id	sid	tid	token	lemma	pos
ejpam-6270	1	1	european	european	PROPN
ejpam-6270	1	2	journal	journal	PROPN
ejpam-6270	1	3	of	of	ADP
ejpam-6270	1	4	pure	pure	ADJ
ejpam-6270	1	5	and	and	CCONJ
ejpam-6270	1	6	applied	applied	ADJ
ejpam-6270	1	7	mathematics	mathematic	NOUN
ejpam-6270	1	8	2025	2025	NUM
ejpam-6270	1	9	,	,	PUNCT
ejpam-6270	1	10	vol	vol	NOUN
ejpam-6270	1	11	.	.	PROPN
ejpam-6270	1	12	18	18	NUM
ejpam-6270	1	13	,	,	PUNCT
ejpam-6270	1	14	issue	issue	NOUN
ejpam-6270	1	15	3	3	NUM
ejpam-6270	1	16	,	,	PUNCT
ejpam-6270	1	17	article	article	NOUN
ejpam-6270	1	18	number	number	NOUN
ejpam-6270	1	19	6270	6270	NUM
ejpam-6270	1	20	issn	issn	PROPN
ejpam-6270	1	21	1307	1307	NUM
ejpam-6270	1	22	-	-	SYM
ejpam-6270	1	23	5543	5543	NUM
ejpam-6270	1	24	–	–	PUNCT
ejpam-6270	1	25	ejpam.com	ejpam.com	X
ejpam-6270	1	26	published	publish	VERB
ejpam-6270	1	27	by	by	ADP
ejpam-6270	1	28	new	new	PROPN
ejpam-6270	1	29	york	york	PROPN
ejpam-6270	1	30	business	business	PROPN
ejpam-6270	1	31	global	global	PROPN
ejpam-6270	1	32	a	a	DET
ejpam-6270	1	33	topological	topological	ADJ
ejpam-6270	1	34	structure	structure	NOUN
ejpam-6270	1	35	on	on	ADP
ejpam-6270	1	36	d	d	PROPN
ejpam-6270	1	37	-	-	PUNCT
ejpam-6270	1	38	algebras	algebras	PROPN
ejpam-6270	1	39	maha	maha	PROPN
ejpam-6270	1	40	w.	w.	PROPN
ejpam-6270	1	41	abdulqader1	abdulqader1	PROPN
ejpam-6270	1	42	,	,	PUNCT
ejpam-6270	1	43	alias	alias	PROPN
ejpam-6270	1	44	b.	b.	PROPN
ejpam-6270	1	45	khalaf1,∗	khalaf1,∗	PROPN
ejpam-6270	1	46	1	1	NUM
ejpam-6270	1	47	department	department	NOUN
ejpam-6270	1	48	of	of	ADP
ejpam-6270	1	49	mathematics	mathematic	NOUN
ejpam-6270	1	50	,	,	PUNCT
ejpam-6270	1	51	college	college	NOUN
ejpam-6270	1	52	of	of	ADP
ejpam-6270	1	53	science	science	NOUN
ejpam-6270	1	54	,	,	PUNCT
ejpam-6270	1	55	university	university	NOUN
ejpam-6270	1	56	of	of	ADP
ejpam-6270	1	57	duhok	duhok	PROPN
ejpam-6270	1	58	,	,	PUNCT
ejpam-6270	1	59	kurdistan	kurdistan	PROPN
ejpam-6270	1	60	region	region	NOUN
ejpam-6270	1	61	,	,	PUNCT
ejpam-6270	1	62	iraq	iraq	PROPN
ejpam-6270	1	63	abstract	abstract	NOUN
ejpam-6270	1	64	.	.	PUNCT
ejpam-6270	2	1	the	the	DET
ejpam-6270	2	2	primary	primary	ADJ
ejpam-6270	2	3	aim	aim	NOUN
ejpam-6270	2	4	of	of	ADP
ejpam-6270	2	5	this	this	DET
ejpam-6270	2	6	paper	paper	NOUN
ejpam-6270	2	7	is	be	AUX
ejpam-6270	2	8	applying	apply	VERB
ejpam-6270	2	9	the	the	DET
ejpam-6270	2	10	concept	concept	NOUN
ejpam-6270	2	11	of	of	ADP
ejpam-6270	2	12	b	b	NOUN
ejpam-6270	2	13	-	-	PUNCT
ejpam-6270	2	14	open	open	ADJ
ejpam-6270	2	15	sets	set	NOUN
ejpam-6270	2	16	in	in	ADP
ejpam-6270	2	17	topological	topological	ADJ
ejpam-6270	2	18	spaces	space	NOUN
ejpam-6270	2	19	to	to	PART
ejpam-6270	2	20	explore	explore	VERB
ejpam-6270	2	21	the	the	DET
ejpam-6270	2	22	idea	idea	NOUN
ejpam-6270	2	23	of	of	ADP
ejpam-6270	2	24	b	b	PROPN
ejpam-6270	2	25	-	-	PUNCT
ejpam-6270	2	26	topological	topological	ADJ
ejpam-6270	2	27	dalgebra	dalgebra	NOUN
ejpam-6270	2	28	(	(	PUNCT
ejpam-6270	2	29	tbd	tbd	NOUN
ejpam-6270	2	30	-	-	PUNCT
ejpam-6270	2	31	algebra	algebra	NOUN
ejpam-6270	2	32	)	)	PUNCT
ejpam-6270	2	33	,	,	PUNCT
ejpam-6270	2	34	which	which	PRON
ejpam-6270	2	35	is	be	AUX
ejpam-6270	2	36	a	a	DET
ejpam-6270	2	37	d	d	NOUN
ejpam-6270	2	38	-	-	PUNCT
ejpam-6270	2	39	algebra	algebra	NOUN
ejpam-6270	2	40	equipped	equip	VERB
ejpam-6270	2	41	with	with	ADP
ejpam-6270	2	42	a	a	DET
ejpam-6270	2	43	specific	specific	ADJ
ejpam-6270	2	44	type	type	NOUN
ejpam-6270	2	45	of	of	ADP
ejpam-6270	2	46	topology	topology	NOUN
ejpam-6270	2	47	that	that	PRON
ejpam-6270	2	48	ensured	ensure	VERB
ejpam-6270	2	49	the	the	DET
ejpam-6270	2	50	binary	binary	PROPN
ejpam-6270	2	51	operation	operation	NOUN
ejpam-6270	2	52	that	that	PRON
ejpam-6270	2	53	is	be	AUX
ejpam-6270	2	54	defined	define	VERB
ejpam-6270	2	55	on	on	ADP
ejpam-6270	2	56	them	they	PRON
ejpam-6270	2	57	to	to	PART
ejpam-6270	2	58	be	be	AUX
ejpam-6270	2	59	d	d	NOUN
ejpam-6270	2	60	-	-	PUNCT
ejpam-6270	2	61	topologically	topologically	ADV
ejpam-6270	2	62	continuous	continuous	ADJ
ejpam-6270	2	63	.	.	PUNCT
ejpam-6270	3	1	this	this	DET
ejpam-6270	3	2	idea	idea	NOUN
ejpam-6270	3	3	generalizes	generalize	VERB
ejpam-6270	3	4	the	the	DET
ejpam-6270	3	5	notion	notion	NOUN
ejpam-6270	3	6	of	of	ADP
ejpam-6270	3	7	topological	topological	ADJ
ejpam-6270	3	8	d	d	PROPN
ejpam-6270	3	9	-	-	PUNCT
ejpam-6270	3	10	algebras	algebras	X
ejpam-6270	3	11	.	.	PUNCT
ejpam-6270	4	1	in	in	ADP
ejpam-6270	4	2	addition	addition	NOUN
ejpam-6270	4	3	,	,	PUNCT
ejpam-6270	4	4	we	we	PRON
ejpam-6270	4	5	present	present	VERB
ejpam-6270	4	6	some	some	DET
ejpam-6270	4	7	relations	relation	NOUN
ejpam-6270	4	8	between	between	ADP
ejpam-6270	4	9	open	open	ADJ
ejpam-6270	4	10	sets	set	NOUN
ejpam-6270	4	11	and	and	CCONJ
ejpam-6270	4	12	b	b	X
ejpam-6270	4	13	-	-	PUNCT
ejpam-6270	4	14	open	open	ADJ
ejpam-6270	4	15	sets	set	NOUN
ejpam-6270	4	16	in	in	ADP
ejpam-6270	4	17	a	a	DET
ejpam-6270	4	18	tbd	tbd	NOUN
ejpam-6270	4	19	-	-	PUNCT
ejpam-6270	4	20	algebra	algebra	NOUN
ejpam-6270	4	21	.	.	PUNCT
ejpam-6270	5	1	we	we	PRON
ejpam-6270	5	2	also	also	ADV
ejpam-6270	5	3	construct	construct	VERB
ejpam-6270	5	4	some	some	DET
ejpam-6270	5	5	relations	relation	NOUN
ejpam-6270	5	6	between	between	ADP
ejpam-6270	5	7	ti	ti	NOUN
ejpam-6270	5	8	and	and	CCONJ
ejpam-6270	5	9	b	b	NOUN
ejpam-6270	5	10	-	-	PUNCT
ejpam-6270	5	11	ti	ti	NOUN
ejpam-6270	5	12	-	-	NOUN
ejpam-6270	5	13	spaces	space	NOUN
ejpam-6270	5	14	for	for	ADP
ejpam-6270	5	15	(	(	PUNCT
ejpam-6270	5	16	i=0,1,2	i=0,1,2	NUM
ejpam-6270	5	17	)	)	PUNCT
ejpam-6270	5	18	.	.	PUNCT
ejpam-6270	6	1	finally	finally	ADV
ejpam-6270	6	2	,	,	PUNCT
ejpam-6270	6	3	we	we	PRON
ejpam-6270	6	4	use	use	VERB
ejpam-6270	6	5	left	left	ADJ
ejpam-6270	6	6	maps	map	NOUN
ejpam-6270	6	7	on	on	ADP
ejpam-6270	6	8	positive	positive	ADJ
ejpam-6270	6	9	implicative	implicative	ADJ
ejpam-6270	6	10	d	d	NOUN
ejpam-6270	6	11	-	-	PUNCT
ejpam-6270	6	12	algebras	algebras	PROPN
ejpam-6270	6	13	to	to	PART
ejpam-6270	6	14	establish	establish	VERB
ejpam-6270	6	15	some	some	DET
ejpam-6270	6	16	tbd	tbd	NOUN
ejpam-6270	6	17	-	-	PUNCT
ejpam-6270	6	18	algebras	algebras	X
ejpam-6270	6	19	.	.	PUNCT
ejpam-6270	7	1	2020	2020	NUM
ejpam-6270	7	2	mathematics	mathematics	PROPN
ejpam-6270	7	3	subject	subject	NOUN
ejpam-6270	7	4	classifications	classification	NOUN
ejpam-6270	7	5	:	:	PUNCT
ejpam-6270	7	6	03g25	03g25	NUM
ejpam-6270	7	7	,	,	PUNCT
ejpam-6270	7	8	22a30	22a30	NUM
ejpam-6270	7	9	,	,	PUNCT
ejpam-6270	7	10	54a05	54a05	NUM
ejpam-6270	7	11	key	key	ADJ
ejpam-6270	7	12	words	word	NOUN
ejpam-6270	7	13	and	and	CCONJ
ejpam-6270	7	14	phrases	phrase	NOUN
ejpam-6270	7	15	:	:	PUNCT
ejpam-6270	7	16	b	b	X
ejpam-6270	7	17	-	-	PUNCT
ejpam-6270	7	18	open	open	ADJ
ejpam-6270	7	19	set	set	NOUN
ejpam-6270	7	20	,	,	PUNCT
ejpam-6270	7	21	d	d	X
ejpam-6270	7	22	-	-	PUNCT
ejpam-6270	7	23	algebra	algebra	ADJ
ejpam-6270	7	24	,	,	PUNCT
ejpam-6270	7	25	positive	positive	ADJ
ejpam-6270	7	26	implicative	implicative	ADJ
ejpam-6270	7	27	d	d	NOUN
ejpam-6270	7	28	-	-	NOUN
ejpam-6270	7	29	algebra	algebra	NOUN
ejpam-6270	7	30	,	,	PUNCT
ejpam-6270	7	31	edge	edge	NOUN
ejpam-6270	7	32	d	d	NOUN
ejpam-6270	7	33	-	-	PUNCT
ejpam-6270	7	34	algebra	algebra	ADJ
ejpam-6270	7	35	,	,	PUNCT
ejpam-6270	7	36	b	b	X
ejpam-6270	7	37	-	-	PUNCT
ejpam-6270	7	38	t2	t2	NOUN
ejpam-6270	7	39	space	space	NOUN
ejpam-6270	7	40	,	,	PUNCT
ejpam-6270	7	41	tbd	tbd	NOUN
ejpam-6270	7	42	-	-	NOUN
ejpam-6270	7	43	algebra	algebra	NOUN
ejpam-6270	7	44	1	1	NUM
ejpam-6270	7	45	.	.	PUNCT
ejpam-6270	8	1	introduction	introduction	NOUN
ejpam-6270	8	2	topology	topology	NOUN
ejpam-6270	8	3	and	and	CCONJ
ejpam-6270	8	4	algebra	algebra	NOUN
ejpam-6270	8	5	are	be	AUX
ejpam-6270	8	6	two	two	NUM
ejpam-6270	8	7	significant	significant	ADJ
ejpam-6270	8	8	areas	area	NOUN
ejpam-6270	8	9	of	of	ADP
ejpam-6270	8	10	pure	pure	ADJ
ejpam-6270	8	11	mathematics	mathematic	NOUN
ejpam-6270	8	12	.	.	PUNCT
ejpam-6270	9	1	topology	topology	NOUN
ejpam-6270	9	2	focuses	focus	VERB
ejpam-6270	9	3	on	on	ADP
ejpam-6270	9	4	concepts	concept	NOUN
ejpam-6270	9	5	such	such	ADJ
ejpam-6270	9	6	as	as	ADP
ejpam-6270	9	7	continuity	continuity	NOUN
ejpam-6270	9	8	and	and	CCONJ
ejpam-6270	9	9	convergence	convergence	NOUN
ejpam-6270	9	10	,	,	PUNCT
ejpam-6270	9	11	while	while	SCONJ
ejpam-6270	9	12	algebra	algebra	NOUN
ejpam-6270	9	13	explores	explore	VERB
ejpam-6270	9	14	various	various	ADJ
ejpam-6270	9	15	operations	operation	NOUN
ejpam-6270	9	16	,	,	PUNCT
ejpam-6270	9	17	forming	form	VERB
ejpam-6270	9	18	the	the	DET
ejpam-6270	9	19	foundation	foundation	NOUN
ejpam-6270	9	20	for	for	ADP
ejpam-6270	9	21	calculations	calculation	NOUN
ejpam-6270	9	22	and	and	CCONJ
ejpam-6270	9	23	algorithms	algorithm	NOUN
ejpam-6270	9	24	.	.	PUNCT
ejpam-6270	10	1	a	a	DET
ejpam-6270	10	2	key	key	ADJ
ejpam-6270	10	3	principle	principle	NOUN
ejpam-6270	10	4	that	that	PRON
ejpam-6270	10	5	links	link	VERB
ejpam-6270	10	6	algebraic	algebraic	ADJ
ejpam-6270	10	7	operations	operation	NOUN
ejpam-6270	10	8	and	and	CCONJ
ejpam-6270	10	9	topology	topology	NOUN
ejpam-6270	10	10	is	be	AUX
ejpam-6270	10	11	the	the	DET
ejpam-6270	10	12	requirement	requirement	NOUN
ejpam-6270	10	13	that	that	SCONJ
ejpam-6270	10	14	these	these	DET
ejpam-6270	10	15	operations	operation	NOUN
ejpam-6270	10	16	be	be	VERB
ejpam-6270	10	17	continuous	continuous	ADJ
ejpam-6270	10	18	topologically	topologically	ADV
ejpam-6270	10	19	,	,	PUNCT
ejpam-6270	10	20	either	either	CCONJ
ejpam-6270	10	21	jointly	jointly	ADV
ejpam-6270	10	22	continuous	continuous	ADJ
ejpam-6270	10	23	or	or	CCONJ
ejpam-6270	10	24	in	in	ADP
ejpam-6270	10	25	the	the	DET
ejpam-6270	10	26	first	first	ADJ
ejpam-6270	10	27	or	or	CCONJ
ejpam-6270	10	28	second	second	ADJ
ejpam-6270	10	29	variable	variable	NOUN
ejpam-6270	10	30	,	,	PUNCT
ejpam-6270	10	31	this	this	DET
ejpam-6270	10	32	field	field	NOUN
ejpam-6270	10	33	is	be	AUX
ejpam-6270	10	34	known	know	VERB
ejpam-6270	10	35	as	as	ADP
ejpam-6270	10	36	topological	topological	ADJ
ejpam-6270	10	37	algebra	algebra	NOUN
