro	micro	ADJ
ejpam-5434	297	16	pre	pre	ADJ
ejpam-5434	297	17	-	-	ADJ
ejpam-5434	297	18	open	open	ADJ
ejpam-5434	297	19	set	set	NOUN
ejpam-5434	297	20	s	s	VERB
ejpam-5434	297	21	such	such	ADJ
ejpam-5434	297	22	that	that	PRON
ejpam-5434	297	23	x	x	X
ejpam-5434	297	24	/∈	/∈	PRON
ejpam-5434	297	25	s	s	PART
ejpam-5434	297	26	and	and	CCONJ
ejpam-5434	297	27	ai0	ai0	PROPN
ejpam-5434	297	28	⊂	⊂	PROPN
ejpam-5434	297	29	s.	s.	PROPN
ejpam-5434	298	1	we	we	PRON
ejpam-5434	298	2	have	have	VERB
ejpam-5434	298	3	⋂	⋂	PROPN
ejpam-5434	298	4	i∈i	i∈i	ADJ
ejpam-5434	298	5	ai	ai	VERB
ejpam-5434	298	6	⊆	⊆	NUM
ejpam-5434	298	7	ai0	ai0	PROPN
ejpam-5434	298	8	⊆	⊆	NUM
ejpam-5434	298	9	s	s	NOUN
ejpam-5434	298	10	and	and	CCONJ
ejpam-5434	298	11	x	x	PROPN
ejpam-5434	298	12	/∈	/∈	PUNCT
ejpam-5434	299	1	s.	s.	PROPN
ejpam-5434	299	2	therefore	therefore	ADV
ejpam-5434	299	3	x	x	PROPN
ejpam-5434	299	4	/∈	/∈	PUNCT
ejpam-5434	299	5	mic	mic	ADJ
ejpam-5434	299	6	-	-	PUNCT
ejpam-5434	299	7	pker	pker	NOUN
ejpam-5434	299	8	{	{	PUNCT
ejpam-5434	299	9	⋂	⋂	PROPN
ejpam-5434	299	10	ai	ai	VERB
ejpam-5434	299	11	/	/	SYM
ejpam-5434	299	12	i	i	NOUN
ejpam-5434	299	13	∈	∈	PROPN
ejpam-5434	299	14	i	i	X
ejpam-5434	299	15	}	}	PUNCT
ejpam-5434	299	16	.	.	PUNCT
ejpam-5434	300	1	hence	hence	ADV
ejpam-5434	300	2	mic	mic	ADJ
ejpam-5434	300	3	-	-	PUNCT
ejpam-5434	300	4	pker	pker	NOUN
ejpam-5434	300	5	(	(	PUNCT
ejpam-5434	300	6	⋂	⋂	PROPN
ejpam-5434	300	7	ai	ai	VERB
ejpam-5434	300	8	/	/	SYM
ejpam-5434	300	9	i	i	NOUN
ejpam-5434	300	10	∈	∈	PROPN
ejpam-5434	300	11	i	i	PRON
ejpam-5434	300	12	)	)	PUNCT
ejpam-5434	300	13	⊆	⊆	NUM
ejpam-5434	300	14	⋂	⋂	PROPN
ejpam-5434	300	15	mic	mic	ADJ
ejpam-5434	300	16	-	-	PUNCT
ejpam-5434	300	17	pker(ai)/i	pker(ai)/i	NOUN
ejpam-5434	300	18	∈	∈	PROPN
ejpam-5434	300	19	i.	i.	NOUN
ejpam-5434	300	20	theorem	theorem	VERB
ejpam-5434	300	21	9	9	NUM
ejpam-5434	300	22	.	.	PUNCT
ejpam-5434	301	1	let	let	VERB
ejpam-5434	301	2	a	a	PRON
ejpam-5434	301	3	and	and	CCONJ
ejpam-5434	301	4	b	b	NOUN
ejpam-5434	301	5	be	be	AUX
ejpam-5434	301	6	subsets	subset	NOUN
ejpam-5434	301	7	of	of	ADP
ejpam-5434	301	8	u	u	NOUN
ejpam-5434	301	9	,	,	PUNCT
ejpam-5434	301	10	then	then	ADV
ejpam-5434	301	11	the	the	DET
ejpam-5434	301	12	following	follow	VERB
ejpam-5434	301	13	conditions	condition	NOUN
ejpam-5434	301	14	hold	hold	VERB
ejpam-5434	301	15	.	.	PUNCT
ejpam-5434	302	1	(	(	PUNCT
ejpam-5434	302	2	i	i	NOUN
ejpam-5434	302	3	)	)	PUNCT
ejpam-5434	302	4	mic	mic	ADJ
ejpam-5434	302	5	-	-	PUNCT
ejpam-5434	302	6	pker(a	pker(a	NOUN
ejpam-5434	302	7	)	)	PUNCT
ejpam-5434	302	8	⊆	⊆	NUM
ejpam-5434	302	9	mic	mic	ADJ
ejpam-5434	302	10	-	-	PUNCT
ejpam-5434	302	11	ker(a	ker(a	NOUN
ejpam-5434	302	12	)	)	PUNCT
ejpam-5434	302	13	.	.	PUNCT
ejpam-5434	303	1	(	(	PUNCT
ejpam-5434	303	2	ii	ii	NOUN
ejpam-5434	303	3	)	)	PUNCT
ejpam-5434	303	4	mic	mic	ADJ
ejpam-5434	303	5	-	-	PUNCT
ejpam-5434	303	6	pker(a	pker(a	NOUN
ejpam-5434	303	7	)	)	PUNCT
ejpam-5434	303	8	∩	∩	ADJ
ejpam-5434	303	9	mic	mic	NOUN
ejpam-5434	303	10	-	-	PUNCT
ejpam-5434	303	11	pker(b	pker(b	NOUN
ejpam-5434	303	12	)	)	PUNCT
ejpam-5434	303	13	⊂	⊂	PROPN
ejpam-5434	303	14	mic	mic	ADJ
ejpam-5434	303	15	-	-	PUNCT
ejpam-5434	303	16	pker(a	pker(a	NOUN
ejpam-5434	303	17	∪	∪	PROPN
ejpam-5434	303	18	b	b	NOUN