ejpam-6270	10	38	.	.	PUNCT
ejpam-6270	11	1	in	in	ADP
ejpam-6270	11	2	recent	recent	ADJ
ejpam-6270	11	3	years	year	NOUN
ejpam-6270	11	4	,	,	PUNCT
ejpam-6270	11	5	numerous	numerous	ADJ
ejpam-6270	11	6	researchers	researcher	NOUN
ejpam-6270	11	7	have	have	AUX
ejpam-6270	11	8	advanced	advance	VERB
ejpam-6270	11	9	this	this	DET
ejpam-6270	11	10	area	area	NOUN
ejpam-6270	11	11	of	of	ADP
ejpam-6270	11	12	study	study	NOUN
ejpam-6270	11	13	.	.	PUNCT
ejpam-6270	12	1	since	since	SCONJ
ejpam-6270	12	2	the	the	DET
ejpam-6270	12	3	early	early	ADJ
ejpam-6270	12	4	twentieth	twentieth	ADJ
ejpam-6270	12	5	century	century	NOUN
ejpam-6270	12	6	,	,	PUNCT
ejpam-6270	12	7	many	many	ADJ
ejpam-6270	12	8	mathematicians	mathematician	NOUN
ejpam-6270	12	9	have	have	AUX
ejpam-6270	12	10	made	make	VERB
ejpam-6270	12	11	substantial	substantial	ADJ
ejpam-6270	12	12	contributions	contribution	NOUN
ejpam-6270	12	13	to	to	ADP
ejpam-6270	12	14	progress	progress	NOUN
ejpam-6270	12	15	of	of	ADP
ejpam-6270	12	16	these	these	DET
ejpam-6270	12	17	interrelated	interrelated	ADJ
ejpam-6270	12	18	subjects	subject	NOUN
ejpam-6270	12	19	.	.	PUNCT
ejpam-6270	13	1	generalized	generalize	VERB
ejpam-6270	13	2	open	open	ADJ
ejpam-6270	13	3	sets	set	NOUN
ejpam-6270	13	4	are	be	AUX
ejpam-6270	13	5	fundamental	fundamental	ADJ
ejpam-6270	13	6	to	to	ADP
ejpam-6270	13	7	general	general	ADJ
ejpam-6270	13	8	topology	topology	NOUN
ejpam-6270	13	9	and	and	CCONJ
ejpam-6270	13	10	are	be	AUX
ejpam-6270	13	11	acknowledged	acknowledge	VERB
ejpam-6270	13	12	as	as	ADP
ejpam-6270	13	13	significant	significant	ADJ
ejpam-6270	13	14	research	research	NOUN
ejpam-6270	13	15	areas	area	NOUN
ejpam-6270	13	16	by	by	ADP
ejpam-6270	13	17	topologists	topologist	NOUN
ejpam-6270	13	18	around	around	ADP
ejpam-6270	13	19	the	the	DET
ejpam-6270	13	20	world	world	NOUN
ejpam-6270	13	21	.	.	PUNCT
ejpam-6270	14	1	these	these	DET
ejpam-6270	14	2	sets	set	NOUN
ejpam-6270	14	3	are	be	AUX
ejpam-6270	14	4	central	central	ADJ
ejpam-6270	14	5	to	to	ADP
ejpam-6270	14	6	major	major	ADJ
ejpam-6270	14	7	themes	theme	NOUN
ejpam-6270	14	8	in	in	ADP
ejpam-6270	14	9	both	both	CCONJ
ejpam-6270	14	10	general	general	ADJ
ejpam-6270	14	11	topology	topology	NOUN
ejpam-6270	14	12	and	and	CCONJ
ejpam-6270	14	13	real	real	ADJ
ejpam-6270	14	14	analysis	analysis	NOUN
ejpam-6270	14	15	,	,	PUNCT
ejpam-6270	14	16	particularly	particularly	ADV
ejpam-6270	14	17	in	in	ADP
ejpam-6270	14	18	connection	connection	NOUN
ejpam-6270	14	19	with	with	ADP
ejpam-6270	14	20	various	various	ADJ
ejpam-6270	14	21	modified	modify	VERB
ejpam-6270	14	22	forms	form	NOUN
ejpam-6270	14	23	of	of	ADP
ejpam-6270	14	24	continuity	continuity	NOUN
ejpam-6270	14	25	,	,	PUNCT
ejpam-6270	14	26	separation	separation	NOUN
ejpam-6270	14	27	axioms	axiom	NOUN
ejpam-6270	14	28	,	,	PUNCT
ejpam-6270	14	29	and	and	CCONJ
ejpam-6270	14	30	other	other	ADJ
ejpam-6270	14	31	related	related	ADJ
ejpam-6270	14	32	concepts	concept	NOUN
ejpam-6270	14	33	.	.	PUNCT
ejpam-6270	15	1	one	one	NUM
ejpam-6270	15	2	of	of	ADP
ejpam-6270	15	3	the	the	DET
ejpam-6270	15	4	forms	form	NOUN
ejpam-6270	15	5	of	of	ADP
ejpam-6270	15	6	generalized	generalized	ADJ
ejpam-6270	15	7	open	open	ADJ
ejpam-6270	15	8	sets	set	NOUN
ejpam-6270	15	9	in	in	ADP
ejpam-6270	15	10	topological	topological	ADJ
ejpam-6270	15	11	spaces	space	NOUN
ejpam-6270	15	12	,	,	PUNCT
ejpam-6270	15	13	known	know	VERB
ejpam-6270	15	14	as	as	ADP
ejpam-6270	15	15	b	b	NOUN
ejpam-6270	15	16	-	-	PUNCT
ejpam-6270	15	17	open	open	ADJ
ejpam-6270	15	18	sets	set	NOUN
ejpam-6270	15	19	,	,	PUNCT
ejpam-6270	15	20	was	be	AUX
ejpam-6270	15	21	introduced	introduce	VERB
ejpam-6270	15	22	by	by	ADP
ejpam-6270	15	23	andrijevic	andrijevic	VERB
ejpam-6270	15	24	[	[	X
ejpam-6270	15	25	1	1	X
ejpam-6270	15	26	]	]	PUNCT
ejpam-6270	15	27	in	in	ADP
ejpam-6270	15	28	1996	1996	NUM
ejpam-6270	15	29	.	.	PUNCT
ejpam-6270	16	1	these	these	DET
ejpam-6270	16	2	sets	set	NOUN
ejpam-6270	16	3	were	be	AUX
ejpam-6270	16	4	presented	present	VERB
ejpam-6270	16	5	by	by	ADP
ejpam-6270	16	6	al	al	PROPN
ejpam-6270	16	7	-	-	PUNCT
ejpam-6270	16	8	etik	etik	NOUN
ejpam-6270	16	9	[	[	X
ejpam-6270	16	10	2	2	NUM
ejpam-6270	16	11	]	]	PUNCT
ejpam-6270	16	12	under	under	ADP
ejpam-6270	16	13	the	the	DET
ejpam-6270	16	14	name	name	NOUN
ejpam-6270	16	15	λ	λ	NOUN
ejpam-6270	16	16	-	-	ADJ
ejpam-6270	16	17	open	open	ADJ
ejpam-6270	16	18	sets	set	NOUN
ejpam-6270	16	19	.	.	PUNCT
ejpam-6270	17	1	furthermore	furthermore	ADV
ejpam-6270	17	2	,	,	PUNCT
ejpam-6270	17	3	caldas	caldas	PROPN
ejpam-6270	17	4	and	and	CCONJ
ejpam-6270	17	5	jafari	jafari	PROPN
ejpam-6270	18	1	[	[	X
ejpam-6270	18	2	3	3	X
ejpam-6270	18	3	]	]	PUNCT
ejpam-6270	18	4	used	use	VERB
ejpam-6270	18	5	open	open	ADJ
ejpam-6270	18	6	sets	set	NOUN
ejpam-6270	18	7	b	b	NOUN
ejpam-6270	18	8	to	to	PART
ejpam-6270	18	9	define	define	VERB
ejpam-6270	18	10	separation	separation	NOUN
ejpam-6270	18	11	axioms	axiom	NOUN
ejpam-6270	18	12	b	b	X
ejpam-6270	18	13	-	-	PUNCT
ejpam-6270	18	14	ti	ti	NOUN
ejpam-6270	18	15	(	(	PUNCT
ejpam-6270	18	16	i	i	NOUN
ejpam-6270	18	17	∈	∈	PROPN
ejpam-6270	18	18	0	0	NUM
ejpam-6270	18	19	,	,	PUNCT
ejpam-6270	18	20	1	1	NUM
ejpam-6270	18	21	,	,	PUNCT
ejpam-6270	18	22	2	2	NUM
ejpam-6270	18	23	)	)	PUNCT
ejpam-6270	18	24	∗corresponding	∗corresponde	VERB
ejpam-6270	18	25	author	author	NOUN
ejpam-6270	18	26	.	.	PUNCT
ejpam-6270	19	1	doi	doi	NOUN
ejpam-6270	19	2	:	:	PUNCT
ejpam-6270	19	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6270	https://doi.org/10.29020/nybg.ejpam.v18i3.6270	PUNCT
ejpam-6270	19	4	email	email	NOUN
ejpam-6270	19	5	addresses	address	NOUN
ejpam-6270	19	6	:	:	PUNCT
ejpam-6270	19	7	maha.waleed@uod.ac	maha.waleed@uod.ac	NOUN
ejpam-6270	19	8	(	(	PUNCT
ejpam-6270	19	9	m.	m.	NOUN
ejpam-6270	19	10	w.	w.	PROPN
ejpam-6270	19	11	abdulqader	abdulqader	PROPN
ejpam-6270	19	12	)	)	PUNCT
ejpam-6270	19	13	,	,	PUNCT
ejpam-6270	19	14	alias.khalaf@uod.ac	alias.khalaf@uod.ac	CCONJ
ejpam-6270	19	15	(	(	PUNCT
ejpam-6270	19	16	a.	a.	PROPN
ejpam-6270	19	17	b.	b.	PROPN
ejpam-6270	19	18	khalaf	khalaf	PROPN
ejpam-6270	19	19	)	)	PUNCT
ejpam-6270	19	20	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6270	20	1	1	1	NUM
ejpam-6270	20	2	copyright	copyright	NOUN
ejpam-6270	20	3	:	:	PUNCT
ejpam-6270	20	4	©	©	PROPN
ejpam-6270	20	5	2025	2025	NUM
ejpam-6270	20	6	the	the	DET
ejpam-6270	20	7	author(s	author(s	NOUN
ejpam-6270	20	8	)	)	PUNCT
ejpam-6270	20	9	.	.	PUNCT
ejpam-6270	21	1	(	(	PUNCT
ejpam-6270	21	2	cc	cc	NOUN
ejpam-6270	21	3	by	by	ADP
ejpam-6270	21	4	-	-	PUNCT
ejpam-6270	21	5	nc	nc	PROPN
ejpam-6270	21	6	4.0	4.0	NUM
ejpam-6270	21	7	)	)	PUNCT
ejpam-6270	21	8	m.	m.	NOUN
ejpam-6270	21	9	w.	w.	PROPN
ejpam-6270	21	10	abdulqader	abdulqader	PROPN
ejpam-6270	21	11	,	,	PUNCT
ejpam-6270	21	12	a.	a.	PROPN
ejpam-6270	21	13	b.	b.	PROPN
ejpam-6270	21	14	khalaf	khalaf	PROPN
ejpam-6270	21	15	/	/	SYM
ejpam-6270	21	16	eur	eur	PROPN
ejpam-6270	21	17	.	.	PUNCT
ejpam-6270	22	1	j.	j.	PROPN
ejpam-6270	22	2	pure	pure	PROPN
ejpam-6270	22	3	appl	appl	PROPN
ejpam-6270	22	4	.	.	PROPN
ejpam-6270	22	5	math	math	PROPN
ejpam-6270	22	6	,	,	PUNCT
ejpam-6270	22	7	18	18	NUM
ejpam-6270	22	8	(	(	PUNCT
ejpam-6270	22	9	3	3	NUM
ejpam-6270	22	10	)	)	PUNCT
ejpam-6270	22	11	(	(	PUNCT
ejpam-6270	22	12	2025	2025	NUM
ejpam-6270	22	13	)	)	PUNCT
ejpam-6270	22	14	,	,	PUNCT
ejpam-6270	22	15	6270	6270	NUM
ejpam-6270	22	16	2	2	NUM
ejpam-6270	22	17	of	of	ADP
ejpam-6270	22	18	17	17	NUM
ejpam-6270	22	19	in	in	ADP
ejpam-6270	22	20	topological	topological	ADJ
ejpam-6270	22	21	spaces	space	NOUN
ejpam-6270	22	22	.	.	PUNCT
ejpam-6270	23	1	the	the	DET
ejpam-6270	23	2	concept	concept	NOUN
ejpam-6270	23	3	of	of	ADP
ejpam-6270	23	4	d	d	X
ejpam-6270	23	5	-	-	PUNCT
ejpam-6270	23	6	algebra	algebra	NOUN
ejpam-6270	23	7	was	be	AUX
ejpam-6270	23	8	introduced	introduce	VERB
ejpam-6270	23	9	by	by	ADP
ejpam-6270	23	10	neggers	negger	NOUN
ejpam-6270	23	11	and	and	CCONJ
ejpam-6270	23	12	kim	kim	PROPN
ejpam-6270	23	13	in	in	ADP
ejpam-6270	23	14	[	[	X
ejpam-6270	23	15	4	4	NUM
ejpam-6270	23	16	]	]	PUNCT
ejpam-6270	23	17	.	.	PUNCT
ejpam-6270	24	1	the	the	DET
ejpam-6270	24	2	topological	topological	ADJ
ejpam-6270	24	3	bck	bck	NOUN
ejpam-6270	24	4	-	-	PUNCT
ejpam-6270	24	5	algebra	algebra	PROPN
ejpam-6270	24	6	and	and	CCONJ
ejpam-6270	24	7	the	the	DET
ejpam-6270	24	8	topological	topological	ADJ
ejpam-6270	24	9	d	d	X
ejpam-6270	24	10	-	-	PUNCT
ejpam-6270	24	11	algebras	algebras	PROPN
ejpam-6270	24	12	were	be	AUX
ejpam-6270	24	13	defined	define	VERB
ejpam-6270	24	14	in	in	ADP
ejpam-6270	24	15	[	[	X
ejpam-6270	24	16	5	5	NUM
ejpam-6270	24	17	]	]	PUNCT
ejpam-6270	24	18	and	and	CCONJ
ejpam-6270	24	19	[	[	X
ejpam-6270	24	20	6	6	NUM
ejpam-6270	24	21	]	]	PUNCT
ejpam-6270	24	22	respectively	respectively	ADV
ejpam-6270	24	23	.	.	PUNCT
ejpam-6270	25	1	recently	recently	ADV
ejpam-6270	25	2	,	,	PUNCT
ejpam-6270	25	3	khalaf	khalaf	PROPN
ejpam-6270	25	4	in	in	ADP
ejpam-6270	25	5	[	[	X
ejpam-6270	25	6	7–9	7–9	X
ejpam-6270	25	7	]	]	PUNCT
ejpam-6270	25	8	introduced	introduce	VERB
ejpam-6270	25	9	some	some	DET
ejpam-6270	25	10	topological	topological	ADJ
ejpam-6270	25	11	notions	notion	NOUN
ejpam-6270	25	12	defined	define	VERB
ejpam-6270	25	13	on	on	ADP
ejpam-6270	25	14	bck	bck	NOUN
ejpam-6270	25	15	-	-	PUNCT
ejpam-6270	25	16	algebras	algebras	PROPN
ejpam-6270	25	17	.	.	PUNCT
ejpam-6270	26	1	we	we	PRON
ejpam-6270	26	2	can	can	AUX
ejpam-6270	26	3	notice	notice	VERB
ejpam-6270	26	4	that	that	SCONJ
ejpam-6270	26	5	the	the	DET
ejpam-6270	26	6	concept	concept	NOUN
ejpam-6270	26	7	of	of	ADP
ejpam-6270	26	8	b	b	X
ejpam-6270	26	9	-	-	PUNCT
ejpam-6270	26	10	open	open	ADJ
ejpam-6270	26	11	was	be	AUX
ejpam-6270	26	12	included	include	VERB
ejpam-6270	26	13	in	in	ADP
ejpam-6270	26	14	many	many	ADJ
ejpam-6270	26	15	topics	topic	NOUN
ejpam-6270	26	16	and	and	CCONJ
ejpam-6270	26	17	here	here	ADV
ejpam-6270	26	18	we	we	PRON
ejpam-6270	26	19	review	review	VERB
ejpam-6270	26	20	some	some	PRON
ejpam-6270	26	21	of	of	ADP
ejpam-6270	26	22	them	they	PRON