ejpam-5434	303	19	)	)	PUNCT
ejpam-5434	303	20	.	.	PUNCT
ejpam-5434	304	1	(	(	PUNCT
ejpam-5434	304	2	iii	iii	X
ejpam-5434	304	3	)	)	PUNCT
ejpam-5434	304	4	mic	mic	ADJ
ejpam-5434	304	5	-	-	PUNCT
ejpam-5434	304	6	pker(a	pker(a	NOUN
ejpam-5434	304	7	∩	∩	ADJ
ejpam-5434	304	8	b	b	X
ejpam-5434	304	9	)	)	PUNCT
ejpam-5434	304	10	⊂	⊂	PROPN
ejpam-5434	304	11	mic	mic	ADJ
ejpam-5434	304	12	-	-	PUNCT
ejpam-5434	304	13	pker(a	pker(a	NOUN
ejpam-5434	304	14	)	)	PUNCT
ejpam-5434	304	15	∪	∪	ADP
ejpam-5434	304	16	mic	mic	NOUN
ejpam-5434	304	17	-	-	PUNCT
ejpam-5434	304	18	pker(b	pker(b	NOUN
ejpam-5434	304	19	)	)	PUNCT
ejpam-5434	304	20	.	.	PUNCT
ejpam-5434	305	1	(	(	PUNCT
ejpam-5434	305	2	iv	iv	X
ejpam-5434	305	3	)	)	PUNCT
ejpam-5434	305	4	mic	mic	ADJ
ejpam-5434	305	5	-	-	PUNCT
ejpam-5434	305	6	pcl(a	pcl(a	NOUN
ejpam-5434	305	7	)	)	PUNCT
ejpam-5434	305	8	∩	∩	ADJ
ejpam-5434	305	9	mic	mic	NOUN
ejpam-5434	305	10	-	-	PUNCT
ejpam-5434	305	11	pker(a	pker(a	NOUN
ejpam-5434	305	12	)	)	PUNCT
ejpam-5434	305	13	=	=	SYM
ejpam-5434	305	14	a.	a.	NOUN
ejpam-5434	305	15	(	(	PUNCT
ejpam-5434	305	16	v	v	NOUN
ejpam-5434	305	17	)	)	PUNCT
ejpam-5434	305	18	mic	mic	ADJ
ejpam-5434	305	19	-	-	PUNCT
ejpam-5434	305	20	pker(a	pker(a	NOUN
ejpam-5434	305	21	)	)	PUNCT
ejpam-5434	305	22	∩	∩	ADJ
ejpam-5434	305	23	mic	mic	NOUN
ejpam-5434	305	24	-	-	PUNCT
ejpam-5434	305	25	pfr(a	pfr(a	NOUN
ejpam-5434	305	26	)	)	PUNCT
ejpam-5434	305	27	=	=	SYM
ejpam-5434	305	28	mic	mic	ADJ
ejpam-5434	305	29	-	-	PUNCT
ejpam-5434	305	30	pbr(a	pbr(a	NOUN
ejpam-5434	305	31	)	)	PUNCT
ejpam-5434	305	32	.	.	PUNCT
ejpam-5434	306	1	proof	proof	NOUN
ejpam-5434	306	2	:	:	PUNCT
ejpam-5434	306	3	references	reference	NOUN
ejpam-5434	306	4	3165	3165	NUM
ejpam-5434	306	5	(	(	PUNCT
ejpam-5434	306	6	i	i	NOUN
ejpam-5434	306	7	)	)	PUNCT
ejpam-5434	306	8	let	let	VERB
ejpam-5434	306	9	x	x	X
ejpam-5434	306	10	∈	∈	PROPN
ejpam-5434	306	11	mic	mic	NOUN
ejpam-5434	306	12	-	-	PUNCT
ejpam-5434	306	13	pker(a	pker(a	NOUN
ejpam-5434	306	14	)	)	PUNCT
ejpam-5434	306	15	.	.	PUNCT
ejpam-5434	307	1	⇒	⇒	PROPN
ejpam-5434	307	2	x	x	X
ejpam-5434	307	3	∈	∈	PROPN
ejpam-5434	307	4	⋂	⋂	PROPN
ejpam-5434	307	5	{	{	PUNCT
ejpam-5434	307	6	m	m	PROPN
ejpam-5434	307	7	/	/	SYM
ejpam-5434	307	8	a	a	DET
ejpam-5434	307	9	⊂	⊂	PROPN
ejpam-5434	307	10	m	m	PROPN
ejpam-5434	307	11	,	,	PUNCT
ejpam-5434	307	12	m	m	PROPN
ejpam-5434	307	13	∈	∈	ADJ
ejpam-5434	307	14	mic	mic	ADJ
ejpam-5434	307	15	-	-	PUNCT
ejpam-5434	307	16	po	po	NOUN
ejpam-5434	307	17	}	}	PUNCT
ejpam-5434	307	18	⇒	⇒	NOUN
ejpam-5434	307	19	x	x	X
ejpam-5434	307	20	∈	∈	PROPN
ejpam-5434	307	21	⋂	⋂	PROPN
ejpam-5434	307	22	{	{	PUNCT
ejpam-5434	307	23	m	m	PROPN
ejpam-5434	307	24	/	/	SYM
ejpam-5434	307	25	a	a	DET
ejpam-5434	307	26	⊂	⊂	PROPN
ejpam-5434	307	27	m	m	PROPN
ejpam-5434	307	28	,	,	PUNCT
ejpam-5434	307	29	m	m	PROPN
ejpam-5434	307	30	∈	∈	PROPN
ejpam-5434	307	31	micro	micro	NOUN
ejpam-5434	307	32	-	-	NOUN
ejpam-5434	307	33	open(µr(x	open(µr(x	NOUN
ejpam-5434	307	34	)	)	PUNCT
ejpam-5434	307	35	)	)	PUNCT
ejpam-5434	307	36	}	}	PUNCT
ejpam-5434	307	37	since	since	SCONJ
ejpam-5434	307	38	every	every	DET
ejpam-5434	307	39	micro	micro	NOUN
ejpam-5434	307	40	open	open	ADJ
ejpam-5434	307	41	is	be	AUX
ejpam-5434	307	42	micro	micro	ADJ
ejpam-5434	307	43	pre	pre	ADJ