ejpam-6270	26	23	,	,	PUNCT
ejpam-6270	26	24	in	in	ADP
ejpam-6270	26	25	[	[	X
ejpam-6270	26	26	10	10	NUM
ejpam-6270	26	27	]	]	PUNCT
ejpam-6270	26	28	the	the	DET
ejpam-6270	26	29	supra	supra	PROPN
ejpam-6270	26	30	-	-	PUNCT
ejpam-6270	26	31	b	b	NOUN
ejpam-6270	26	32	limit	limit	NOUN
ejpam-6270	26	33	points	point	NOUN
ejpam-6270	26	34	and	and	CCONJ
ejpam-6270	26	35	supra	supra	ADJ
ejpam-6270	26	36	-	-	PUNCT
ejpam-6270	26	37	b	b	NOUN
ejpam-6270	26	38	separation	separation	NOUN
ejpam-6270	26	39	axioms	axiom	NOUN
ejpam-6270	26	40	were	be	AUX
ejpam-6270	26	41	investigated	investigate	VERB
ejpam-6270	26	42	,	,	PUNCT
ejpam-6270	26	43	also	also	ADV
ejpam-6270	26	44	in	in	ADP
ejpam-6270	26	45	[	[	PUNCT
ejpam-6270	26	46	11	11	NUM
ejpam-6270	26	47	]	]	SYM
ejpam-6270	26	48	b	b	X
ejpam-6270	26	49	-	-	PUNCT
ejpam-6270	26	50	open	open	ADJ
ejpam-6270	26	51	sets	set	NOUN
ejpam-6270	26	52	via	via	ADP
ejpam-6270	26	53	infra	infra	NOUN
ejpam-6270	26	54	soft	soft	ADJ
ejpam-6270	26	55	topological	topological	ADJ
ejpam-6270	26	56	spaces	space	NOUN
ejpam-6270	26	57	were	be	AUX
ejpam-6270	26	58	studied	study	VERB
ejpam-6270	26	59	.	.	PUNCT
ejpam-6270	27	1	limit	limit	NOUN
ejpam-6270	27	2	points	point	NOUN
ejpam-6270	27	3	and	and	CCONJ
ejpam-6270	27	4	separation	separation	NOUN
ejpam-6270	27	5	axioms	axiom	NOUN
ejpam-6270	27	6	with	with	ADP
ejpam-6270	27	7	respect	respect	NOUN
ejpam-6270	27	8	to	to	ADP
ejpam-6270	27	9	supra	supra	NOUN
ejpam-6270	27	10	semi	semi	ADJ
ejpam-6270	27	11	-	-	ADJ
ejpam-6270	27	12	open	open	ADJ
ejpam-6270	27	13	sets	set	NOUN
ejpam-6270	27	14	were	be	AUX
ejpam-6270	27	15	established	establish	VERB
ejpam-6270	27	16	in	in	ADP
ejpam-6270	27	17	[	[	X
ejpam-6270	27	18	12	12	NUM
ejpam-6270	27	19	]	]	PUNCT
ejpam-6270	27	20	.	.	PUNCT
ejpam-6270	28	1	by	by	ADP
ejpam-6270	28	2	(	(	PUNCT
ejpam-6270	28	3	w	w	PROPN
ejpam-6270	28	4	,	,	PUNCT
ejpam-6270	28	5	ω	ω	NOUN
ejpam-6270	28	6	)	)	PUNCT
ejpam-6270	28	7	we	we	PRON
ejpam-6270	28	8	mean	mean	VERB
ejpam-6270	28	9	a	a	DET
ejpam-6270	28	10	topological	topological	ADJ
ejpam-6270	28	11	space	space	NOUN
ejpam-6270	28	12	and	and	CCONJ
ejpam-6270	28	13	if	if	SCONJ
ejpam-6270	28	14	m	m	NOUN
ejpam-6270	28	15	is	be	AUX
ejpam-6270	28	16	any	any	DET
ejpam-6270	28	17	subset	subset	NOUN
ejpam-6270	28	18	of	of	ADP
ejpam-6270	28	19	a	a	DET
ejpam-6270	28	20	topological	topological	ADJ
ejpam-6270	28	21	space	space	NOUN
ejpam-6270	28	22	(	(	PUNCT
ejpam-6270	28	23	w	w	PROPN
ejpam-6270	28	24	,	,	PUNCT
ejpam-6270	28	25	ω	ω	NOUN
ejpam-6270	28	26	)	)	PUNCT
ejpam-6270	28	27	,	,	PUNCT
ejpam-6270	28	28	then	then	ADV
ejpam-6270	28	29	the	the	DET
ejpam-6270	28	30	interior	interior	ADJ
ejpam-6270	28	31	and	and	CCONJ
ejpam-6270	28	32	closure	closure	NOUN
ejpam-6270	28	33	of	of	ADP
ejpam-6270	28	34	m	m	NOUN
ejpam-6270	28	35	are	be	AUX
ejpam-6270	28	36	denoted	denote	VERB
ejpam-6270	28	37	by	by	ADP
ejpam-6270	28	38	int(m	int(m	PROPN
ejpam-6270	28	39	)	)	PUNCT
ejpam-6270	28	40	and	and	CCONJ
ejpam-6270	28	41	cl(m	cl(m	NUM
ejpam-6270	28	42	)	)	PUNCT
ejpam-6270	28	43	,	,	PUNCT
ejpam-6270	28	44	respectively	respectively	ADV
ejpam-6270	28	45	.	.	PUNCT
ejpam-6270	29	1	2	2	X
ejpam-6270	29	2	.	.	X
ejpam-6270	29	3	preliminaries	preliminary	NOUN
ejpam-6270	29	4	in	in	ADP
ejpam-6270	29	5	this	this	DET
ejpam-6270	29	6	section	section	NOUN
ejpam-6270	29	7	,	,	PUNCT
ejpam-6270	29	8	we	we	PRON
ejpam-6270	29	9	recall	recall	VERB
ejpam-6270	29	10	some	some	DET
ejpam-6270	29	11	definitions	definition	NOUN
ejpam-6270	29	12	and	and	CCONJ
ejpam-6270	29	13	results	result	NOUN
ejpam-6270	29	14	that	that	PRON
ejpam-6270	29	15	are	be	AUX
ejpam-6270	29	16	needed	need	VERB
ejpam-6270	29	17	in	in	ADP
ejpam-6270	29	18	the	the	DET
ejpam-6270	29	19	next	next	ADJ
ejpam-6270	29	20	section	section	NOUN
ejpam-6270	29	21	.	.	PUNCT
ejpam-6270	30	1	definition	definition	NOUN
ejpam-6270	30	2	1	1	NUM
ejpam-6270	30	3	.	.	PUNCT
ejpam-6270	31	1	in	in	ADP
ejpam-6270	31	2	a	a	DET
ejpam-6270	31	3	topological	topological	ADJ
ejpam-6270	31	4	space	space	NOUN
ejpam-6270	31	5	w	w	PROPN
ejpam-6270	31	6	,	,	PUNCT
ejpam-6270	31	7	a	a	DET
ejpam-6270	31	8	subset	subset	NOUN
ejpam-6270	31	9	m	m	AUX
ejpam-6270	31	10	is	be	AUX
ejpam-6270	31	11	called	call	VERB
ejpam-6270	31	12	b	b	NOUN
ejpam-6270	31	13	-	-	PUNCT
ejpam-6270	31	14	open	open	ADJ
ejpam-6270	31	15	[	[	X
ejpam-6270	31	16	1	1	NUM
ejpam-6270	31	17	]	]	PUNCT
ejpam-6270	31	18	(	(	PUNCT
ejpam-6270	31	19	resp	resp	NOUN
ejpam-6270	31	20	.	.	PUNCT
ejpam-6270	32	1	,	,	PUNCT
ejpam-6270	32	2	regular	regular	ADJ
ejpam-6270	32	3	open	open	ADJ
ejpam-6270	32	4	[	[	PUNCT
ejpam-6270	32	5	13	13	NUM
ejpam-6270	32	6	]	]	PUNCT
ejpam-6270	32	7	,	,	PUNCT
ejpam-6270	32	8	semi	semi	ADJ
ejpam-6270	32	9	-	-	ADJ
ejpam-6270	32	10	open	open	ADJ
ejpam-6270	32	11	[	[	X
ejpam-6270	32	12	14	14	NUM
ejpam-6270	32	13	]	]	PUNCT
ejpam-6270	32	14	,	,	PUNCT
ejpam-6270	32	15	pre	pre	ADJ
ejpam-6270	32	16	-	-	ADJ
ejpam-6270	32	17	open	open	ADJ
ejpam-6270	32	18	[	[	X
ejpam-6270	32	19	15	15	NUM
ejpam-6270	32	20	]	]	SYM
ejpam-6270	32	21	)	)	PUNCT
ejpam-6270	32	22	if	if	SCONJ
ejpam-6270	32	23	m	m	PROPN
ejpam-6270	32	24	⊆	⊆	NUM
ejpam-6270	32	25	int(cl(m	int(cl(m	PROPN
ejpam-6270	32	26	)	)	PUNCT
ejpam-6270	32	27	)	)	PUNCT
ejpam-6270	32	28	∪	∪	ADP
ejpam-6270	32	29	cl(int(m	cl(int(m	NOUN
ejpam-6270	32	30	)	)	PUNCT
ejpam-6270	32	31	)	)	PUNCT
ejpam-6270	32	32	(	(	PUNCT
ejpam-6270	32	33	resp	resp	NOUN
ejpam-6270	32	34	.	.	PUNCT
ejpam-6270	32	35	,	,	PUNCT
ejpam-6270	32	36	m	m	VERB
ejpam-6270	32	37	=	=	ADJ
ejpam-6270	32	38	int(cl(m	int(cl(m	PROPN
ejpam-6270	32	39	)	)	PUNCT
ejpam-6270	32	40	)	)	PUNCT
ejpam-6270	32	41	,	,	PUNCT
ejpam-6270	32	42	m	m	VERB
ejpam-6270	32	43	⊆	⊆	NUM
ejpam-6270	32	44	cl(int(m	cl(int(m	NOUN
ejpam-6270	32	45	)	)	PUNCT
ejpam-6270	32	46	)	)	PUNCT
ejpam-6270	32	47	,	,	PUNCT
ejpam-6270	32	48	m	m	VERB
ejpam-6270	32	49	⊆	⊆	NUM
ejpam-6270	32	50	int(cl(m	int(cl(m	PROPN
ejpam-6270	32	51	)	)	PUNCT
ejpam-6270	32	52	)	)	PUNCT
ejpam-6270	32	53	)	)	PUNCT
ejpam-6270	32	54	.	.	PUNCT
ejpam-6270	33	1	lemma	lemma	PROPN
ejpam-6270	33	2	1	1	NUM
ejpam-6270	33	3	.	.	PUNCT
ejpam-6270	34	1	[	[	X
ejpam-6270	34	2	1	1	X
ejpam-6270	34	3	]	]	PUNCT
ejpam-6270	34	4	the	the	DET
ejpam-6270	34	5	intersection	intersection	NOUN
ejpam-6270	34	6	of	of	ADP
ejpam-6270	34	7	an	an	DET
ejpam-6270	34	8	open	open	ADJ
ejpam-6270	34	9	and	and	CCONJ
ejpam-6270	34	10	a	a	DET
ejpam-6270	34	11	b	b	NOUN
ejpam-6270	34	12	-	-	PUNCT
ejpam-6270	34	13	open	open	ADJ
ejpam-6270	34	14	set	set	NOUN
ejpam-6270	34	15	is	be	AUX
ejpam-6270	34	16	a	a	DET
ejpam-6270	34	17	b	b	NOUN
ejpam-6270	34	18	-	-	PUNCT
ejpam-6270	34	19	open	open	ADJ
ejpam-6270	34	20	set	set	NOUN
ejpam-6270	34	21	.	.	PUNCT
ejpam-6270	35	1	lemma	lemma	PROPN
ejpam-6270	35	2	2	2	NUM
ejpam-6270	35	3	.	.	PUNCT
ejpam-6270	36	1	[	[	X
ejpam-6270	36	2	1	1	X
ejpam-6270	36	3	]	]	PUNCT
ejpam-6270	36	4	in	in	ADP
ejpam-6270	36	5	a	a	DET
ejpam-6270	36	6	topological	topological	ADJ
ejpam-6270	36	7	space	space	NOUN
ejpam-6270	36	8	w	w	PROPN
ejpam-6270	36	9	,	,	PUNCT
ejpam-6270	36	10	a	a	DET
ejpam-6270	36	11	subset	subset	NOUN
ejpam-6270	36	12	m	m	AUX
ejpam-6270	36	13	is	be	AUX
ejpam-6270	36	14	b	b	NOUN
ejpam-6270	36	15	-	-	PUNCT
ejpam-6270	36	16	open	open	ADJ
ejpam-6270	36	17	if	if	SCONJ
ejpam-6270	36	18	and	and	CCONJ
ejpam-6270	36	19	only	only	ADV
ejpam-6270	36	20	if	if	SCONJ
ejpam-6270	36	21	m	m	VERB
ejpam-6270	36	22	=(	=(	ADJ
ejpam-6270	36	23	m	m	PROPN
ejpam-6270	36	24	∩	∩	ADJ
ejpam-6270	36	25	int(cl(m	int(cl(m	PROPN
ejpam-6270	36	26	)	)	PUNCT
ejpam-6270	36	27	)	)	PUNCT
ejpam-6270	36	28	)	)	PUNCT
ejpam-6270	37	1	∪	∪	ADV
ejpam-6270	37	2	(	(	PUNCT
ejpam-6270	37	3	m	m	NOUN
ejpam-6270	37	4	∩	∩	ADJ
ejpam-6270	37	5	cl(int(m	cl(int(m	NOUN
ejpam-6270	37	6	)	)	PUNCT
ejpam-6270	37	7	)	)	PUNCT
ejpam-6270	37	8	)	)	PUNCT
ejpam-6270	37	9	definition	definition	NOUN
ejpam-6270	37	10	2	2	NUM
ejpam-6270	37	11	.	.	PUNCT
ejpam-6270	38	1	[	[	X
ejpam-6270	38	2	16	16	NUM
ejpam-6270	38	3	]	]	PUNCT
ejpam-6270	38	4	a	a	DET
ejpam-6270	38	5	topological	topological	ADJ
ejpam-6270	38	6	space	space	NOUN
ejpam-6270	38	7	(	(	PUNCT
ejpam-6270	38	8	w	w	PROPN
ejpam-6270	38	9	,	,	PUNCT
ejpam-6270	38	10	ω	ω	NOUN
ejpam-6270	38	11	)	)	PUNCT
ejpam-6270	38	12	is	be	AUX
ejpam-6270	38	13	called	call	VERB
ejpam-6270	38	14	:	:	PUNCT
ejpam-6270	38	15	(	(	PUNCT
ejpam-6270	38	16	i	i	NOUN
ejpam-6270	38	17	)	)	PUNCT
ejpam-6270	38	18	locally	locally	ADV
ejpam-6270	38	19	indiscrete	indiscrete	ADJ
ejpam-6270	38	20	if	if	SCONJ
ejpam-6270	38	21	every	every	DET
ejpam-6270	38	22	open	open	ADJ
ejpam-6270	38	23	set	set	NOUN
ejpam-6270	38	24	is	be	AUX
ejpam-6270	38	25	closed	closed	ADJ
ejpam-6270	38	26	.	.	PUNCT
ejpam-6270	39	1	(	(	PUNCT
ejpam-6270	39	2	ii	ii	NOUN
ejpam-6270	39	3	)	)	PUNCT
ejpam-6270	39	4	extremally	extremally	ADV
ejpam-6270	39	5	disconnected	disconnect	VERB
ejpam-6270	39	6	if	if	SCONJ
ejpam-6270	39	7	cl(u	cl(u	NUM
ejpam-6270	39	8	)	)	PUNCT
ejpam-6270	39	9	∈	∈	PROPN
ejpam-6270	39	10	ω	ω	PROPN
ejpam-6270	39	11	for	for	ADP
ejpam-6270	39	12	every	every	DET
ejpam-6270	39	13	u	u	PROPN
ejpam-6270	39	14	∈	∈	PROPN
ejpam-6270	39	15	ω	ω	PROPN
ejpam-6270	39	16	.	.	PUNCT
ejpam-6270	40	1	(	(	PUNCT
ejpam-6270	40	2	iii	iii	NOUN
ejpam-6270	40	3	)	)	PUNCT
ejpam-6270	40	4	submaximal	submaximal	ADJ
ejpam-6270	40	5	if	if	SCONJ
ejpam-6270	40	6	every	every	DET
ejpam-6270	40	7	dense	dense	ADJ
ejpam-6270	40	8	subset	subset	NOUN
ejpam-6270	40	9	of	of	ADP
ejpam-6270	40	10	w	w	PROPN
ejpam-6270	40	11	is	be	AUX
ejpam-6270	40	12	open	open	ADJ
ejpam-6270	40	13	.	.	PUNCT
ejpam-6270	41	1	lemma	lemma	PROPN
ejpam-6270	41	2	3	3	X
ejpam-6270	41	3	.	.	PUNCT
ejpam-6270	42	1	[	[	X
ejpam-6270	42	2	16	16	NUM
ejpam-6270	42	3	]	]	PUNCT
ejpam-6270	42	4	(	(	PUNCT
ejpam-6270	42	5	i	i	NOUN
ejpam-6270	42	6	)	)	PUNCT
ejpam-6270	42	7	in	in	ADP
ejpam-6270	42	8	a	a	DET
ejpam-6270	42	9	locally	locally	ADV
ejpam-6270	42	10	indiscrete	indiscrete	ADJ
ejpam-6270	42	11	space	space	NOUN
ejpam-6270	42	12	,	,	PUNCT
ejpam-6270	42	13	every	every	DET
ejpam-6270	42	14	subset	subset	NOUN
ejpam-6270	42	15	of	of	ADP
ejpam-6270	42	16	w	w	PROPN
ejpam-6270	42	17	is	be	AUX
ejpam-6270	42	18	pre	pre	ADJ
ejpam-6270	42	19	-	-	ADJ
ejpam-6270	42	20	open	open	ADJ
ejpam-6270	42	21	.	.	PUNCT
ejpam-6270	43	1	(	(	PUNCT
ejpam-6270	43	2	ii	ii	NOUN
ejpam-6270	43	3	)	)	PUNCT
ejpam-6270	43	4	in	in	ADP
ejpam-6270	43	5	a	a	DET
ejpam-6270	43	6	submaximal	submaximal	ADJ
ejpam-6270	43	7	space	space	NOUN
ejpam-6270	43	8	,	,	PUNCT
ejpam-6270	43	9	every	every	DET
ejpam-6270	43	10	pre	pre	ADJ
ejpam-6270	43	11	-	-	ADJ
ejpam-6270	43	12	open	open	ADJ
ejpam-6270	43	13	set	set	NOUN
ejpam-6270	43	14	is	be	AUX
ejpam-6270	43	15	open	open	ADJ
ejpam-6270	43	16	.	.	PUNCT
ejpam-6270	44	1	lemma	lemma	PROPN
ejpam-6270	44	2	4	4	NUM
ejpam-6270	44	3	.	.	PUNCT
ejpam-6270	45	1	[	[	X
ejpam-6270	45	2	2	2	X
ejpam-6270	45	3	]	]	X
ejpam-6270	45	4	if	if	SCONJ
ejpam-6270	45	5	(	(	PUNCT
ejpam-6270	45	6	w	w	PROPN
ejpam-6270	45	7	,	,	PUNCT
ejpam-6270	45	8	ω	ω	NOUN
ejpam-6270	45	9	)	)	PUNCT
ejpam-6270	45	10	is	be	AUX
ejpam-6270	45	11	an	an	DET
ejpam-6270	45	12	extremally	extremally	ADV
ejpam-6270	45	13	disconnected	disconnect	VERB
ejpam-6270	45	14	,	,	PUNCT
ejpam-6270	45	15	then	then	ADV
ejpam-6270	45	16	(	(	PUNCT
ejpam-6270	45	17	i	i	NOUN
ejpam-6270	45	18	)	)	PUNCT
ejpam-6270	45	19	every	every	DET
ejpam-6270	45	20	b	b	X
ejpam-6270	45	21	-	-	PUNCT
ejpam-6270	45	22	open	open	ADJ
ejpam-6270	45	23	set	set	NOUN
ejpam-6270	45	24	is	be	AUX
ejpam-6270	45	25	pre	pre	ADJ
ejpam-6270	45	26	-	-	ADJ
ejpam-6270	45	27	open	open	ADJ
ejpam-6270	45	28	.	.	PUNCT
ejpam-6270	46	1	(	(	PUNCT
ejpam-6270	46	2	ii	ii	NOUN
ejpam-6270	46	3	)	)	PUNCT
ejpam-6270	46	4	a	a	DET
ejpam-6270	46	5	subset	subset	NOUN
ejpam-6270	46	6	m	m	VERB
ejpam-6270	46	7	of	of	ADP
ejpam-6270	46	8	w	w	PROPN
ejpam-6270	46	9	is	be	AUX
ejpam-6270	46	10	b	b	NOUN
ejpam-6270	46	11	-	-	PUNCT
ejpam-6270	46	12	open	open	ADJ
ejpam-6270	46	13	if	if	SCONJ
ejpam-6270	46	14	and	and	CCONJ
ejpam-6270	46	15	only	only	ADV
ejpam-6270	46	16	if	if	SCONJ
ejpam-6270	46	17	w	w	PROPN
ejpam-6270	46	18	\m	\m	NOUN
ejpam-6270	46	19	is	be	AUX
ejpam-6270	46	20	dense	dense	ADJ
ejpam-6270	46	21	.	.	PUNCT
ejpam-6270	47	1	m.	m.	NOUN
ejpam-6270	47	2	w.	w.	PROPN
ejpam-6270	47	3	abdulqader	abdulqader	PROPN
ejpam-6270	47	4	,	,	PUNCT
ejpam-6270	47	5	a.	a.	PROPN
ejpam-6270	47	6	b.	b.	PROPN
ejpam-6270	47	7	khalaf	khalaf	PROPN
ejpam-6270	47	8	/	/	SYM
ejpam-6270	47	9	eur	eur	PROPN
ejpam-6270	47	10	.	.	PUNCT
ejpam-6270	48	1	j.	j.	PROPN
ejpam-6270	48	2	pure	pure	PROPN
ejpam-6270	48	3	appl	appl	PROPN
ejpam-6270	48	4	.	.	PROPN
ejpam-6270	48	5	math	math	PROPN
ejpam-6270	48	6	,	,	PUNCT
ejpam-6270	48	7	18	18	NUM
ejpam-6270	48	8	(	(	PUNCT
ejpam-6270	48	9	3	3	NUM
ejpam-6270	48	10	)	)	PUNCT
ejpam-6270	48	11	(	(	PUNCT
ejpam-6270	48	12	2025	2025	NUM
ejpam-6270	48	13	)	)	PUNCT
ejpam-6270	48	14	,	,	PUNCT
ejpam-6270	48	15	6270	6270	NUM
ejpam-6270	48	16	3	3	NUM
ejpam-6270	48	17	of	of	ADP
ejpam-6270	48	18	17	17	NUM
ejpam-6270	48	19	lemma	lemma	PROPN
ejpam-6270	48	20	5	5	NUM
ejpam-6270	48	21	.	.	PUNCT
ejpam-6270	49	1	[	[	X
ejpam-6270	49	2	2	2	NUM
ejpam-6270	49	3	]	]	PUNCT
ejpam-6270	49	4	(	(	PUNCT
ejpam-6270	49	5	i	i	NOUN
ejpam-6270	49	6	)	)	PUNCT
ejpam-6270	49	7	if	if	SCONJ
ejpam-6270	49	8	m	m	NOUN
ejpam-6270	49	9	is	be	AUX
ejpam-6270	49	10	both	both	CCONJ
ejpam-6270	49	11	open	open	ADJ
ejpam-6270	49	12	and	and	CCONJ
ejpam-6270	49	13	b	b	X
ejpam-6270	49	14	-	-	PUNCT
ejpam-6270	49	15	closed	closed	ADJ
ejpam-6270	49	16	subset	subset	NOUN
ejpam-6270	49	17	in	in	ADP
ejpam-6270	49	18	w	w	PROPN
ejpam-6270	49	19	,	,	PUNCT
ejpam-6270	49	20	then	then	ADV
ejpam-6270	49	21	it	it	PRON
ejpam-6270	49	22	is	be	AUX
ejpam-6270	49	23	semi	semi	ADJ
ejpam-6270	49	24	-	-	ADJ
ejpam-6270	49	25	closed	closed	ADJ
ejpam-6270	49	26	.	.	PUNCT
ejpam-6270	50	1	(	(	PUNCT
ejpam-6270	50	2	ii	ii	NOUN
ejpam-6270	50	3	)	)	PUNCT
ejpam-6270	50	4	if	if	SCONJ
ejpam-6270	50	5	m	m	NOUN
ejpam-6270	50	6	is	be	AUX
ejpam-6270	50	7	a	a	DET
ejpam-6270	50	8	b	b	NOUN
ejpam-6270	50	9	-	-	PUNCT
ejpam-6270	50	10	closed	closed	ADJ
ejpam-6270	50	11	subset	subset	NOUN
ejpam-6270	50	12	of	of	ADP
ejpam-6270	50	13	a	a	DET
ejpam-6270	50	14	b	b	NOUN
ejpam-6270	50	15	-	-	ADJ
ejpam-6270	50	16	compact	compact	ADJ
ejpam-6270	50	17	space	space	NOUN
ejpam-6270	50	18	w	w	NOUN
ejpam-6270	50	19	,	,	PUNCT
ejpam-6270	50	20	then	then	ADV
ejpam-6270	50	21	it	it	PRON
ejpam-6270	50	22	is	be	AUX
ejpam-6270	50	23	b	b	NOUN
ejpam-6270	50	24	-	-	ADJ
ejpam-6270	50	25	compact	compact	ADJ
ejpam-6270	50	26	.	.	PUNCT
ejpam-6270	51	1	definition	definition	NOUN
ejpam-6270	51	2	3	3	NUM
ejpam-6270	51	3	.	.	PUNCT
ejpam-6270	52	1	[	[	X
ejpam-6270	52	2	17	17	NUM
ejpam-6270	52	3	]	]	PUNCT
ejpam-6270	52	4	a	a	DET
ejpam-6270	52	5	topological	topological	ADJ
ejpam-6270	52	6	space	space	NOUN
ejpam-6270	52	7	w	w	NOUN
ejpam-6270	52	8	is	be	AUX
ejpam-6270	52	9	semi	semi	ADJ
ejpam-6270	52	10	-	-	ADJ
ejpam-6270	52	11	disconnected	disconnected	ADJ
ejpam-6270	52	12	if	if	SCONJ
ejpam-6270	52	13	it	it	PRON
ejpam-6270	52	14	can	can	AUX
ejpam-6270	52	15	be	be	AUX
ejpam-6270	52	16	partitioned	partition	VERB
ejpam-6270	52	17	into	into	ADP
ejpam-6270	52	18	two	two	NUM
ejpam-6270	52	19	non	non	ADJ
ejpam-6270	52	20	-	-	ADJ
ejpam-6270	52	21	empty	empty	ADJ
ejpam-6270	52	22	open	open	ADJ
ejpam-6270	52	23	sets	set	NOUN
ejpam-6270	52	24	u	u	NOUN
ejpam-6270	52	25	and	and	CCONJ
ejpam-6270	52	26	v	v	ADP
ejpam-6270	52	27	such	such	ADJ
ejpam-6270	52	28	that	that	DET
ejpam-6270	52	29	cl(u	cl(u	NOUN
ejpam-6270	52	30	)	)	PUNCT
ejpam-6270	52	31	∩	∩	NOUN
ejpam-6270	52	32	v	v	NOUN
ejpam-6270	52	33	=	=	SYM
ejpam-6270	52	34	∅	∅	NOUN
ejpam-6270	52	35	and	and	CCONJ
ejpam-6270	52	36	cl(v	cl(v	NOUN
ejpam-6270	52	37	)	)	PUNCT
ejpam-6270	52	38	∩	∩	NOUN
ejpam-6270	52	39	u	u	NOUN
ejpam-6270	52	40	=	=	X
ejpam-6270	52	41	∅.	∅.	NOUN
ejpam-6270	52	42	definition	definition	NOUN
ejpam-6270	52	43	4	4	NUM
ejpam-6270	52	44	.	.	PUNCT
ejpam-6270	53	1	[	[	X
ejpam-6270	53	2	3	3	NUM
ejpam-6270	53	3	,	,	PUNCT
ejpam-6270	53	4	13	13	NUM
ejpam-6270	53	5	]	]	PUNCT
ejpam-6270	53	6	a	a	DET
ejpam-6270	53	7	topological	topological	ADJ
ejpam-6270	53	8	space	space	NOUN
ejpam-6270	53	9	(	(	PUNCT
ejpam-6270	53	10	w	w	PROPN
ejpam-6270	53	11	,	,	PUNCT
ejpam-6270	53	12	ω	ω	NOUN
ejpam-6270	53	13	)	)	PUNCT
ejpam-6270	53	14	is	be	AUX
ejpam-6270	53	15	said	say	VERB
ejpam-6270	53	16	to	to	PART
ejpam-6270	53	17	be	be	AUX
ejpam-6270	53	18	:	:	PUNCT
ejpam-6270	53	19	(	(	PUNCT
ejpam-6270	53	20	i	i	NOUN
ejpam-6270	53	21	)	)	PUNCT
ejpam-6270	53	22	b	b	X
ejpam-6270	53	23	-	-	PUNCT
ejpam-6270	53	24	t0	t0	PROPN
ejpam-6270	53	25	(	(	PUNCT
ejpam-6270	53	26	resp	resp	PROPN
ejpam-6270	53	27	.	.	PUNCT
ejpam-6270	53	28	,	,	PUNCT
ejpam-6270	53	29	t0	t0	PROPN
ejpam-6270	53	30	)	)	PUNCT
ejpam-6270	53	31	∀	∀	X
ejpam-6270	53	32	ζ	ζ	NOUN
ejpam-6270	53	33	,	,	PUNCT
ejpam-6270	53	34	η	η	PROPN
ejpam-6270	53	35	∈	∈	PROPN
ejpam-6270	53	36	w	w	PROPN
ejpam-6270	53	37	,	,	PUNCT
ejpam-6270	53	38	∃	∃	PROPN
ejpam-6270	53	39	a	a	DET
ejpam-6270	53	40	b	b	NOUN
ejpam-6270	53	41	-	-	PUNCT
ejpam-6270	53	42	open	open	ADJ
ejpam-6270	53	43	(	(	PUNCT
ejpam-6270	53	44	open	open	ADJ
ejpam-6270	53	45	)	)	PUNCT
ejpam-6270	53	46	set	set	NOUN
ejpam-6270	53	47	containing	contain	VERB
ejpam-6270	53	48	one	one	NUM
ejpam-6270	53	49	of	of	ADP
ejpam-6270	53	50	them	they	PRON
ejpam-6270	53	51	but	but	CCONJ
ejpam-6270	53	52	not	not	PART
ejpam-6270	53	53	the	the	DET
ejpam-6270	53	54	other	other	ADJ
ejpam-6270	53	55	.	.	PUNCT
ejpam-6270	54	1	(	(	PUNCT
ejpam-6270	54	2	ii	ii	NOUN
ejpam-6270	54	3	)	)	PUNCT
ejpam-6270	54	4	b	b	PROPN
ejpam-6270	54	5	-	-	PUNCT
ejpam-6270	54	6	t1	t1	NOUN
ejpam-6270	54	7	(	(	PUNCT
ejpam-6270	54	8	resp	resp	NOUN
ejpam-6270	54	9	.	.	PUNCT
ejpam-6270	54	10	,	,	PUNCT
ejpam-6270	54	11	t1	t1	NOUN
ejpam-6270	54	12	)	)	PUNCT
ejpam-6270	54	13	if	if	SCONJ
ejpam-6270	54	14	∀	∀	NOUN
ejpam-6270	54	15	ζ	ζ	NOUN
ejpam-6270	54	16	,	,	PUNCT
ejpam-6270	54	17	η	η	PROPN
ejpam-6270	54	18	∈	∈	PROPN
ejpam-6270	54	19	w	w	PROPN
ejpam-6270	54	20	,	,	PUNCT
ejpam-6270	54	21	∃	∃	PROPN
ejpam-6270	54	22	b	b	PROPN
ejpam-6270	54	23	-	-	PUNCT
ejpam-6270	54	24	open	open	ADJ
ejpam-6270	54	25	(	(	PUNCT
ejpam-6270	54	26	open	open	ADJ
ejpam-6270	54	27	)	)	PUNCT
ejpam-6270	54	28	sets	set	VERB
ejpam-6270	54	29	g	g	NOUN
ejpam-6270	54	30	,	,	PUNCT
ejpam-6270	54	31	h	h	NOUN
ejpam-6270	54	32	such	such	ADJ
ejpam-6270	54	33	that	that	SCONJ
ejpam-6270	54	34	ζ	ζ	PROPN
ejpam-6270	54	35	∈	∈	PROPN
ejpam-6270	54	36	g	g	PROPN
ejpam-6270	54	37	,	,	PUNCT
ejpam-6270	54	38	η	η	PROPN
ejpam-6270	54	39	/∈	/∈	PROPN
ejpam-6270	54	40	g	g	PROPN
ejpam-6270	54	41	and	and	CCONJ
ejpam-6270	54	42	η	η	PROPN
ejpam-6270	54	43	∈	∈	PROPN
ejpam-6270	54	44	h	h	NOUN
ejpam-6270	54	45	,	,	PUNCT
ejpam-6270	54	46	ζ	ζ	NOUN
ejpam-6270	54	47	/∈	/∈	PUNCT
ejpam-6270	55	1	h.	h.	PROPN
ejpam-6270	55	2	(	(	PUNCT
ejpam-6270	55	3	iii	iii	NOUN
ejpam-6270	55	4	)	)	PUNCT
ejpam-6270	55	5	b	b	NOUN
ejpam-6270	55	6	-	-	PUNCT
ejpam-6270	55	7	t2	t2	NOUN
ejpam-6270	55	8	(	(	PUNCT
ejpam-6270	55	9	resp	resp	NOUN
ejpam-6270	55	10	.	.	PUNCT
ejpam-6270	55	11	,	,	PUNCT
ejpam-6270	55	12	t2	t2	PROPN
ejpam-6270	55	13	)	)	PUNCT
ejpam-6270	55	14	if	if	SCONJ
ejpam-6270	55	15	∀	∀	NOUN
ejpam-6270	55	16	ζ	ζ	NOUN
ejpam-6270	55	17	,	,	PUNCT
ejpam-6270	55	18	η	η	PROPN
ejpam-6270	55	19	∈	∈	PROPN
ejpam-6270	55	20	w	w	PROPN
ejpam-6270	55	21	,	,	PUNCT
ejpam-6270	55	22	∃	∃	PROPN
ejpam-6270	55	23	b	b	PROPN
ejpam-6270	55	24	-	-	PUNCT
ejpam-6270	55	25	open	open	ADJ
ejpam-6270	55	26	(	(	PUNCT
ejpam-6270	55	27	open	open	ADJ
ejpam-6270	55	28	)	)	PUNCT
ejpam-6270	55	29	sets	set	VERB
ejpam-6270	55	30	g	g	NOUN
ejpam-6270	55	31	,	,	PUNCT
ejpam-6270	55	32	h	h	NOUN
ejpam-6270	55	33	such	such	ADJ
ejpam-6270	55	34	that	that	SCONJ
ejpam-6270	55	35	ζ	ζ	PROPN
ejpam-6270	55	36	∈	∈	PROPN
ejpam-6270	55	37	g	g	PROPN
ejpam-6270	55	38	,	,	PUNCT
ejpam-6270	55	39	η	η	PROPN
ejpam-6270	55	40	∈	∈	PROPN
ejpam-6270	55	41	h	h	NOUN
ejpam-6270	55	42	,	,	PUNCT
ejpam-6270	55	43	g	g	PROPN
ejpam-6270	55	44	∩h	∩h	NOUN