ejpam-5434	307	44	-	-	ADJ
ejpam-5434	307	45	open	open	ADJ
ejpam-5434	307	46	,	,	PUNCT
ejpam-5434	307	47	x	x	SYM
ejpam-5434	307	48	∈	∈	PROPN
ejpam-5434	307	49	mic	mic	NOUN
ejpam-5434	307	50	-	-	PUNCT
ejpam-5434	307	51	ker(a	ker(a	NOUN
ejpam-5434	307	52	)	)	PUNCT
ejpam-5434	307	53	.	.	PUNCT
ejpam-5434	308	1	(	(	PUNCT
ejpam-5434	308	2	ii	ii	X
ejpam-5434	308	3	)	)	PUNCT
ejpam-5434	308	4	let	let	AUX
ejpam-5434	308	5	x	x	SYM
ejpam-5434	308	6	∈{mic	∈{mic	ADJ
ejpam-5434	308	7	-	-	ADJ
ejpam-5434	308	8	pker(a	pker(a	ADJ
ejpam-5434	308	9	)	)	PUNCT
ejpam-5434	308	10	∩	∩	ADJ
ejpam-5434	308	11	mic	mic	NOUN
ejpam-5434	308	12	-	-	PUNCT
ejpam-5434	308	13	pker(b	pker(b	NOUN
ejpam-5434	308	14	)	)	PUNCT
ejpam-5434	308	15	}	}	PUNCT
ejpam-5434	308	16	⇒	⇒	VERB
ejpam-5434	308	17	x	x	SYM
ejpam-5434	308	18	∈	∈	PROPN
ejpam-5434	308	19	mic	mic	NOUN
ejpam-5434	308	20	-	-	PUNCT
ejpam-5434	308	21	pker(a	pker(a	NOUN
ejpam-5434	308	22	)	)	PUNCT
ejpam-5434	308	23	and	and	CCONJ
ejpam-5434	308	24	x	x	PUNCT
ejpam-5434	308	25	∈	∈	PROPN
ejpam-5434	308	26	mic	mic	NOUN
ejpam-5434	308	27	-	-	PUNCT
ejpam-5434	308	28	pker(b	pker(b	NOUN
ejpam-5434	308	29	)	)	PUNCT
ejpam-5434	308	30	therefore	therefore	ADV
ejpam-5434	308	31	,	,	PUNCT
ejpam-5434	308	32	x	x	SYM
ejpam-5434	308	33	∈	∈	PROPN
ejpam-5434	308	34	mic	mic	NOUN
ejpam-5434	308	35	-	-	PUNCT
ejpam-5434	308	36	pker(a	pker(a	NOUN
ejpam-5434	308	37	∪	∪	PROPN
ejpam-5434	308	38	b	b	NOUN
ejpam-5434	308	39	)	)	PUNCT
ejpam-5434	308	40	.	.	PUNCT
ejpam-5434	309	1	(	(	PUNCT
ejpam-5434	309	2	iii	iii	X
ejpam-5434	309	3	)	)	PUNCT
ejpam-5434	309	4	let	let	VERB
ejpam-5434	309	5	x	x	X
ejpam-5434	309	6	∈	∈	PROPN
ejpam-5434	309	7	mic	mic	ADJ
ejpam-5434	309	8	-	-	PUNCT
ejpam-5434	309	9	pker(a	pker(a	NOUN
ejpam-5434	309	10	∩	∩	ADJ
ejpam-5434	309	11	b	b	NOUN
ejpam-5434	309	12	)	)	PUNCT
ejpam-5434	309	13	⇒	⇒	NOUN
ejpam-5434	309	14	x	x	SYM
ejpam-5434	309	15	∈	∈	PROPN
ejpam-5434	309	16	mic	mic	NOUN
ejpam-5434	309	17	-	-	PUNCT
ejpam-5434	309	18	pker(a	pker(a	NOUN
ejpam-5434	309	19	)	)	PUNCT
ejpam-5434	309	20	and	and	CCONJ
ejpam-5434	309	21	x	x	PUNCT
ejpam-5434	309	22	∈	∈	PROPN
ejpam-5434	309	23	mic	mic	NOUN
ejpam-5434	309	24	-	-	PUNCT
ejpam-5434	309	25	pker(b	pker(b	NOUN
ejpam-5434	309	26	)	)	PUNCT
ejpam-5434	309	27	therefore	therefore	ADV
ejpam-5434	309	28	,	,	PUNCT
ejpam-5434	309	29	x	x	SYM
ejpam-5434	309	30	∈	∈	PROPN
ejpam-5434	309	31	mic	mic	NOUN
ejpam-5434	309	32	-	-	PUNCT
ejpam-5434	309	33	pker(a	pker(a	NOUN
ejpam-5434	309	34	)	)	PUNCT
ejpam-5434	309	35	∪	∪	ADP
ejpam-5434	309	36	mic	mic	NOUN
ejpam-5434	309	37	-	-	PUNCT
ejpam-5434	309	38	pker(b	pker(b	NOUN
ejpam-5434	309	39	)	)	PUNCT
ejpam-5434	309	40	.	.	PUNCT
ejpam-5434	310	1	(	(	PUNCT
ejpam-5434	310	2	iv	iv	X
ejpam-5434	310	3	)	)	PUNCT
ejpam-5434	310	4	let	let	VERB
ejpam-5434	310	5	x	x	X
ejpam-5434	310	6	∈	∈	PROPN
ejpam-5434	310	7	mic	mic	ADJ
ejpam-5434	310	8	-	-	PUNCT
ejpam-5434	310	9	pcl(a	pcl(a	NOUN
ejpam-5434	310	10	)	)	PUNCT
ejpam-5434	310	11	∩	∩	ADJ
ejpam-5434	310	12	mic	mic	NOUN
ejpam-5434	310	13	-	-	PUNCT
ejpam-5434	310	14	pker(a	pker(a	NOUN
ejpam-5434	310	15	)	)	PUNCT
ejpam-5434	310	16	by	by	ADP
ejpam-5434	310	17	lemma	lemma	PROPN
ejpam-5434	310	18	3.7(1	3.7(1	NUM
ejpam-5434	310	19	)	)	PUNCT
ejpam-5434	311	1	[	[	X
ejpam-5434	311	2	7	7	X