ejpam-6270	55	45	=	=	PUNCT
ejpam-6270	56	1	ϕ.	ϕ.	ADJ
ejpam-6270	56	2	definition	definition	NOUN
ejpam-6270	56	3	5	5	NUM
ejpam-6270	56	4	.	.	PUNCT
ejpam-6270	57	1	[	[	X
ejpam-6270	57	2	4	4	NUM
ejpam-6270	57	3	]	]	X
ejpam-6270	57	4	d	d	X
ejpam-6270	57	5	-	-	PUNCT
ejpam-6270	57	6	algebra	algebra	NOUN
ejpam-6270	57	7	is	be	AUX
ejpam-6270	57	8	an	an	DET
ejpam-6270	57	9	algebra	algebra	NOUN
ejpam-6270	57	10	(	(	PUNCT
ejpam-6270	57	11	w,⊙	w,⊙	PROPN
ejpam-6270	57	12	,	,	PUNCT
ejpam-6270	57	13	0	0	NUM
ejpam-6270	57	14	)	)	PUNCT
ejpam-6270	57	15	of	of	ADP
ejpam-6270	57	16	type	type	NOUN
ejpam-6270	57	17	(	(	PUNCT
ejpam-6270	57	18	2	2	NUM
ejpam-6270	57	19	,	,	PUNCT
ejpam-6270	57	20	0	0	NUM
ejpam-6270	57	21	)	)	PUNCT
ejpam-6270	57	22	such	such	ADJ
ejpam-6270	57	23	that	that	SCONJ
ejpam-6270	57	24	⊙	⊙	PROPN
ejpam-6270	57	25	is	be	AUX
ejpam-6270	57	26	a	a	DET
ejpam-6270	57	27	binary	binary	ADJ
ejpam-6270	57	28	operation	operation	NOUN
ejpam-6270	57	29	and	and	CCONJ
ejpam-6270	57	30	0	0	NUM
ejpam-6270	57	31	is	be	AUX
ejpam-6270	57	32	a	a	DET
ejpam-6270	57	33	fixed	fix	VERB
ejpam-6270	57	34	element	element	NOUN
ejpam-6270	57	35	,	,	PUNCT
ejpam-6270	57	36	satisfy	satisfy	VERB
ejpam-6270	57	37	the	the	DET
ejpam-6270	57	38	axioms	axiom	NOUN
ejpam-6270	57	39	listed	list	VERB
ejpam-6270	57	40	below	below	ADV
ejpam-6270	57	41	:	:	PUNCT
ejpam-6270	57	42	for	for	ADP
ejpam-6270	57	43	each	each	DET
ejpam-6270	57	44	ζ	ζ	NOUN
ejpam-6270	57	45	,	,	PUNCT
ejpam-6270	57	46	η	η	PROPN
ejpam-6270	57	47	,	,	PUNCT
ejpam-6270	57	48	θ	θ	PROPN
ejpam-6270	57	49	∈	∈	PROPN
ejpam-6270	57	50	w	w	PROPN
ejpam-6270	57	51	,	,	PUNCT
ejpam-6270	57	52	(	(	PUNCT
ejpam-6270	57	53	i	i	NOUN
ejpam-6270	57	54	)	)	PUNCT
ejpam-6270	57	55	ζ	ζ	PROPN
ejpam-6270	57	56	⊙	⊙	X
ejpam-6270	57	57	ζ	ζ	X
ejpam-6270	57	58	=	=	SYM
ejpam-6270	57	59	0	0	NUM
ejpam-6270	57	60	,	,	PUNCT
ejpam-6270	57	61	(	(	PUNCT
ejpam-6270	57	62	ii	ii	NOUN
ejpam-6270	57	63	)	)	PUNCT
ejpam-6270	57	64	ζ	ζ	PROPN
ejpam-6270	57	65	⊙	⊙	PROPN
ejpam-6270	57	66	η	η	PROPN
ejpam-6270	57	67	=	=	PROPN
ejpam-6270	57	68	0	0	NUM
ejpam-6270	57	69	and	and	CCONJ
ejpam-6270	57	70	η	η	PROPN
ejpam-6270	57	71	⊙	⊙	PROPN
ejpam-6270	57	72	ζ	ζ	PROPN
ejpam-6270	57	73	=	=	SYM
ejpam-6270	57	74	0	0	NUM
ejpam-6270	57	75	⇒	⇒	NOUN
ejpam-6270	57	76	ζ	ζ	X
ejpam-6270	57	77	=	=	SYM
ejpam-6270	57	78	η	η	PROPN
ejpam-6270	57	79	,	,	PUNCT
ejpam-6270	57	80	(	(	PUNCT
ejpam-6270	57	81	iii	iii	X
ejpam-6270	57	82	)	)	PUNCT
ejpam-6270	57	83	0⊙	0⊙	NOUN
ejpam-6270	57	84	ζ	ζ	NOUN
ejpam-6270	57	85	=	=	SYM
ejpam-6270	57	86	0	0	NUM
ejpam-6270	57	87	.	.	PUNCT
ejpam-6270	58	1	moreover	moreover	ADV
ejpam-6270	58	2	,	,	PUNCT
ejpam-6270	58	3	if	if	SCONJ
ejpam-6270	58	4	a	a	DET
ejpam-6270	58	5	d	d	NOUN
ejpam-6270	58	6	-	-	PUNCT
ejpam-6270	58	7	algebra	algebra	NOUN
ejpam-6270	58	8	satisfies	satisfy	VERB
ejpam-6270	58	9	the	the	DET
ejpam-6270	58	10	following	follow	VERB
ejpam-6270	58	11	axioms	axiom	NOUN
ejpam-6270	58	12	(	(	PUNCT
ejpam-6270	58	13	i	i	NOUN
ejpam-6270	58	14	)	)	PUNCT
ejpam-6270	58	15	(	(	PUNCT
ejpam-6270	58	16	b1	b1	PROPN
ejpam-6270	58	17	)	)	PUNCT
ejpam-6270	58	18	(	(	PUNCT
ejpam-6270	58	19	(	(	PUNCT
ejpam-6270	58	20	ζ	ζ	PROPN
ejpam-6270	58	21	⊙	⊙	PROPN
ejpam-6270	58	22	η)⊙	η)⊙	PROPN
ejpam-6270	58	23	(	(	PUNCT
ejpam-6270	58	24	ζ	ζ	PROPN
ejpam-6270	58	25	⊙	⊙	X
ejpam-6270	58	26	θ))⊙	θ))⊙	PROPN
ejpam-6270	58	27	(	(	PUNCT
ejpam-6270	58	28	θ	θ	PROPN
ejpam-6270	58	29	⊙	⊙	PROPN
ejpam-6270	58	30	η	η	PROPN
ejpam-6270	58	31	)	)	PUNCT
ejpam-6270	58	32	=	=	SYM
ejpam-6270	58	33	0	0	NUM
ejpam-6270	58	34	,	,	PUNCT
ejpam-6270	58	35	(	(	PUNCT
ejpam-6270	58	36	ii	ii	NOUN
ejpam-6270	58	37	)	)	PUNCT
ejpam-6270	58	38	(	(	PUNCT
ejpam-6270	58	39	b2	b2	NOUN
ejpam-6270	58	40	)	)	PUNCT
ejpam-6270	58	41	(	(	PUNCT
ejpam-6270	58	42	ζ	ζ	NOUN
ejpam-6270	58	43	⊙	⊙	NOUN
ejpam-6270	58	44	(	(	PUNCT
ejpam-6270	58	45	ζ	ζ	PROPN
ejpam-6270	58	46	⊙	⊙	PROPN
ejpam-6270	58	47	η))⊙	η))⊙	PROPN
ejpam-6270	58	48	η	η	PROPN
ejpam-6270	58	49	=	=	PROPN
ejpam-6270	58	50	0	0	PROPN
ejpam-6270	58	51	.	.	PUNCT
ejpam-6270	59	1	then	then	ADV
ejpam-6270	59	2	it	it	PRON
ejpam-6270	59	3	is	be	AUX
ejpam-6270	59	4	a	a	DET
ejpam-6270	59	5	bck	bck	NOUN
ejpam-6270	59	6	-	-	PUNCT
ejpam-6270	59	7	algebra	algebra	NOUN
ejpam-6270	59	8	.	.	PUNCT
ejpam-6270	60	1	we	we	PRON
ejpam-6270	60	2	indicate	indicate	VERB
ejpam-6270	60	3	a	a	DET
ejpam-6270	60	4	partial	partial	ADJ
ejpam-6270	60	5	order	order	NOUN
ejpam-6270	60	6	relation	relation	NOUN
ejpam-6270	60	7	(	(	PUNCT
ejpam-6270	60	8	≤	≤	NOUN
ejpam-6270	60	9	)	)	PUNCT
ejpam-6270	60	10	by	by	ADP
ejpam-6270	60	11	ζ	ζ	PROPN
ejpam-6270	60	12	≤	≤	NUM
ejpam-6270	60	13	η	η	PROPN
ejpam-6270	60	14	⇐	⇐	PROPN
ejpam-6270	60	15	⇒	⇒	PROPN
ejpam-6270	60	16	ζ	ζ	PROPN
ejpam-6270	60	17	⊙	⊙	PROPN
ejpam-6270	60	18	η	η	PROPN
ejpam-6270	60	19	=	=	PROPN
ejpam-6270	60	20	0	0	PROPN
ejpam-6270	60	21	.	.	PUNCT
ejpam-6270	61	1	definition	definition	NOUN
ejpam-6270	61	2	6	6	NUM
ejpam-6270	61	3	.	.	PUNCT
ejpam-6270	62	1	[	[	X
ejpam-6270	62	2	18	18	NUM
ejpam-6270	62	3	]	]	PUNCT
ejpam-6270	62	4	a	a	DET
ejpam-6270	62	5	d	d	NOUN
ejpam-6270	62	6	-	-	PUNCT
ejpam-6270	62	7	algebra	algebra	NOUN
ejpam-6270	62	8	(	(	PUNCT
ejpam-6270	62	9	w,⊙	w,⊙	PROPN
ejpam-6270	62	10	,	,	PUNCT
ejpam-6270	62	11	0	0	NUM
ejpam-6270	62	12	)	)	PUNCT
ejpam-6270	62	13	is	be	AUX
ejpam-6270	62	14	said	say	VERB
ejpam-6270	62	15	to	to	PART
ejpam-6270	62	16	be	be	AUX
ejpam-6270	62	17	edge	edge	VERB
ejpam-6270	62	18	d	d	NOUN
ejpam-6270	62	19	-	-	PUNCT
ejpam-6270	62	20	algebra	algebra	NOUN
ejpam-6270	62	21	,	,	PUNCT
ejpam-6270	62	22	if	if	SCONJ
ejpam-6270	62	23	ζ	ζ	ADJ
ejpam-6270	62	24	⊙w	⊙w	NOUN
ejpam-6270	62	25	=	=	PUNCT
ejpam-6270	62	26	{	{	PUNCT
ejpam-6270	62	27	ζ	ζ	NOUN
ejpam-6270	62	28	,	,	PUNCT
ejpam-6270	62	29	0	0	NUM
ejpam-6270	62	30	}	}	PUNCT
ejpam-6270	62	31	for	for	ADP
ejpam-6270	62	32	all	all	DET
ejpam-6270	62	33	ζ	ζ	PROPN
ejpam-6270	62	34	∈	∈	PROPN
ejpam-6270	62	35	w	w	NOUN
ejpam-6270	62	36	lemma	lemma	PROPN
ejpam-6270	62	37	6	6	NUM
ejpam-6270	62	38	.	.	PUNCT
ejpam-6270	63	1	[	[	X
ejpam-6270	63	2	4	4	X
ejpam-6270	63	3	]	]	X
ejpam-6270	63	4	if	if	SCONJ
ejpam-6270	63	5	(	(	PUNCT
ejpam-6270	63	6	w,⊙	w,⊙	NOUN
ejpam-6270	63	7	,	,	PUNCT
ejpam-6270	63	8	0	0	NUM
ejpam-6270	63	9	)	)	PUNCT
ejpam-6270	63	10	is	be	AUX
ejpam-6270	63	11	an	an	DET
ejpam-6270	63	12	edge	edge	NOUN
ejpam-6270	63	13	d	d	NOUN
ejpam-6270	63	14	-	-	PUNCT
ejpam-6270	63	15	algebra	algebra	NOUN
ejpam-6270	63	16	,	,	PUNCT
ejpam-6270	63	17	then	then	ADV
ejpam-6270	63	18	it	it	PRON
ejpam-6270	63	19	satisfies	satisfy	VERB
ejpam-6270	63	20	condition	condition	NOUN
ejpam-6270	63	21	(	(	PUNCT
ejpam-6270	63	22	b2	b2	NOUN
ejpam-6270	63	23	)	)	PUNCT
ejpam-6270	63	24	.	.	PUNCT
ejpam-6270	64	1	definition	definition	NOUN
ejpam-6270	64	2	7	7	NUM
ejpam-6270	64	3	.	.	PUNCT
ejpam-6270	65	1	[	[	X
ejpam-6270	65	2	6	6	NUM
ejpam-6270	65	3	]	]	PUNCT
ejpam-6270	65	4	a	a	DET
ejpam-6270	65	5	nonempty	nonempty	NOUN
ejpam-6270	65	6	subset	subset	VERB
ejpam-6270	65	7	i	i	PRON
ejpam-6270	65	8	of	of	ADP
ejpam-6270	65	9	a	a	DET
ejpam-6270	65	10	d	d	NOUN
ejpam-6270	65	11	-	-	PUNCT
ejpam-6270	65	12	algebra	algebra	NOUN
ejpam-6270	65	13	(	(	PUNCT
ejpam-6270	65	14	w,⊙	w,⊙	PROPN
ejpam-6270	65	15	,	,	PUNCT
ejpam-6270	65	16	0	0	NUM
ejpam-6270	65	17	)	)	PUNCT
ejpam-6270	65	18	is	be	AUX
ejpam-6270	65	19	said	say	VERB
ejpam-6270	65	20	to	to	PART
ejpam-6270	65	21	be	be	AUX
ejpam-6270	65	22	an	an	DET
ejpam-6270	65	23	ideal	ideal	NOUN
ejpam-6270	65	24	of	of	ADP
ejpam-6270	65	25	w	w	NOUN
ejpam-6270	65	26	if	if	SCONJ
ejpam-6270	65	27	both	both	PRON
ejpam-6270	65	28	of	of	ADP
ejpam-6270	65	29	the	the	DET
ejpam-6270	65	30	following	follow	VERB
ejpam-6270	65	31	conditions	condition	NOUN
ejpam-6270	65	32	are	be	AUX
ejpam-6270	65	33	met	meet	VERB
ejpam-6270	65	34	:	:	PUNCT
ejpam-6270	65	35	(	(	PUNCT
ejpam-6270	65	36	i	i	NOUN
ejpam-6270	65	37	)	)	PUNCT
ejpam-6270	65	38	0	0	PUNCT
ejpam-6270	66	1	∈	∈	PROPN
ejpam-6270	67	1	i	i	PRON
ejpam-6270	67	2	,	,	PUNCT
ejpam-6270	67	3	(	(	PUNCT
ejpam-6270	67	4	ii	ii	NOUN
ejpam-6270	67	5	)	)	PUNCT
ejpam-6270	67	6	∀	∀	PUNCT
ejpam-6270	67	7	ζ	ζ	PROPN
ejpam-6270	67	8	∈	∈	PROPN
ejpam-6270	67	9	w	w	PROPN
ejpam-6270	67	10	,	,	PUNCT
ejpam-6270	67	11	∀η	∀η	X
ejpam-6270	67	12	∈	∈	PROPN
ejpam-6270	68	1	i	i	PRON
ejpam-6270	68	2	,	,	PUNCT
ejpam-6270	68	3	if	if	SCONJ
ejpam-6270	68	4	ζ	ζ	PROPN
ejpam-6270	68	5	⊙	⊙	PROPN
ejpam-6270	68	6	η	η	PROPN
ejpam-6270	68	7	∈	∈	PROPN
ejpam-6270	69	1	i	i	PRON
ejpam-6270	69	2	,	,	PUNCT
ejpam-6270	69	3	then	then	ADV
ejpam-6270	69	4	ζ	ζ	PROPN
ejpam-6270	69	5	∈	∈	PROPN
ejpam-6270	69	6	i.	i.	PROPN
ejpam-6270	69	7	m.	m.	PROPN
ejpam-6270	69	8	w.	w.	PROPN
ejpam-6270	69	9	abdulqader	abdulqader	PROPN
ejpam-6270	69	10	,	,	PUNCT
ejpam-6270	69	11	a.	a.	PROPN
ejpam-6270	69	12	b.	b.	PROPN
ejpam-6270	69	13	khalaf	khalaf	PROPN
ejpam-6270	69	14	/	/	SYM
ejpam-6270	69	15	eur	eur	PROPN
ejpam-6270	69	16	.	.	PUNCT
ejpam-6270	70	1	j.	j.	PROPN
ejpam-6270	70	2	pure	pure	PROPN
ejpam-6270	70	3	appl	appl	PROPN
ejpam-6270	70	4	.	.	PROPN
ejpam-6270	70	5	math	math	PROPN
ejpam-6270	70	6	,	,	PUNCT
ejpam-6270	70	7	18	18	NUM
ejpam-6270	70	8	(	(	PUNCT
ejpam-6270	70	9	3	3	NUM
ejpam-6270	70	10	)	)	PUNCT
ejpam-6270	70	11	(	(	PUNCT
ejpam-6270	70	12	2025	2025	NUM
ejpam-6270	70	13	)	)	PUNCT
ejpam-6270	70	14	,	,	PUNCT
ejpam-6270	70	15	6270	6270	NUM
ejpam-6270	70	16	4	4	NUM
ejpam-6270	70	17	of	of	ADP
ejpam-6270	70	18	17	17	NUM
ejpam-6270	70	19	definition	definition	NOUN
ejpam-6270	70	20	8	8	NUM
ejpam-6270	70	21	.	.	PUNCT
ejpam-6270	71	1	[	[	X
ejpam-6270	71	2	19	19	NUM
ejpam-6270	71	3	]	]	PUNCT
ejpam-6270	71	4	let	let	VERB
ejpam-6270	71	5	α	α	PRON
ejpam-6270	71	6	be	be	AUX
ejpam-6270	71	7	an	an	DET
ejpam-6270	71	8	element	element	NOUN
ejpam-6270	71	9	of	of	ADP
ejpam-6270	71	10	a	a	DET
ejpam-6270	71	11	d	d	NOUN
ejpam-6270	71	12	-	-	NOUN
ejpam-6270	71	13	algebra	algebra	NOUN
ejpam-6270	71	14	w.	w.	NOUN
ejpam-6270	71	15	α	α	PROPN
ejpam-6270	71	16	is	be	AUX
ejpam-6270	71	17	said	say	VERB
ejpam-6270	71	18	to	to	PART