ejpam-5434	311	3	]	]	PUNCT
ejpam-5434	311	4	a	a	DET
ejpam-5434	311	5	⊆	⊆	NUM
ejpam-5434	311	6	mic	mic	ADJ
ejpam-5434	311	7	-	-	PUNCT
ejpam-5434	311	8	pcl(a	pcl(a	NOUN
ejpam-5434	311	9	)	)	PUNCT
ejpam-5434	311	10	and	and	CCONJ
ejpam-5434	311	11	by	by	ADP
ejpam-5434	311	12	(	(	PUNCT
ejpam-5434	311	13	1	1	X
ejpam-5434	311	14	)	)	PUNCT
ejpam-5434	311	15	a	a	DET
ejpam-5434	311	16	⊆	⊆	NUM
ejpam-5434	311	17	mic	mic	ADJ
ejpam-5434	311	18	-	-	PUNCT
ejpam-5434	311	19	pker(a	pker(a	NOUN
ejpam-5434	311	20	)	)	PUNCT
ejpam-5434	311	21	.	.	PUNCT
ejpam-5434	312	1	⇒	⇒	PROPN
ejpam-5434	312	2	x	x	PUNCT
ejpam-5434	312	3	∈	∈	PROPN
ejpam-5434	312	4	a	a	DET
ejpam-5434	312	5	⊆	⊆	NUM
ejpam-5434	312	6	mic	mic	ADJ
ejpam-5434	312	7	-	-	PUNCT
ejpam-5434	312	8	pcl(a	pcl(a	NOUN
ejpam-5434	312	9	)	)	PUNCT
ejpam-5434	312	10	and	and	CCONJ
ejpam-5434	312	11	x	x	PUNCT
ejpam-5434	312	12	∈	∈	PROPN
ejpam-5434	312	13	a	a	DET
ejpam-5434	312	14	⊆	⊆	NUM
ejpam-5434	312	15	mic	mic	ADJ
ejpam-5434	312	16	-	-	PUNCT
ejpam-5434	312	17	pker(a	pker(a	NOUN
ejpam-5434	312	18	)	)	PUNCT
ejpam-5434	312	19	.	.	PUNCT
ejpam-5434	313	1	therefore	therefore	ADV
ejpam-5434	313	2	,	,	PUNCT
ejpam-5434	313	3	x	x	PUNCT
ejpam-5434	313	4	∈	∈	NOUN
ejpam-5434	313	5	a.	a.	NOUN
ejpam-5434	313	6	(	(	PUNCT
ejpam-5434	313	7	v	v	NOUN
ejpam-5434	313	8	)	)	PUNCT
ejpam-5434	313	9	let	let	VERB
ejpam-5434	313	10	x	x	X
ejpam-5434	313	11	∈	∈	PROPN
ejpam-5434	313	12	mic	mic	ADJ
ejpam-5434	313	13	-	-	PUNCT
ejpam-5434	313	14	pker(a	pker(a	NOUN
ejpam-5434	313	15	)	)	PUNCT
ejpam-5434	313	16	∩	∩	ADJ
ejpam-5434	313	17	mic	mic	NOUN
ejpam-5434	313	18	-	-	PUNCT
ejpam-5434	313	19	pfr(a	pfr(a	NOUN
ejpam-5434	313	20	)	)	PUNCT
ejpam-5434	313	21	.	.	PUNCT
ejpam-5434	314	1	to	to	PART
ejpam-5434	314	2	prove	prove	VERB
ejpam-5434	314	3	,	,	PUNCT
ejpam-5434	314	4	x	x	SYM
ejpam-5434	314	5	∈	∈	PROPN
ejpam-5434	314	6	mic	mic	ADJ
ejpam-5434	314	7	-	-	PUNCT
ejpam-5434	314	8	pbr(a	pbr(a	NOUN
ejpam-5434	314	9	)	)	PUNCT
ejpam-5434	314	10	i.e	i.e	PROPN
ejpam-5434	314	11	,	,	PUNCT
ejpam-5434	314	12	x	x	SYM
ejpam-5434	314	13	∈	∈	NOUN
ejpam-5434	314	14	a−	a−	PROPN
ejpam-5434	314	15	micpint(a	micpint(a	PROPN
ejpam-5434	314	16	)	)	PUNCT
ejpam-5434	314	17	.	.	PUNCT
ejpam-5434	315	1	since	since	SCONJ
ejpam-5434	315	2	mic	mic	ADJ
ejpam-5434	315	3	-	-	PUNCT
ejpam-5434	315	4	pker(a	pker(a	NOUN
ejpam-5434	315	5	)	)	PUNCT
ejpam-5434	315	6	=	=	SYM
ejpam-5434	315	7	⋂	⋂	PROPN
ejpam-5434	315	8	{	{	PUNCT
ejpam-5434	315	9	m	m	PROPN
ejpam-5434	315	10	/	/	SYM
ejpam-5434	315	11	a	a	PRON
ejpam-5434	315	12	⊂	⊂	PROPN
ejpam-5434	315	13	m	m	PROPN
ejpam-5434	315	14	,	,	PUNCT
ejpam-5434	315	15	m	m	PROPN
ejpam-5434	315	16	∈	∈	ADJ
ejpam-5434	315	17	mic	mic	ADJ
ejpam-5434	315	18	-	-	PUNCT
ejpam-5434	315	19	po	po	NOUN
ejpam-5434	315	20	}	}	PUNCT
ejpam-5434	315	21	and	and	CCONJ
ejpam-5434	315	22	mic	mic	ADJ
ejpam-5434	315	23	-	-	PUNCT
ejpam-5434	315	24	pfr(a	pfr(a	NOUN
ejpam-5434	315	25	)	)	PUNCT
ejpam-5434	315	26	=	=	SYM
ejpam-5434	315	27	mic	mic	ADJ
ejpam-5434	315	28	-	-	PUNCT
ejpam-5434	315	29	pcl(a)−mic	pcl(a)−mic	ADJ
ejpam-5434	315	30	-	-	PUNCT
ejpam-5434	315	31	pint(a	pint(a	NOUN
ejpam-5434	315	32	)	)	PUNCT
ejpam-5434	315	33	.	.	PUNCT
ejpam-5434	315	34	⇒	⇒	NOUN
ejpam-5434	316	1	x	x	X
ejpam-5434	316	2	∈	∈	PROPN
ejpam-5434	316	3	⋂	⋂	PROPN
ejpam-5434	316	4	{	{	PUNCT
ejpam-5434	316	5	m	m	PROPN
ejpam-5434	316	6	/	/	SYM
ejpam-5434	316	7	a	a	DET
ejpam-5434	316	8	⊂	⊂	PROPN
ejpam-5434	316	9	m	m	PROPN
ejpam-5434	316	10	,	,	PUNCT
ejpam-5434	316	11	m	m	PROPN
ejpam-5434	316	12	∈	∈	ADJ
ejpam-5434	316	13	mic	mic	ADJ
ejpam-5434	316	14	-	-	PUNCT
ejpam-5434	316	15	po	po	NOUN
ejpam-5434	316	16	}	}	PUNCT
ejpam-5434	316	17	∩	∩	ADJ
ejpam-5434	316	18	mic	mic	ADJ
ejpam-5434	316	19	-	-	PUNCT
ejpam-5434	316	20	pcl(a)−mic	pcl(a)−mic	ADJ
ejpam-5434	316	21	-	-	PUNCT
ejpam-5434	316	22	pint(a	pint(a	NOUN
ejpam-5434	316	23	)	)	PUNCT
ejpam-5434	316	24	.	.	PUNCT
ejpam-5434	317	1	by	by	ADP
ejpam-5434	317	2	lemma	lemma	PROPN
ejpam-5434	317	3	3.7(1	3.7(1	NUM
ejpam-5434	317	4	)	)	PUNCT
ejpam-5434	317	5	[	[	X
ejpam-5434	317	6	7	7	X
ejpam-5434	317	7	]	]	PUNCT
ejpam-5434	317	8	and	and	CCONJ
ejpam-5434	317	9	lemma	lemma	PROPN
ejpam-5434	317	10	4(1	4(1	NOUN
ejpam-5434	317	11	)	)	PUNCT
ejpam-5434	317	12	,	,	PUNCT
ejpam-5434	317	13	we	we	PRON
ejpam-5434	317	14	have	have	VERB
ejpam-5434	317	15	⇒	⇒	NOUN
ejpam-5434	317	16	x	x	PUNCT
ejpam-5434	317	17	∈	∈	PROPN
ejpam-5434	317	18	a	a	DET
ejpam-5434	317	19	∩	∩	NOUN
ejpam-5434	317	20	(	(	PUNCT
ejpam-5434	317	21	a	a	DET
ejpam-5434	317	22	−	−	PROPN
ejpam-5434	317	23	mic	mic	ADJ
ejpam-5434	317	24	-	-	PUNCT
ejpam-5434	317	25	pint(a	pint(a	NOUN
ejpam-5434	317	26	)	)	PUNCT
ejpam-5434	317	27	)	)	PUNCT
ejpam-5434	317	28	⇒	⇒	NOUN
ejpam-5434	317	29	x	x	PUNCT
ejpam-5434	317	30	∈	∈	PROPN
ejpam-5434	317	31	a	a	PRON
ejpam-5434	317	32	and	and	CCONJ
ejpam-5434	317	33	x	x	SYM
ejpam-5434	317	34	∈	∈	PROPN
ejpam-5434	317	35	a	a	DET
ejpam-5434	317	36	−	−	NOUN
ejpam-5434	317	37	mic	mic	ADJ
ejpam-5434	317	38	-	-	PUNCT
ejpam-5434	317	39	pint(a	pint(a	NOUN
ejpam-5434	317	40	)	)	PUNCT
ejpam-5434	317	41	⇒	⇒	NOUN
ejpam-5434	317	42	x	x	X
ejpam-5434	317	43	∈	∈	PROPN
ejpam-5434	317	44	a	a	DET
ejpam-5434	317	45	and	and	CCONJ
ejpam-5434	317	46	x	x	PROPN
ejpam-5434	317	47	∈	∈	PROPN
ejpam-5434	317	48	mic	mic	ADJ
ejpam-5434	317	49	-	-	PUNCT
ejpam-5434	317	50	pbr(a	pbr(a	NOUN
ejpam-5434	317	51	)	)	PUNCT
ejpam-5434	317	52	therefore	therefore	ADV
ejpam-5434	317	53	,	,	PUNCT
ejpam-5434	317	54	x	x	SYM
ejpam-5434	317	55	∈	∈	PROPN
ejpam-5434	317	56	mic	mic	ADJ
ejpam-5434	317	57	-	-	PUNCT
ejpam-5434	317	58	pbr(a	pbr(a	NOUN
ejpam-5434	317	59	)	)	PUNCT
ejpam-5434	317	60	.	.	PUNCT
ejpam-5434	318	1	6	6	X
ejpam-5434	318	2	.	.	X
ejpam-5434	318	3	conclusion	conclusion	NOUN
ejpam-5434	318	4	in	in	ADP
ejpam-5434	318	5	this	this	DET
ejpam-5434	318	6	paper	paper	NOUN
ejpam-5434	318	7	,	,	PUNCT
ejpam-5434	318	8	we	we	PRON
ejpam-5434	318	9	introduced	introduce	VERB
ejpam-5434	318	10	the	the	DET
ejpam-5434	318	11	notions	notion	NOUN
ejpam-5434	318	12	of	of	ADP
ejpam-5434	318	13	micro	micro	ADJ
ejpam-5434	318	14	pre	pre	NOUN
ejpam-5434	318	15	-	-	NOUN
ejpam-5434	318	16	frontier	frontier	ADJ
ejpam-5434	318	17	,	,	PUNCT
ejpam-5434	318	18	micro	micro	ADJ
ejpam-5434	318	19	pre	pre	ADJ
ejpam-5434	318	20	-	-	ADJ
ejpam-5434	318	21	exterior	exterior	ADJ
ejpam-5434	318	22	,	,	PUNCT
ejpam-5434	318	23	micro	micro	ADJ
ejpam-5434	318	24	pre	pre	ADJ
ejpam-5434	318	25	-	-	ADJ
ejpam-5434	318	26	border	border	ADJ
ejpam-5434	318	27	and	and	CCONJ
ejpam-5434	318	28	micro	micro	ADJ