ejpam-6270	71	19	be	be	AUX
ejpam-6270	71	20	an	an	DET
ejpam-6270	71	21	atom	atom	NOUN
ejpam-6270	71	22	in	in	ADP
ejpam-6270	71	23	w	w	NOUN
ejpam-6270	71	24	if	if	SCONJ
ejpam-6270	71	25	,	,	PUNCT
ejpam-6270	71	26	for	for	ADP
ejpam-6270	71	27	any	any	DET
ejpam-6270	71	28	ζ	ζ	PROPN
ejpam-6270	71	29	∈	∈	PROPN
ejpam-6270	71	30	w	w	PROPN
ejpam-6270	71	31	,	,	PUNCT
ejpam-6270	71	32	α⊙	α⊙	NOUN
ejpam-6270	71	33	ζ	ζ	NOUN
ejpam-6270	71	34	=	=	SYM
ejpam-6270	71	35	0	0	NUM
ejpam-6270	71	36	implies	imply	VERB
ejpam-6270	71	37	α	α	PROPN
ejpam-6270	71	38	=	=	SYM
ejpam-6270	71	39	ζ	ζ	PROPN
ejpam-6270	71	40	.	.	NOUN
ejpam-6270	71	41	definition	definition	NOUN
ejpam-6270	71	42	9	9	NUM
ejpam-6270	71	43	.	.	PUNCT
ejpam-6270	72	1	[	[	X
ejpam-6270	72	2	4	4	X
ejpam-6270	72	3	]	]	PUNCT
ejpam-6270	72	4	let	let	VERB
ejpam-6270	72	5	z	z	PRON
ejpam-6270	72	6	be	be	AUX
ejpam-6270	72	7	a	a	DET
ejpam-6270	72	8	subset	subset	NOUN
ejpam-6270	72	9	of	of	ADP
ejpam-6270	72	10	a	a	DET
ejpam-6270	72	11	d	d	NOUN
ejpam-6270	72	12	-	-	NOUN
ejpam-6270	72	13	algebra	algebra	NOUN
ejpam-6270	72	14	w	w	NOUN
ejpam-6270	72	15	,	,	PUNCT
ejpam-6270	72	16	z	z	PROPN
ejpam-6270	72	17	is	be	AUX
ejpam-6270	72	18	called	call	VERB
ejpam-6270	72	19	a	a	DET
ejpam-6270	72	20	d	d	NOUN
ejpam-6270	72	21	-	-	PUNCT
ejpam-6270	72	22	subalgebra	subalgebra	ADJ
ejpam-6270	72	23	if	if	SCONJ
ejpam-6270	72	24	it	it	PRON
ejpam-6270	72	25	is	be	AUX
ejpam-6270	72	26	also	also	ADV
ejpam-6270	72	27	a	a	DET
ejpam-6270	72	28	d	d	NOUN
ejpam-6270	72	29	-	-	NOUN
ejpam-6270	72	30	algebra	algebra	NOUN
ejpam-6270	72	31	.	.	PUNCT
ejpam-6270	73	1	definition	definition	NOUN
ejpam-6270	73	2	10	10	NUM
ejpam-6270	73	3	.	.	PUNCT
ejpam-6270	74	1	[	[	X
ejpam-6270	74	2	6	6	NUM
ejpam-6270	74	3	]	]	PUNCT
ejpam-6270	74	4	let	let	VERB
ejpam-6270	74	5	w	w	PART
ejpam-6270	74	6	be	be	AUX
ejpam-6270	74	7	a	a	DET
ejpam-6270	74	8	d	d	NOUN
ejpam-6270	74	9	-	-	NOUN
ejpam-6270	74	10	algebra	algebra	NOUN
ejpam-6270	74	11	,	,	PUNCT
ejpam-6270	74	12	α	α	PROPN
ejpam-6270	74	13	∈	∈	PROPN
ejpam-6270	74	14	w.	w.	PROPN
ejpam-6270	74	15	a	a	DET
ejpam-6270	74	16	left	left	ADJ
ejpam-6270	74	17	map	map	NOUN
ejpam-6270	74	18	lα	lα	ADP
ejpam-6270	74	19	:	:	PUNCT
ejpam-6270	74	20	w	w	X
ejpam-6270	74	21	→	→	SYM
ejpam-6270	74	22	w	w	ADP
ejpam-6270	74	23	defined	define	VERB
ejpam-6270	74	24	by	by	ADP
ejpam-6270	74	25	,	,	PUNCT
ejpam-6270	74	26	lα(ζ	lα(ζ	PUNCT
ejpam-6270	74	27	)	)	PUNCT
ejpam-6270	74	28	=	=	SYM
ejpam-6270	75	1	α⊙	α⊙	NOUN
ejpam-6270	75	2	ζ,∀ζ	ζ,∀ζ	X
ejpam-6270	75	3	∈	∈	PROPN
ejpam-6270	75	4	w	w	NOUN
ejpam-6270	75	5	and	and	CCONJ
ejpam-6270	75	6	a	a	DET
ejpam-6270	75	7	right	right	ADJ
ejpam-6270	75	8	map	map	NOUN
ejpam-6270	75	9	rα	rα	INTJ
ejpam-6270	75	10	:	:	PUNCT
ejpam-6270	75	11	w	w	X
ejpam-6270	75	12	→	→	SYM
ejpam-6270	75	13	w	w	NOUN
ejpam-6270	75	14	by	by	ADP
ejpam-6270	75	15	rα(ζ	rα(ζ	NOUN
ejpam-6270	75	16	)	)	PUNCT
ejpam-6270	75	17	=	=	SYM
ejpam-6270	75	18	ζ	ζ	NOUN
ejpam-6270	75	19	⊙	⊙	NOUN
ejpam-6270	75	20	α	α	PROPN
ejpam-6270	75	21	∀ζ	∀ζ	PROPN
ejpam-6270	75	22	∈	∈	PROPN
ejpam-6270	75	23	w.	w.	NOUN
ejpam-6270	75	24	l(w	l(w	PROPN
ejpam-6270	75	25	)	)	PUNCT
ejpam-6270	75	26	represents	represent	VERB
ejpam-6270	75	27	the	the	DET
ejpam-6270	75	28	family	family	NOUN
ejpam-6270	75	29	of	of	ADP
ejpam-6270	75	30	all	all	DET
ejpam-6270	75	31	left	leave	VERB
ejpam-6270	75	32	maps	map	NOUN
ejpam-6270	75	33	on	on	ADP
ejpam-6270	75	34	w	w	NOUN
ejpam-6270	75	35	,	,	PUNCT
ejpam-6270	75	36	while	while	SCONJ
ejpam-6270	75	37	r(w	r(w	PROPN
ejpam-6270	75	38	)	)	PUNCT
ejpam-6270	75	39	represents	represent	VERB
ejpam-6270	75	40	the	the	DET
ejpam-6270	75	41	family	family	NOUN
ejpam-6270	75	42	of	of	ADP
ejpam-6270	75	43	all	all	DET
ejpam-6270	75	44	right	right	ADJ
ejpam-6270	75	45	maps	map	NOUN
ejpam-6270	75	46	.	.	PUNCT
ejpam-6270	76	1	w	w	NOUN
ejpam-6270	76	2	is	be	AUX
ejpam-6270	76	3	denoted	denote	VERB
ejpam-6270	76	4	by	by	ADP
ejpam-6270	76	5	and	and	CCONJ
ejpam-6270	76	6	the	the	DET
ejpam-6270	76	7	family	family	NOUN
ejpam-6270	76	8	of	of	ADP
ejpam-6270	76	9	all	all	DET
ejpam-6270	76	10	right	right	ADJ
ejpam-6270	76	11	maps	map	NOUN
ejpam-6270	76	12	if	if	SCONJ
ejpam-6270	76	13	s	s	VERB
ejpam-6270	76	14	⊆	⊆	NUM
ejpam-6270	76	15	w	w	NOUN
ejpam-6270	76	16	then	then	ADV
ejpam-6270	76	17	lα(s	lα(s	PUNCT
ejpam-6270	76	18	)	)	PUNCT
ejpam-6270	77	1	=	=	SYM
ejpam-6270	77	2	α⊙s	α⊙	NOUN
ejpam-6270	77	3	and	and	CCONJ
ejpam-6270	77	4	rα(s	rα(s	NUM
ejpam-6270	77	5	)	)	PUNCT
ejpam-6270	78	1	=	=	PRON
ejpam-6270	78	2	s	s	PROPN
ejpam-6270	78	3	⊙	⊙	PROPN
ejpam-6270	78	4	α	α	PROPN
ejpam-6270	78	5	.	.	PUNCT
ejpam-6270	79	1	definition	definition	NOUN
ejpam-6270	79	2	11	11	NUM
ejpam-6270	79	3	.	.	PUNCT
ejpam-6270	80	1	[	[	X
ejpam-6270	80	2	20	20	NUM
ejpam-6270	80	3	]	]	SYM
ejpam-6270	80	4	a	a	DET
ejpam-6270	80	5	d	d	X
ejpam-6270	80	6	-	-	PUNCT
ejpam-6270	80	7	algebra	algebra	NOUN
ejpam-6270	80	8	w	w	NOUN
ejpam-6270	80	9	is	be	AUX
ejpam-6270	80	10	known	know	VERB
ejpam-6270	80	11	as	as	ADP
ejpam-6270	80	12	a	a	DET
ejpam-6270	80	13	positive	positive	ADJ
ejpam-6270	80	14	implicative	implicative	ADJ
ejpam-6270	80	15	d	d	NOUN
ejpam-6270	80	16	-	-	PUNCT
ejpam-6270	80	17	algebra	algebra	NOUN
ejpam-6270	80	18	,	,	PUNCT
ejpam-6270	80	19	if	if	SCONJ
ejpam-6270	80	20	(	(	PUNCT
ejpam-6270	80	21	η	η	PROPN
ejpam-6270	80	22	⊙	⊙	PROPN
ejpam-6270	80	23	ζ)⊙	ζ)⊙	PROPN
ejpam-6270	80	24	(	(	PUNCT
ejpam-6270	80	25	θ	θ	PROPN
ejpam-6270	80	26	⊙	⊙	PROPN
ejpam-6270	80	27	ζ	ζ	NOUN
ejpam-6270	80	28	)	)	PUNCT
ejpam-6270	80	29	=	=	SYM
ejpam-6270	80	30	(	(	PUNCT
ejpam-6270	80	31	η	η	PROPN
ejpam-6270	80	32	⊙	⊙	PROPN
ejpam-6270	80	33	θ)⊙	θ)⊙	PROPN
ejpam-6270	80	34	ζ	ζ	PROPN
ejpam-6270	80	35	for	for	ADP
ejpam-6270	80	36	all	all	DET
ejpam-6270	80	37	ζ	ζ	PROPN
ejpam-6270	80	38	,	,	PUNCT
ejpam-6270	80	39	η	η	PROPN
ejpam-6270	80	40	,	,	PUNCT
ejpam-6270	80	41	θ	θ	PROPN
ejpam-6270	80	42	∈	∈	PROPN
ejpam-6270	80	43	w.	w.	NOUN
ejpam-6270	80	44	definition	definition	NOUN
ejpam-6270	80	45	12	12	NUM
ejpam-6270	80	46	.	.	PUNCT
ejpam-6270	81	1	[	[	X
ejpam-6270	81	2	5	5	NUM
ejpam-6270	81	3	]	]	PUNCT
ejpam-6270	81	4	a	a	DET
ejpam-6270	81	5	bck	bck	NOUN
ejpam-6270	81	6	-	-	PUNCT
ejpam-6270	81	7	algebraw	algebraw	NOUN
ejpam-6270	81	8	with	with	ADP
ejpam-6270	81	9	a	a	DET
ejpam-6270	81	10	topology	topology	NOUN
ejpam-6270	81	11	ω	ω	NOUN
ejpam-6270	81	12	is	be	AUX
ejpam-6270	81	13	a	a	DET
ejpam-6270	81	14	tbck	tbck	NOUN
ejpam-6270	81	15	-	-	PUNCT
ejpam-6270	81	16	algebra	algebra	NOUN
ejpam-6270	81	17	if	if	SCONJ
ejpam-6270	81	18	the	the	DET
ejpam-6270	81	19	function	function	NOUN
ejpam-6270	81	20	f	f	X
ejpam-6270	81	21	:	:	PUNCT
ejpam-6270	81	22	w	w	PROPN
ejpam-6270	81	23	×	×	PROPN
ejpam-6270	81	24	w	w	PROPN
ejpam-6270	81	25	→	→	PUNCT
ejpam-6270	81	26	w	w	ADP
ejpam-6270	81	27	known	know	VERB
ejpam-6270	81	28	as	as	ADP
ejpam-6270	81	29	f(ζ	f(ζ	PROPN
ejpam-6270	81	30	,	,	PUNCT
ejpam-6270	81	31	η	η	NOUN
ejpam-6270	81	32	)	)	PUNCT
ejpam-6270	81	33	=	=	SYM
ejpam-6270	81	34	ζ	ζ	PROPN
ejpam-6270	81	35	⊙	⊙	PROPN
ejpam-6270	81	36	η	η	PROPN
ejpam-6270	81	37	possesses	possess	VERB
ejpam-6270	81	38	the	the	DET
ejpam-6270	81	39	attribute	attribute	NOUN
ejpam-6270	81	40	that	that	PRON
ejpam-6270	81	41	for	for	ADP
ejpam-6270	81	42	every	every	DET
ejpam-6270	81	43	open	open	ADJ
ejpam-6270	81	44	set	set	NOUN
ejpam-6270	81	45	o	o	NOUN
ejpam-6270	81	46	having	have	VERB
ejpam-6270	81	47	ζ	ζ	PROPN
ejpam-6270	81	48	⊙	⊙	PROPN
ejpam-6270	81	49	η	η	PROPN
ejpam-6270	81	50	,	,	PUNCT
ejpam-6270	81	51	there	there	PRON
ejpam-6270	81	52	exist	exist	VERB
ejpam-6270	81	53	open	open	ADJ
ejpam-6270	81	54	sets	set	NOUN
ejpam-6270	81	55	u	u	NOUN
ejpam-6270	81	56	,	,	PUNCT
ejpam-6270	81	57	v	v	ADP
ejpam-6270	81	58	having	have	VERB
ejpam-6270	81	59	ζ	ζ	NOUN
ejpam-6270	81	60	,	,	PUNCT
ejpam-6270	81	61	η	η	X
ejpam-6270	81	62	correspondingly	correspondingly	ADV
ejpam-6270	81	63	such	such	ADJ
ejpam-6270	81	64	that	that	SCONJ
ejpam-6270	81	65	f(u	f(u	PROPN
ejpam-6270	81	66	,	,	PUNCT
ejpam-6270	81	67	v	v	NOUN
ejpam-6270	81	68	)	)	PUNCT
ejpam-6270	82	1	=	=	SYM
ejpam-6270	82	2	u	u	PROPN
ejpam-6270	82	3	⊙	⊙	VERB
ejpam-6270	82	4	v	v	ADP
ejpam-6270	82	5	⊆	⊆	NUM
ejpam-6270	82	6	o	o	NOUN
ejpam-6270	82	7	∀	∀	NOUN
ejpam-6270	82	8	ζ	ζ	NOUN
ejpam-6270	82	9	,	,	PUNCT
ejpam-6270	82	10	η	η	PROPN
ejpam-6270	82	11	∈	∈	PROPN
ejpam-6270	82	12	w.	w.	NOUN
ejpam-6270	82	13	definition	definition	NOUN
ejpam-6270	82	14	13	13	NUM
ejpam-6270	82	15	.	.	PUNCT
ejpam-6270	83	1	[	[	X
ejpam-6270	83	2	6	6	NUM
ejpam-6270	83	3	]	]	PUNCT
ejpam-6270	83	4	a	a	DET
ejpam-6270	83	5	d	d	NOUN
ejpam-6270	83	6	-	-	NOUN
ejpam-6270	83	7	algebraw	algebraw	ADJ
ejpam-6270	83	8	with	with	ADP
ejpam-6270	83	9	a	a	DET
ejpam-6270	83	10	topology	topology	NOUN
ejpam-6270	83	11	ω	ω	NOUN
ejpam-6270	83	12	is	be	AUX
ejpam-6270	83	13	called	call	VERB
ejpam-6270	83	14	an	an	DET
ejpam-6270	83	15	td	td	NOUN
ejpam-6270	83	16	-	-	PUNCT
ejpam-6270	83	17	algebra	algebra	NOUN
ejpam-6270	83	18	if	if	SCONJ
ejpam-6270	83	19	the	the	DET
ejpam-6270	83	20	function	function	NOUN
ejpam-6270	83	21	f	f	X
ejpam-6270	83	22	:	:	PUNCT
ejpam-6270	83	23	w	w	PROPN
ejpam-6270	83	24	×	×	PROPN
ejpam-6270	83	25	w	w	PROPN
ejpam-6270	83	26	→	→	PUNCT
ejpam-6270	83	27	w	w	ADP
ejpam-6270	83	28	known	know	VERB
ejpam-6270	83	29	as	as	ADP
ejpam-6270	83	30	f(ζ	f(ζ	PROPN
ejpam-6270	83	31	,	,	PUNCT
ejpam-6270	83	32	η	η	NOUN
ejpam-6270	83	33	)	)	PUNCT
ejpam-6270	83	34	=	=	SYM
ejpam-6270	83	35	ζ	ζ	PROPN
ejpam-6270	83	36	⊙	⊙	PROPN
ejpam-6270	83	37	η	η	PROPN
ejpam-6270	83	38	possesses	possess	VERB
ejpam-6270	83	39	the	the	DET
ejpam-6270	83	40	attribute	attribute	NOUN
ejpam-6270	83	41	that	that	PRON
ejpam-6270	83	42	for	for	ADP
ejpam-6270	83	43	every	every	DET
ejpam-6270	83	44	open	open	ADJ
ejpam-6270	83	45	set	set	NOUN
ejpam-6270	83	46	o	o	NOUN
ejpam-6270	83	47	having	have	VERB
ejpam-6270	83	48	ζ	ζ	PROPN
ejpam-6270	83	49	⊙	⊙	PROPN
ejpam-6270	83	50	η	η	PROPN
ejpam-6270	83	51	,	,	PUNCT
ejpam-6270	83	52	there	there	PRON
ejpam-6270	83	53	exist	exist	VERB