ejpam-5434	318	29	pre	pre	NOUN
ejpam-5434	318	30	-	-	NOUN
ejpam-5434	318	31	kernel	kernel	NOUN
ejpam-5434	318	32	by	by	ADP
ejpam-5434	318	33	employing	employ	VERB
ejpam-5434	318	34	the	the	DET
ejpam-5434	318	35	concept	concept	NOUN
ejpam-5434	318	36	of	of	ADP
ejpam-5434	318	37	frontier	frontier	NOUN
ejpam-5434	318	38	,	,	PUNCT
ejpam-5434	318	39	exterior	exterior	ADJ
ejpam-5434	318	40	,	,	PUNCT
ejpam-5434	318	41	border	border	NOUN
ejpam-5434	318	42	and	and	CCONJ
ejpam-5434	318	43	kernel	kernel	PROPN
ejpam-5434	318	44	elucidating	elucidate	VERB
ejpam-5434	318	45	various	various	ADJ
ejpam-5434	318	46	associated	associated	ADJ
ejpam-5434	318	47	properties	property	NOUN
ejpam-5434	318	48	.	.	PUNCT
ejpam-5434	319	1	our	our	PRON
ejpam-5434	319	2	intent	intent	NOUN
ejpam-5434	319	3	is	be	AUX
ejpam-5434	319	4	to	to	PART
ejpam-5434	319	5	further	far	ADV
ejpam-5434	319	6	elaborate	elaborate	VERB
ejpam-5434	319	7	on	on	ADP
ejpam-5434	319	8	these	these	DET
ejpam-5434	319	9	findings	finding	NOUN
ejpam-5434	319	10	in	in	ADP
ejpam-5434	319	11	forthcoming	forthcome	VERB
ejpam-5434	319	12	research	research	NOUN
ejpam-5434	319	13	endeavors	endeavor	NOUN
ejpam-5434	319	14	,	,	PUNCT
ejpam-5434	319	15	with	with	ADP
ejpam-5434	319	16	a	a	DET
ejpam-5434	319	17	particular	particular	ADJ
ejpam-5434	319	18	focus	focus	NOUN
ejpam-5434	319	19	on	on	ADP
ejpam-5434	319	20	exploring	explore	VERB
ejpam-5434	319	21	practical	practical	ADJ
ejpam-5434	319	22	applications	application	NOUN
ejpam-5434	319	23	.	.	PUNCT
ejpam-5434	320	1	references	reference	NOUN
ejpam-5434	320	2	[	[	X
ejpam-5434	320	3	1	1	NUM
ejpam-5434	320	4	]	]	X
ejpam-5434	320	5	lellis	lellis	PROPN
ejpam-5434	320	6	thivagar	thivagar	NOUN
ejpam-5434	320	7	.	.	PUNCT
ejpam-5434	321	1	m	m	PROPN
ejpam-5434	321	2	and	and	CCONJ
ejpam-5434	321	3	carmel	carmel	PROPN
ejpam-5434	321	4	richard	richard	PROPN
ejpam-5434	321	5	.	.	PUNCT
ejpam-5434	322	1	on	on	ADP
ejpam-5434	322	2	nano	nano	NOUN
ejpam-5434	322	3	forms	form	NOUN
ejpam-5434	322	4	of	of	ADP
ejpam-5434	322	5	weakly	weakly	ADJ
ejpam-5434	322	6	open	open	ADJ
ejpam-5434	322	7	sets	set	NOUN
ejpam-5434	322	8	.	.	PUNCT
ejpam-5434	323	1	international	international	ADJ
ejpam-5434	323	2	journal	journal	NOUN
ejpam-5434	323	3	of	of	ADP
ejpam-5434	323	4	mathematics	mathematics	PROPN
ejpam-5434	323	5	and	and	CCONJ
ejpam-5434	323	6	statistics	statistic	NOUN
ejpam-5434	323	7	invention	invention	NOUN
ejpam-5434	323	8	,	,	PUNCT
ejpam-5434	323	9	1(1):31–37	1(1):31–37	NUM
ejpam-5434	323	10	,	,	PUNCT
ejpam-5434	323	11	2013	2013	NUM
ejpam-5434	323	12	.	.	PUNCT
ejpam-5434	324	1	[	[	X
ejpam-5434	324	2	2	2	X
ejpam-5434	324	3	]	]	X
ejpam-5434	324	4	james	james	PROPN
ejpam-5434	324	5	r.	r.	PROPN
ejpam-5434	324	6	munkres	munkres	PROPN
ejpam-5434	324	7	.	.	PUNCT
ejpam-5434	325	1	topology	topology	NOUN
ejpam-5434	325	2	.	.	PUNCT
ejpam-5434	326	1	pearson	pearson	PROPN
ejpam-5434	326	2	education	education	PROPN
ejpam-5434	326	3	,	,	PUNCT
ejpam-5434	326	4	india	india	PROPN
ejpam-5434	326	5	,	,	PUNCT
ejpam-5434	326	6	2018	2018	NUM
ejpam-5434	326	7	.	.	PUNCT
ejpam-5434	327	1	[	[	X
ejpam-5434	327	2	3	3	NUM
ejpam-5434	327	3	]	]	X
ejpam-5434	327	4	levine	levine	PROPN
ejpam-5434	327	5	.	.	PUNCT
ejpam-5434	327	6	n.	n.	PROPN