ejpam-6270	83	54	open	open	ADJ
ejpam-6270	83	55	sets	set	NOUN
ejpam-6270	83	56	u	u	NOUN
ejpam-6270	83	57	,	,	PUNCT
ejpam-6270	83	58	v	v	ADP
ejpam-6270	83	59	having	have	VERB
ejpam-6270	83	60	ζ	ζ	NOUN
ejpam-6270	83	61	,	,	PUNCT
ejpam-6270	83	62	η	η	X
ejpam-6270	83	63	correspondingly	correspondingly	ADV
ejpam-6270	83	64	such	such	ADJ
ejpam-6270	83	65	that	that	SCONJ
ejpam-6270	83	66	f(u	f(u	PROPN
ejpam-6270	83	67	,	,	PUNCT
ejpam-6270	83	68	v	v	NOUN
ejpam-6270	83	69	)	)	PUNCT
ejpam-6270	83	70	=	=	SYM
ejpam-6270	83	71	u	u	PROPN
ejpam-6270	83	72	⊙	⊙	VERB
ejpam-6270	83	73	v	v	ADP
ejpam-6270	83	74	⊆	⊆	NUM
ejpam-6270	83	75	o,∀	o,∀	ADV
ejpam-6270	83	76	ζ	ζ	NOUN
ejpam-6270	83	77	,	,	PUNCT
ejpam-6270	83	78	η	η	PROPN
ejpam-6270	83	79	∈	∈	PROPN
ejpam-6270	83	80	w.	w.	PROPN
ejpam-6270	83	81	3	3	NUM
ejpam-6270	83	82	.	.	PUNCT
ejpam-6270	84	1	b	b	X
ejpam-6270	84	2	-	-	PUNCT
ejpam-6270	84	3	topological	topological	ADJ
ejpam-6270	84	4	d	d	NOUN
ejpam-6270	84	5	-	-	PUNCT
ejpam-6270	84	6	algebras	algebra	VERB
ejpam-6270	84	7	this	this	DET
ejpam-6270	84	8	section	section	NOUN
ejpam-6270	84	9	presents	present	VERB
ejpam-6270	84	10	the	the	DET
ejpam-6270	84	11	idea	idea	NOUN
ejpam-6270	84	12	of	of	ADP
ejpam-6270	84	13	b	b	NOUN
ejpam-6270	84	14	-	-	PUNCT
ejpam-6270	84	15	topological	topological	ADJ
ejpam-6270	84	16	d	d	NOUN
ejpam-6270	84	17	-	-	PUNCT
ejpam-6270	84	18	algebras	algebra	NOUN
ejpam-6270	84	19	and	and	CCONJ
ejpam-6270	84	20	covers	cover	VERB
ejpam-6270	84	21	some	some	PRON
ejpam-6270	84	22	of	of	ADP
ejpam-6270	84	23	its	its	PRON
ejpam-6270	84	24	properties	property	NOUN
ejpam-6270	84	25	.	.	PUNCT
ejpam-6270	85	1	definition	definition	NOUN
ejpam-6270	85	2	14	14	NUM
ejpam-6270	85	3	.	.	PUNCT
ejpam-6270	86	1	a	a	DET
ejpam-6270	86	2	d	d	X
ejpam-6270	86	3	-	-	NOUN
ejpam-6270	86	4	algebra	algebra	NOUN
ejpam-6270	86	5	w	w	NOUN
ejpam-6270	86	6	equipped	equip	VERB
ejpam-6270	86	7	with	with	ADP
ejpam-6270	86	8	a	a	DET
ejpam-6270	86	9	topology	topology	NOUN
ejpam-6270	86	10	ω	ω	NOUN
ejpam-6270	86	11	is	be	AUX
ejpam-6270	86	12	known	know	VERB
ejpam-6270	86	13	as	as	ADP
ejpam-6270	86	14	b	b	NOUN
ejpam-6270	86	15	-	-	PUNCT
ejpam-6270	86	16	topological	topological	ADJ
ejpam-6270	86	17	d	d	NOUN
ejpam-6270	86	18	-	-	PUNCT
ejpam-6270	86	19	algebra	algebra	NOUN
ejpam-6270	86	20	(	(	PUNCT
ejpam-6270	86	21	tbd	tbd	NOUN
ejpam-6270	86	22	-	-	PUNCT
ejpam-6270	86	23	algebra	algebra	NOUN
ejpam-6270	86	24	)	)	PUNCT
ejpam-6270	86	25	if	if	SCONJ
ejpam-6270	86	26	f	f	PROPN
ejpam-6270	86	27	:	:	PUNCT
ejpam-6270	86	28	w	w	PROPN
ejpam-6270	86	29	×	×	PROPN
ejpam-6270	86	30	w	w	PROPN
ejpam-6270	86	31	→	→	PUNCT
ejpam-6270	86	32	w	w	ADP
ejpam-6270	86	33	defined	define	VERB
ejpam-6270	86	34	by	by	ADP
ejpam-6270	86	35	f(ζ	f(ζ	PROPN
ejpam-6270	86	36	,	,	PUNCT
ejpam-6270	86	37	η	η	NOUN
ejpam-6270	86	38	)	)	PUNCT
ejpam-6270	86	39	=	=	SYM
ejpam-6270	86	40	ζ	ζ	PROPN
ejpam-6270	86	41	⊙	⊙	PROPN
ejpam-6270	86	42	η	η	PROPN
ejpam-6270	86	43	has	have	VERB
ejpam-6270	86	44	the	the	DET
ejpam-6270	86	45	property	property	NOUN
ejpam-6270	86	46	that	that	PRON
ejpam-6270	86	47	for	for	ADP
ejpam-6270	86	48	each	each	DET
ejpam-6270	86	49	open	open	ADJ
ejpam-6270	86	50	set	set	VERB
ejpam-6270	86	51	o	o	NOUN
ejpam-6270	86	52	having	have	VERB
ejpam-6270	86	53	ζ	ζ	PROPN
ejpam-6270	86	54	⊙	⊙	PROPN
ejpam-6270	86	55	η	η	PROPN
ejpam-6270	86	56	,	,	PUNCT
ejpam-6270	86	57	,	,	PUNCT
ejpam-6270	86	58	there	there	PRON
ejpam-6270	86	59	are	be	VERB
ejpam-6270	86	60	b	b	NOUN
ejpam-6270	86	61	-	-	PUNCT
ejpam-6270	86	62	open	open	ADJ
ejpam-6270	86	63	sets	set	NOUN
ejpam-6270	86	64	u	u	NOUN
ejpam-6270	86	65	,	,	PUNCT
ejpam-6270	86	66	v	v	ADP
ejpam-6270	86	67	having	have	VERB
ejpam-6270	86	68	ζ	ζ	NOUN
ejpam-6270	86	69	,	,	PUNCT
ejpam-6270	86	70	η	η	PROPN
ejpam-6270	86	71	respectively	respectively	ADV
ejpam-6270	86	72	,	,	PUNCT
ejpam-6270	86	73	such	such	ADJ
ejpam-6270	86	74	that	that	SCONJ
ejpam-6270	86	75	f(u	f(u	PROPN
ejpam-6270	86	76	,	,	PUNCT
ejpam-6270	86	77	v	v	NOUN
ejpam-6270	86	78	)	)	PUNCT
ejpam-6270	87	1	=	=	SYM
ejpam-6270	87	2	u	u	PROPN
ejpam-6270	87	3	⊙	⊙	VERB
ejpam-6270	87	4	v	v	ADP
ejpam-6270	87	5	⊆	⊆	NUM
ejpam-6270	87	6	o	o	NOUN
ejpam-6270	87	7	∀	∀	NOUN
ejpam-6270	87	8	ζ	ζ	NOUN
ejpam-6270	87	9	,	,	PUNCT
ejpam-6270	87	10	η	η	PROPN
ejpam-6270	87	11	∈	∈	PROPN
ejpam-6270	87	12	w.	w.	NOUN
ejpam-6270	87	13	by	by	ADP
ejpam-6270	87	14	the	the	DET
ejpam-6270	87	15	definitions	definition	NOUN
ejpam-6270	87	16	of	of	ADP
ejpam-6270	87	17	tbck	tbck	NOUN
ejpam-6270	87	18	-	-	PUNCT
ejpam-6270	87	19	algebra	algebra	NOUN
ejpam-6270	87	20	and	and	CCONJ
ejpam-6270	87	21	td	td	NOUN
ejpam-6270	87	22	-	-	PUNCT
ejpam-6270	87	23	algebra	algebra	NOUN
ejpam-6270	87	24	,	,	PUNCT
ejpam-6270	87	25	and	and	CCONJ
ejpam-6270	87	26	since	since	SCONJ
ejpam-6270	87	27	every	every	DET
ejpam-6270	87	28	bck	bck	NOUN
ejpam-6270	87	29	-	-	PUNCT
ejpam-6270	87	30	algebra	algebra	NOUN
ejpam-6270	87	31	is	be	AUX
ejpam-6270	87	32	a	a	DET
ejpam-6270	87	33	d	d	NOUN
ejpam-6270	87	34	-	-	NOUN
ejpam-6270	87	35	algebra	algebra	NOUN
ejpam-6270	87	36	,	,	PUNCT
ejpam-6270	87	37	we	we	PRON
ejpam-6270	87	38	deduce	deduce	VERB
ejpam-6270	87	39	that	that	SCONJ
ejpam-6270	87	40	every	every	DET
ejpam-6270	87	41	tbck	tbck	NOUN
ejpam-6270	87	42	-	-	PUNCT
ejpam-6270	87	43	algebra	algebra	NOUN
ejpam-6270	87	44	is	be	AUX
ejpam-6270	87	45	a	a	DET
ejpam-6270	87	46	td	td	NOUN
ejpam-6270	87	47	-	-	PUNCT
ejpam-6270	87	48	algebra	algebra	NOUN
ejpam-6270	87	49	and	and	CCONJ
ejpam-6270	87	50	every	every	DET
ejpam-6270	87	51	td	td	NOUN
ejpam-6270	87	52	-	-	PUNCT
ejpam-6270	87	53	algebra	algebra	NOUN
ejpam-6270	87	54	is	be	AUX
ejpam-6270	87	55	a	a	DET
ejpam-6270	87	56	tbd	tbd	NOUN
ejpam-6270	87	57	-	-	PUNCT
ejpam-6270	87	58	algebra	algebra	NOUN
ejpam-6270	87	59	.	.	PUNCT
ejpam-6270	88	1	the	the	DET
ejpam-6270	88	2	following	follow	VERB
ejpam-6270	88	3	example	example	NOUN
ejpam-6270	88	4	shows	show	VERB
ejpam-6270	88	5	that	that	SCONJ
ejpam-6270	88	6	the	the	DET
ejpam-6270	88	7	implication	implication	NOUN
ejpam-6270	88	8	is	be	AUX
ejpam-6270	88	9	not	not	PART
ejpam-6270	88	10	reversible	reversible	ADJ
ejpam-6270	88	11	in	in	ADP
ejpam-6270	88	12	general	general	ADJ
ejpam-6270	88	13	.	.	PUNCT
ejpam-6270	88	14	example	example	NOUN
ejpam-6270	89	1	1	1	NUM
ejpam-6270	89	2	.	.	PUNCT
ejpam-6270	89	3	let	let	VERB
ejpam-6270	89	4	w	w	VERB
ejpam-6270	89	5	=	=	PUNCT
ejpam-6270	89	6	{	{	PUNCT
ejpam-6270	89	7	0	0	NUM
ejpam-6270	89	8	,	,	PUNCT
ejpam-6270	89	9	α	α	X
ejpam-6270	89	10	,	,	PUNCT
ejpam-6270	89	11	β	β	X
ejpam-6270	89	12	,	,	PUNCT
ejpam-6270	89	13	γ	γ	X
ejpam-6270	89	14	}	}	PUNCT
ejpam-6270	89	15	and	and	CCONJ
ejpam-6270	89	16	⊙	⊙	NOUN
ejpam-6270	89	17	be	be	AUX
ejpam-6270	89	18	given	give	VERB
ejpam-6270	89	19	as	as	ADP
ejpam-6270	89	20	in	in	ADP
ejpam-6270	89	21	the	the	DET
ejpam-6270	89	22	cayley	cayley	ADJ
ejpam-6270	89	23	table	table	NOUN
ejpam-6270	89	24	as	as	SCONJ
ejpam-6270	89	25	follows	follow	VERB
ejpam-6270	89	26	:	:	PUNCT
ejpam-6270	89	27	it	it	PRON
ejpam-6270	89	28	is	be	AUX
ejpam-6270	89	29	easy	easy	ADJ
ejpam-6270	89	30	to	to	PART
ejpam-6270	89	31	verify	verify	VERB
ejpam-6270	89	32	that	that	SCONJ
ejpam-6270	89	33	from	from	ADP
ejpam-6270	89	34	table	table	NOUN
ejpam-6270	89	35	2	2	NUM
ejpam-6270	89	36	.	.	PUNCT
ejpam-6270	90	1	next	next	ADJ
ejpam-6270	90	2	think	think	VERB
ejpam-6270	90	3	about	about	ADP
ejpam-6270	90	4	the	the	DET
ejpam-6270	90	5	topology	topology	NOUN
ejpam-6270	90	6	ω	ω	PROPN
ejpam-6270	90	7	on	on	ADP
ejpam-6270	90	8	w	w	PROPN
ejpam-6270	90	9	given	give	VERB
ejpam-6270	90	10	as	as	ADP
ejpam-6270	90	11	:	:	PUNCT
ejpam-6270	90	12	ω	ω	NUM
ejpam-6270	90	13	=	=	SYM
ejpam-6270	90	14	{	{	PUNCT
ejpam-6270	90	15	ϕ	ϕ	NOUN
ejpam-6270	90	16	,	,	PUNCT
ejpam-6270	90	17	{	{	PUNCT
ejpam-6270	90	18	α	α	NOUN
ejpam-6270	90	19	}	}	PUNCT
ejpam-6270	90	20	,	,	PUNCT
ejpam-6270	90	21	{	{	PUNCT
ejpam-6270	90	22	γ	γ	X
ejpam-6270	90	23	}	}	PUNCT
ejpam-6270	90	24	,	,	PUNCT
ejpam-6270	90	25	{	{	PUNCT
ejpam-6270	90	26	α	α	NOUN
ejpam-6270	90	27	,	,	PUNCT
ejpam-6270	90	28	γ},w	γ},w	PROPN
ejpam-6270	90	29	}	}	PUNCT
ejpam-6270	90	30	.	.	PUNCT
ejpam-6270	91	1	then	then	ADV
ejpam-6270	91	2	w	w	NOUN
ejpam-6270	91	3	is	be	AUX
ejpam-6270	91	4	not	not	PART
ejpam-6270	91	5	a	a	DET
ejpam-6270	91	6	td	td	NOUN
ejpam-6270	91	7	-	-	PUNCT
ejpam-6270	91	8	algebra	algebra	NOUN
ejpam-6270	91	9	because	because	SCONJ
ejpam-6270	91	10	γ	γ	X
ejpam-6270	91	11	⊙	⊙	PROPN
ejpam-6270	91	12	β	β	X
ejpam-6270	91	13	=	=	SYM
ejpam-6270	91	14	γ	γ	X
ejpam-6270	91	15	,	,	PUNCT
ejpam-6270	91	16	and	and	CCONJ
ejpam-6270	91	17	the	the	DET
ejpam-6270	91	18	only	only	ADJ
ejpam-6270	91	19	open	open	ADJ
ejpam-6270	91	20	set	set	NOUN
ejpam-6270	91	21	having	have	VERB
ejpam-6270	91	22	β	β	X
ejpam-6270	91	23	is	be	AUX
ejpam-6270	91	24	w	w	NOUN
ejpam-6270	91	25	and	and	CCONJ
ejpam-6270	91	26	{	{	PUNCT
ejpam-6270	91	27	γ	γ	NOUN
ejpam-6270	91	28	}	}	PUNCT
ejpam-6270	91	29	×	×	PROPN
ejpam-6270	91	30	w	w	PROPN
ejpam-6270	91	31	̸⊆	̸⊆	NOUN
ejpam-6270	91	32	{	{	PUNCT
ejpam-6270	91	33	γ	γ	X
ejpam-6270	91	34	}	}	PUNCT
ejpam-6270	91	35	.	.	PUNCT
ejpam-6270	92	1	it	it	PRON
ejpam-6270	92	2	is	be	AUX
ejpam-6270	92	3	easy	easy	ADJ
ejpam-6270	92	4	to	to	PART
ejpam-6270	92	5	confirm	confirm	VERB
ejpam-6270	92	6	that	that	SCONJ
ejpam-6270	92	7	the	the	DET
ejpam-6270	92	8	b	b	NOUN
ejpam-6270	92	9	-	-	PUNCT
ejpam-6270	92	10	open	open	ADJ
ejpam-6270	92	11	sets	set	NOUN
ejpam-6270	92	12	in	in	ADP
ejpam-6270	92	13	(	(	PUNCT
ejpam-6270	92	14	w	w	PROPN
ejpam-6270	92	15	,	,	PUNCT
ejpam-6270	92	16	ω	ω	NOUN
ejpam-6270	92	17	)	)	PUNCT
ejpam-6270	92	18	are	be	AUX
ejpam-6270	92	19	p	p	X
ejpam-6270	92	20	(	(	PUNCT
ejpam-6270	92	21	w	w	NOUN
ejpam-6270	92	22	)	)	PUNCT
ejpam-6270	92	23	\	\	NOUN
ejpam-6270	92	24	(	(	PUNCT
ejpam-6270	92	25	{	{	PUNCT
ejpam-6270	92	26	0	0	NUM
ejpam-6270	92	27	}	}	PUNCT
ejpam-6270	92	28	,	,	PUNCT
ejpam-6270	92	29	{	{	PUNCT
ejpam-6270	92	30	β	β	X
ejpam-6270	92	31	}	}	PUNCT
ejpam-6270	92	32	,	,	PUNCT
ejpam-6270	92	33	{	{	PUNCT