ejpam-5434	327	7	generalized	generalize	VERB
ejpam-5434	327	8	closed	closed	ADJ
ejpam-5434	327	9	sets	set	NOUN
ejpam-5434	327	10	in	in	ADP
ejpam-5434	327	11	topology	topology	NOUN
ejpam-5434	327	12	.	.	PUNCT
ejpam-5434	328	1	rendiconti	rendiconti	VERB
ejpam-5434	328	2	del	del	PROPN
ejpam-5434	328	3	circolo	circolo	PROPN
ejpam-5434	328	4	matematico	matematico	NOUN
ejpam-5434	328	5	di	di	X
ejpam-5434	328	6	parlermo	parlermo	NOUN
ejpam-5434	328	7	,	,	PUNCT
ejpam-5434	328	8	19(2):89–96	19(2):89–96	NUM
ejpam-5434	328	9	,	,	PUNCT
ejpam-5434	328	10	1970	1970	NUM
ejpam-5434	328	11	.	.	PUNCT
ejpam-5434	329	1	references	reference	NOUN
ejpam-5434	329	2	3166	3166	NUM
ejpam-5434	330	1	[	[	X
ejpam-5434	330	2	4	4	NUM
ejpam-5434	330	3	]	]	PUNCT
ejpam-5434	330	4	chandrasekar	chandrasekar	NOUN
ejpam-5434	330	5	.	.	PUNCT
ejpam-5434	331	1	s.	s.	PROPN
ejpam-5434	331	2	on	on	ADP
ejpam-5434	331	3	micro	micro	PROPN
ejpam-5434	331	4	topological	topological	ADJ
ejpam-5434	331	5	spaces	space	NOUN
ejpam-5434	331	6	.	.	PUNCT
ejpam-5434	332	1	journal	journal	NOUN
ejpam-5434	332	2	of	of	ADP
ejpam-5434	332	3	new	new	ADJ
ejpam-5434	332	4	theory	theory	NOUN
ejpam-5434	332	5	,	,	PUNCT
ejpam-5434	332	6	26:23–31	26:23–31	NUM
ejpam-5434	332	7	,	,	PUNCT
ejpam-5434	332	8	2019	2019	NUM
ejpam-5434	332	9	.	.	PUNCT
ejpam-5434	333	1	[	[	X
ejpam-5434	333	2	5	5	NUM
ejpam-5434	333	3	]	]	PUNCT
ejpam-5434	333	4	chandrasekar	chandrasekar	NOUN
ejpam-5434	333	5	.	.	PUNCT
ejpam-5434	334	1	s	s	PART
ejpam-5434	334	2	and	and	CCONJ
ejpam-5434	334	3	swathi	swathi	NOUN
ejpam-5434	334	4	.	.	PUNCT
ejpam-5434	335	1	s.	s.	PROPN
ejpam-5434	335	2	micro	micro	PROPN
ejpam-5434	335	3	α	α	PROPN
ejpam-5434	335	4	-	-	ADJ
ejpam-5434	335	5	open	open	ADJ
ejpam-5434	335	6	sets	set	NOUN
ejpam-5434	335	7	in	in	ADP
ejpam-5434	335	8	micro	micro	ADJ
ejpam-5434	335	9	topological	topological	ADJ
ejpam-5434	335	10	spaces	space	NOUN
ejpam-5434	335	11	.	.	PUNCT
ejpam-5434	336	1	international	international	ADJ
ejpam-5434	336	2	journal	journal	PROPN
ejpam-5434	336	3	of	of	ADP
ejpam-5434	336	4	research	research	NOUN
ejpam-5434	336	5	in	in	ADP
ejpam-5434	336	6	advent	advent	ADJ
ejpam-5434	336	7	technology	technology	NOUN
ejpam-5434	336	8	,	,	PUNCT
ejpam-5434	336	9	6(10):2633–2637	6(10):2633–2637	NUM
ejpam-5434	336	10	,	,	PUNCT
ejpam-5434	336	11	2018	2018	NUM
ejpam-5434	336	12	.	.	PUNCT
ejpam-5434	337	1	[	[	X
ejpam-5434	337	2	6	6	NUM
ejpam-5434	337	3	]	]	PUNCT
ejpam-5434	337	4	dhanasekaran	dhanasekaran	PROPN
ejpam-5434	338	1	p.	p.	PROPN
ejpam-5434	338	2	k.	k.	PROPN
ejpam-5434	339	1	sathishmohan	sathishmohan	PROPN
ejpam-5434	339	2	.	.	PUNCT
ejpam-5434	340	1	p	p	X
ejpam-5434	340	2	,	,	PUNCT
ejpam-5434	340	3	rajendran	rajendran	NOUN
ejpam-5434	340	4	.	.	PUNCT
ejpam-5434	341	1	v	v	X
ejpam-5434	341	2	and	and	CCONJ
ejpam-5434	341	3	vignesh	vignesh	PROPN
ejpam-5434	341	4	kumar	kumar	PROPN
ejpam-5434	341	5	.	.	PUNCT
ejpam-5434	342	1	c.	c.	PROPN
ejpam-5434	342	2	more	more	ADV
ejpam-5434	342	3	on	on	ADP
ejpam-5434	342	4	nano	nano	NOUN
ejpam-5434	342	5	preneighbourhoods	preneighbourhood	NOUN
ejpam-5434	342	6	in	in	ADP
ejpam-5434	342	7	nano	nano	NOUN
ejpam-5434	342	8	topological	topological	ADJ
ejpam-5434	342	9	spaces	space	NOUN
ejpam-5434	342	10	.	.	PUNCT
ejpam-5434	343	1	journal	journal	NOUN
ejpam-5434	343	2	of	of	ADP
ejpam-5434	343	3	applied	apply	VERB
ejpam-5434	343	4	science	science	NOUN
ejpam-5434	343	5	and	and	CCONJ
ejpam-5434	343	6	computations	computation	NOUN
ejpam-5434	343	7	.	.	PUNCT
ejpam-5434	343	8	,	,	PUNCT
ejpam-5434	343	9	10(5):899–907	10(5):899–907	PROPN
ejpam-5434	343	10	,	,	PUNCT
ejpam-5434	343	11	2018	2018	NUM
ejpam-5434	343	12	.	.	PUNCT
ejpam-5434	344	1	[	[	X
ejpam-5434	344	2	7	7	NUM
ejpam-5434	344	3	]	]	X
ejpam-5434	344	4	stanley	stanley	PROPN
ejpam-5434	344	5	roshan	roshan	PROPN
ejpam-5434	344	6	.	.	PUNCT
ejpam-5434	344	7	s	s	VERB
ejpam-5434	344	8	sathishmohan	sathishmohan	NOUN
ejpam-5434	344	9	.	.	PUNCT
ejpam-5434	345	1	p	p	NOUN
ejpam-5434	345	2	and	and	CCONJ
ejpam-5434	345	3	rajalakshmi	rajalakshmi	NOUN
ejpam-5434	345	4	.	.	PUNCT
ejpam-5434	346	1	k.	k.	PROPN
ejpam-5434	347	1	on	on	ADP
ejpam-5434	347	2	micro	micro	PROPN
ejpam-5434	347	3	pre	pre	PROPN
ejpam-5434	347	4	neighborhoods	neighborhood	NOUN
ejpam-5434	347	5	in	in	ADP
ejpam-5434	347	6	micro	micro	ADJ
ejpam-5434	347	7	topological	topological	ADJ
ejpam-5434	347	8	space	space	NOUN
ejpam-5434	347	9	.	.	PUNCT
ejpam-5434	348	1	indian	indian	ADJ
ejpam-5434	348	2	journal	journal	PROPN
ejpam-5434	348	3	of	of	ADP
ejpam-5434	348	4	science	science	NOUN
ejpam-5434	348	5	and	and	CCONJ
ejpam-5434	348	6	technology	technology	NOUN
ejpam-5434	348	7	,	,	PUNCT
ejpam-5434	348	8	17(22):2346	17(22):2346	NUM
ejpam-5434	348	9	–	–	PUNCT
ejpam-5434	348	10	2351	2351	NUM
ejpam-5434	348	11	,	,	PUNCT
ejpam-5434	348	12	2024	2024	NUM
ejpam-5434	348	13	.	.	PUNCT
ejpam-5434	349	1	[	[	X
ejpam-5434	349	2	8	8	NUM
ejpam-5434	349	3	]	]	X
ejpam-5434	349	4	antony	antony	PROPN
ejpam-5434	349	5	rex	rex	PROPN
ejpam-5434	349	6	rodgio	rodgio	PROPN
ejpam-5434	349	7	.	.	PUNCT
ejpam-5434	350	1	jessie	jessie	PROPN
ejpam-5434	350	2	theodore	theodore	PROPN
ejpam-5434	350	3	and	and	CCONJ
ejpam-5434	350	4	hanaselvi	hanaselvi	PROPN
ejpam-5434	350	5	.	.	PUNCT
ejpam-5434	351	1	notions	notion	NOUN
ejpam-5434	351	2	via	via	ADP
ejpam-5434	351	3	β∗-open	β∗-open	ADJ
ejpam-5434	351	4	sets	set	NOUN
ejpam-5434	351	5	in	in	ADP
ejpam-5434	351	6	topological	topological	ADJ
ejpam-5434	351	7	spaces	space	NOUN
ejpam-5434	351	8	.	.	PUNCT
ejpam-5434	352	1	iosr	iosr	ADJ
ejpam-5434	352	2	journal	journal	PROPN
ejpam-5434	352	3	of	of	ADP
ejpam-5434	352	4	mathematics	mathematic	NOUN
ejpam-5434	352	5	,	,	PUNCT
ejpam-5434	352	6	6(3):25–29	6(3):25–29	NUM
ejpam-5434	352	7	,	,	PUNCT
ejpam-5434	352	8	2013	2013	NUM
ejpam-5434	352	9	.	.	PUNCT
ejpam-5434	353	1	[	[	X
ejpam-5434	353	2	9	9	X
ejpam-5434	353	3	]	]	X
ejpam-5434	353	4	ibrahim	ibrahim	PROPN
ejpam-5434	353	5	h.	h.	PROPN
ejpam-5434	353	6	z.	z.	PROPN
ejpam-5434	353	7	micro	micro	PROPN
ejpam-5434	353	8	β	β	PROPN
ejpam-5434	353	9	-	-	ADJ
ejpam-5434	353	10	open	open	ADJ
ejpam-5434	353	11	sets	set	NOUN
ejpam-5434	353	12	in	in	ADP
ejpam-5434	353	13	micro	micro	PROPN
ejpam-5434	353	14	topology	topology	PROPN
ejpam-5434	353	15	.	.	PUNCT
ejpam-5434	354	1	general	general	ADJ
ejpam-5434	354	2	letters	letter	NOUN
ejpam-5434	354	3	in	in	ADP
ejpam-5434	354	4	mathematics	mathematic	NOUN
ejpam-5434	354	5	,	,	PUNCT
ejpam-5434	354	6	8(1):8–15	8(1):8–15	NUM
ejpam-5434	354	7	,	,	PUNCT
ejpam-5434	354	8	2020	2020	NUM
ejpam-5434	354	9	.	.	PUNCT