ejpam-6270	92	34	0	0	NUM
ejpam-6270	92	35	,	,	PUNCT
ejpam-6270	92	36	β	β	NOUN
ejpam-6270	92	37	}	}	PUNCT
ejpam-6270	92	38	)	)	PUNCT
ejpam-6270	92	39	and	and	CCONJ
ejpam-6270	92	40	we	we	PRON
ejpam-6270	92	41	can	can	AUX
ejpam-6270	92	42	show	show	VERB
ejpam-6270	92	43	by	by	ADP
ejpam-6270	92	44	basic	basic	ADJ
ejpam-6270	92	45	computation	computation	NOUN
ejpam-6270	92	46	that	that	SCONJ
ejpam-6270	92	47	(	(	PUNCT
ejpam-6270	92	48	w	w	PROPN
ejpam-6270	92	49	,	,	PUNCT
ejpam-6270	92	50	ω	ω	NOUN
ejpam-6270	92	51	)	)	PUNCT
ejpam-6270	92	52	is	be	AUX
ejpam-6270	92	53	a	a	DET
ejpam-6270	92	54	tbd	tbd	NOUN
ejpam-6270	92	55	-	-	PUNCT
ejpam-6270	92	56	algebra	algebra	NOUN
ejpam-6270	92	57	.	.	PUNCT
ejpam-6270	93	1	m.	m.	NOUN
ejpam-6270	93	2	w.	w.	PROPN
ejpam-6270	93	3	abdulqader	abdulqader	PROPN
ejpam-6270	93	4	,	,	PUNCT
ejpam-6270	93	5	a.	a.	PROPN
ejpam-6270	93	6	b.	b.	PROPN
ejpam-6270	93	7	khalaf	khalaf	PROPN
ejpam-6270	93	8	/	/	SYM
ejpam-6270	93	9	eur	eur	PROPN
ejpam-6270	93	10	.	.	PUNCT
ejpam-6270	94	1	j.	j.	PROPN
ejpam-6270	94	2	pure	pure	PROPN
ejpam-6270	94	3	appl	appl	PROPN
ejpam-6270	94	4	.	.	PROPN
ejpam-6270	94	5	math	math	PROPN
ejpam-6270	94	6	,	,	PUNCT
ejpam-6270	94	7	18	18	NUM
ejpam-6270	94	8	(	(	PUNCT
ejpam-6270	94	9	3	3	NUM
ejpam-6270	94	10	)	)	PUNCT
ejpam-6270	94	11	(	(	PUNCT
ejpam-6270	94	12	2025	2025	NUM
ejpam-6270	94	13	)	)	PUNCT
ejpam-6270	94	14	,	,	PUNCT
ejpam-6270	94	15	6270	6270	NUM
ejpam-6270	94	16	5	5	NUM
ejpam-6270	94	17	of	of	ADP
ejpam-6270	94	18	17	17	NUM
ejpam-6270	94	19	⊙	⊙	NOUN
ejpam-6270	94	20	0	0	PUNCT
ejpam-6270	95	1	α	α	PRON
ejpam-6270	95	2	β	β	X
ejpam-6270	95	3	γ	γ	X
ejpam-6270	95	4	0	0	PROPN
ejpam-6270	95	5	0	0	NUM
ejpam-6270	95	6	0	0	NUM
ejpam-6270	95	7	0	0	NUM
ejpam-6270	95	8	0	0	NUM
ejpam-6270	95	9	α	α	PRON
ejpam-6270	95	10	α	α	NOUN
ejpam-6270	95	11	0	0	NUM
ejpam-6270	95	12	0	0	NUM
ejpam-6270	96	1	α	α	NOUN
ejpam-6270	96	2	β	β	X
ejpam-6270	96	3	β	β	X
ejpam-6270	96	4	β	β	X
ejpam-6270	96	5	0	0	NUM
ejpam-6270	96	6	0	0	NUM
ejpam-6270	96	7	γ	γ	PROPN
ejpam-6270	96	8	γ	γ	X
ejpam-6270	96	9	γ	γ	X
ejpam-6270	96	10	γ	γ	X
ejpam-6270	96	11	0	0	NUM
ejpam-6270	96	12	table	table	NOUN
ejpam-6270	96	13	1	1	NUM
ejpam-6270	96	14	:	:	PUNCT
ejpam-6270	96	15	a	a	DET
ejpam-6270	96	16	tbd	tbd	NOUN
ejpam-6270	96	17	-	-	PUNCT
ejpam-6270	96	18	algebra	algebra	NOUN
ejpam-6270	96	19	which	which	PRON
ejpam-6270	96	20	is	be	AUX
ejpam-6270	96	21	not	not	PART
ejpam-6270	96	22	td	td	NOUN
ejpam-6270	96	23	-	-	PUNCT
ejpam-6270	96	24	algebra	algebra	ADJ
ejpam-6270	96	25	proposition	proposition	NOUN
ejpam-6270	96	26	1	1	NUM
ejpam-6270	96	27	.	.	PUNCT
ejpam-6270	97	1	for	for	ADP
ejpam-6270	97	2	each	each	DET
ejpam-6270	97	3	subset	subset	NOUN
ejpam-6270	97	4	m	m	PROPN
ejpam-6270	97	5	of	of	ADP
ejpam-6270	97	6	a	a	DET
ejpam-6270	97	7	tbd	tbd	NOUN
ejpam-6270	97	8	-	-	PUNCT
ejpam-6270	97	9	algebra	algebra	NOUN
ejpam-6270	97	10	w	w	NOUN
ejpam-6270	97	11	and	and	CCONJ
ejpam-6270	97	12	any	any	DET
ejpam-6270	97	13	element	element	NOUN
ejpam-6270	97	14	ζ	ζ	NOUN
ejpam-6270	97	15	∈	∈	PROPN
ejpam-6270	97	16	w	w	PROPN
ejpam-6270	97	17	,	,	PUNCT
ejpam-6270	97	18	the	the	DET
ejpam-6270	97	19	following	following	ADJ
ejpam-6270	97	20	statements	statement	NOUN
ejpam-6270	97	21	are	be	AUX
ejpam-6270	97	22	true	true	ADJ
ejpam-6270	97	23	:	:	PUNCT
ejpam-6270	97	24	(	(	PUNCT
ejpam-6270	97	25	i	i	NOUN
ejpam-6270	97	26	)	)	PUNCT
ejpam-6270	97	27	clb(m)⊙	clb(m)⊙	VERB
ejpam-6270	97	28	ζ	ζ	NOUN
ejpam-6270	97	29	⊆	⊆	NUM
ejpam-6270	97	30	cl(m	cl(m	NOUN
ejpam-6270	97	31	⊙	⊙	PROPN
ejpam-6270	97	32	ζ	ζ	PROPN
ejpam-6270	97	33	)	)	PUNCT
ejpam-6270	97	34	.	.	PUNCT
ejpam-6270	98	1	(	(	PUNCT
ejpam-6270	98	2	ii	ii	NOUN
ejpam-6270	98	3	)	)	PUNCT
ejpam-6270	98	4	if	if	SCONJ
ejpam-6270	98	5	clb(m)⊙	clb(m)⊙	NOUN
ejpam-6270	98	6	ζ	ζ	NOUN
ejpam-6270	98	7	is	be	AUX
ejpam-6270	98	8	closed	closed	ADJ
ejpam-6270	98	9	,	,	PUNCT
ejpam-6270	98	10	then	then	ADV
ejpam-6270	98	11	clb(m)⊙	clb(m)⊙	NOUN
ejpam-6270	98	12	ζ	ζ	NOUN
ejpam-6270	98	13	=	=	SYM
ejpam-6270	98	14	cl(m	cl(m	NOUN
ejpam-6270	98	15	⊙	⊙	PROPN
ejpam-6270	98	16	ζ	ζ	PROPN
ejpam-6270	98	17	)	)	PUNCT
ejpam-6270	98	18	.	.	PUNCT
ejpam-6270	99	1	proof	proof	NOUN
ejpam-6270	99	2	.	.	PUNCT
ejpam-6270	100	1	(	(	PUNCT
ejpam-6270	100	2	i	i	NOUN
ejpam-6270	100	3	)	)	PUNCT
ejpam-6270	100	4	suppose	suppose	VERB
ejpam-6270	100	5	that	that	SCONJ
ejpam-6270	100	6	η	η	PROPN
ejpam-6270	100	7	=	=	PROPN
ejpam-6270	100	8	α	α	PROPN
ejpam-6270	100	9	⊙	⊙	VERB
ejpam-6270	100	10	ζ	ζ	PROPN
ejpam-6270	100	11	∈	∈	PROPN
ejpam-6270	100	12	clb(m	clb(m	PROPN
ejpam-6270	100	13	)	)	PUNCT
ejpam-6270	100	14	⊙	⊙	PROPN
ejpam-6270	100	15	ζ	ζ	PROPN
ejpam-6270	100	16	where	where	SCONJ
ejpam-6270	100	17	α	α	PROPN
ejpam-6270	100	18	∈	∈	PROPN
ejpam-6270	100	19	clb(m	clb(m	PROPN
ejpam-6270	100	20	)	)	PUNCT
ejpam-6270	100	21	and	and	CCONJ
ejpam-6270	100	22	u	u	NOUN
ejpam-6270	100	23	is	be	AUX
ejpam-6270	100	24	any	any	DET
ejpam-6270	100	25	open	open	ADJ
ejpam-6270	100	26	set	set	NOUN
ejpam-6270	100	27	having	have	VERB
ejpam-6270	100	28	η	η	PROPN
ejpam-6270	100	29	.	.	PROPN
ejpam-6270	101	1	since	since	SCONJ
ejpam-6270	101	2	w	w	PROPN
ejpam-6270	101	3	is	be	AUX
ejpam-6270	101	4	a	a	DET
ejpam-6270	101	5	tbd	tbd	NOUN
ejpam-6270	101	6	-	-	PUNCT
ejpam-6270	101	7	algebra	algebra	NOUN
ejpam-6270	101	8	,	,	PUNCT
ejpam-6270	101	9	so	so	SCONJ
ejpam-6270	101	10	there	there	PRON
ejpam-6270	101	11	exist	exist	VERB
ejpam-6270	101	12	b	b	X
ejpam-6270	101	13	-	-	PUNCT
ejpam-6270	101	14	open	open	ADJ
ejpam-6270	101	15	sets	set	NOUN
ejpam-6270	101	16	v	v	NOUN
ejpam-6270	101	17	that	that	PRON
ejpam-6270	101	18	have	have	VERB
ejpam-6270	101	19	α	α	NOUN
ejpam-6270	101	20	and	and	CCONJ
ejpam-6270	101	21	g	g	NOUN
ejpam-6270	101	22	having	have	VERB
ejpam-6270	101	23	ζ	ζ	NOUN
ejpam-6270	101	24	such	such	ADJ
ejpam-6270	101	25	that	that	DET
ejpam-6270	101	26	v	v	NOUN
ejpam-6270	101	27	⊙g	⊙g	PROPN
ejpam-6270	101	28	⊆	⊆	NUM
ejpam-6270	101	29	u	u	NOUN
ejpam-6270	101	30	.	.	PUNCT
ejpam-6270	102	1	also	also	ADV
ejpam-6270	102	2	,	,	PUNCT
ejpam-6270	102	3	we	we	PRON
ejpam-6270	102	4	have	have	AUX
ejpam-6270	102	5	α	α	NUM
ejpam-6270	102	6	∈	∈	PROPN
ejpam-6270	102	7	clb(m	clb(m	PROPN
ejpam-6270	102	8	)	)	PUNCT
ejpam-6270	102	9	implies	imply	VERB
ejpam-6270	102	10	that	that	SCONJ
ejpam-6270	102	11	m	m	PROPN
ejpam-6270	102	12	∩	∩	NOUN
ejpam-6270	102	13	v	v	ADP
ejpam-6270	102	14	̸=	̸=	PROPN
ejpam-6270	102	15	ϕ.	ϕ.	PROPN
ejpam-6270	102	16	now	now	ADV
ejpam-6270	102	17	assume	assume	VERB
ejpam-6270	102	18	that	that	SCONJ
ejpam-6270	102	19	θ	θ	PROPN
ejpam-6270	102	20	∈	∈	PROPN
ejpam-6270	102	21	m	m	NOUN
ejpam-6270	102	22	∩	∩	ADJ
ejpam-6270	102	23	v	v	ADJ
ejpam-6270	102	24	,	,	PUNCT
ejpam-6270	102	25	so	so	ADV
ejpam-6270	102	26	θ	θ	PROPN
ejpam-6270	102	27	⊙	⊙	X
ejpam-6270	102	28	ζ	ζ	PROPN
ejpam-6270	102	29	∈	∈	PROPN
ejpam-6270	102	30	m	m	VERB
ejpam-6270	102	31	⊙	⊙	NOUN
ejpam-6270	102	32	ζ	ζ	PROPN
ejpam-6270	102	33	and	and	CCONJ
ejpam-6270	102	34	θ	θ	PROPN
ejpam-6270	102	35	⊙	⊙	X
ejpam-6270	102	36	ζ	ζ	PROPN
ejpam-6270	102	37	∈	∈	PROPN
ejpam-6270	102	38	v	v	ADP
ejpam-6270	102	39	⊙	⊙	PROPN
ejpam-6270	102	40	ζ	ζ	PROPN
ejpam-6270	102	41	⊆	⊆	PROPN
ejpam-6270	102	42	v	v	ADP
ejpam-6270	102	43	⊙	⊙	NOUN
ejpam-6270	102	44	g	g	PROPN
ejpam-6270	102	45	⊆	⊆	NUM
ejpam-6270	102	46	u	u	NOUN
ejpam-6270	102	47	.	.	PUNCT
ejpam-6270	103	1	hence	hence	ADV
ejpam-6270	103	2	θ⊙ζ	θ⊙ζ	PROPN
ejpam-6270	103	3	∈	∈	PROPN
ejpam-6270	103	4	u∩(m⊙ζ	u∩(m⊙ζ	PROPN
ejpam-6270	103	5	)	)	PUNCT
ejpam-6270	103	6	implies	imply	VERB
ejpam-6270	103	7	that	that	SCONJ
ejpam-6270	103	8	η	η	PROPN
ejpam-6270	103	9	∈	∈	PROPN
ejpam-6270	103	10	cl(m⊙ζ	cl(m⊙ζ	NOUN
ejpam-6270	103	11	)	)	PUNCT
ejpam-6270	103	12	.	.	PUNCT
ejpam-6270	104	1	thus	thus	ADV
ejpam-6270	104	2	,	,	PUNCT
ejpam-6270	104	3	clb(m)⊙ζ	clb(m)⊙ζ	NOUN
ejpam-6270	104	4	⊆	⊆	NUM
ejpam-6270	104	5	cl(m⊙ζ	cl(m⊙ζ	NOUN
ejpam-6270	104	6	)	)	PUNCT
ejpam-6270	104	7	.	.	PUNCT
ejpam-6270	105	1	(	(	PUNCT
ejpam-6270	105	2	ii	ii	NOUN
ejpam-6270	105	3	)	)	PUNCT
ejpam-6270	105	4	suppose	suppose	VERB
ejpam-6270	105	5	that	that	SCONJ
ejpam-6270	105	6	clb(m)⊙	clb(m)⊙	NOUN
ejpam-6270	105	7	ζ	ζ	NOUN
ejpam-6270	105	8	is	be	AUX
ejpam-6270	105	9	closed	closed	ADJ
ejpam-6270	105	10	,	,	PUNCT
ejpam-6270	105	11	we	we	PRON
ejpam-6270	105	12	have	have	VERB
ejpam-6270	105	13	m	m	PROPN
ejpam-6270	105	14	⊙	⊙	NOUN
ejpam-6270	105	15	ζ	ζ	PROPN
ejpam-6270	105	16	⊆	⊆	NUM
ejpam-6270	105	17	clb(m)⊙	clb(m)⊙	NOUN
ejpam-6270	105	18	ζ	ζ	NOUN
ejpam-6270	105	19	and	and	CCONJ
ejpam-6270	105	20	hence	hence	ADV
ejpam-6270	105	21	cl(m	cl(m	PROPN
ejpam-6270	105	22	⊙	⊙	PROPN
ejpam-6270	105	23	ζ	ζ	PROPN
ejpam-6270	105	24	)	)	PUNCT
ejpam-6270	105	25	⊆	⊆	NUM
ejpam-6270	105	26	clb(m)⊙	clb(m)⊙	NOUN
ejpam-6270	105	27	ζ	ζ	NOUN
ejpam-6270	105	28	.	.	PUNCT
ejpam-6270	106	1	therefore	therefore	ADV
ejpam-6270	106	2	,	,	PUNCT
ejpam-6270	106	3	by	by	ADP
ejpam-6270	106	4	(	(	PUNCT
ejpam-6270	106	5	i	i	NOUN
ejpam-6270	106	6	)	)	PUNCT
ejpam-6270	106	7	we	we	PRON
ejpam-6270	106	8	get	get	VERB
ejpam-6270	106	9	the	the	DET
ejpam-6270	106	10	equality	equality	NOUN
ejpam-6270	106	11	.	.	PUNCT
ejpam-6270	107	1	in	in	ADP
ejpam-6270	107	2	general	general	ADJ
ejpam-6270	107	3	,	,	PUNCT
ejpam-6270	107	4	the	the	DET
ejpam-6270	107	5	inclusion	inclusion	NOUN
ejpam-6270	107	6	of	of	ADP
ejpam-6270	107	7	(	(	PUNCT
ejpam-6270	107	8	i	i	NOUN
ejpam-6270	107	9	)	)	PUNCT
ejpam-6270	107	10	can	can	AUX
ejpam-6270	107	11	not	not	PART
ejpam-6270	107	12	replaced	replace	VERB
ejpam-6270	107	13	by	by	ADP
ejpam-6270	107	14	equality	equality	NOUN
ejpam-6270	107	15	as	as	SCONJ
ejpam-6270	107	16	it	it	PRON
ejpam-6270	107	17	can	can	AUX
ejpam-6270	107	18	be	be	AUX
ejpam-6270	107	19	seen	see	VERB
ejpam-6270	107	20	in	in	ADP
ejpam-6270	107	21	example	example	NOUN
ejpam-6270	107	22	1	1	NUM
ejpam-6270	107	23	,	,	PUNCT
ejpam-6270	107	24	if	if	SCONJ
ejpam-6270	107	25	we	we	PRON
ejpam-6270	107	26	take	take	VERB
ejpam-6270	107	27	m	m	VERB
ejpam-6270	107	28	=	=	PUNCT
ejpam-6270	107	29	{	{	PUNCT
ejpam-6270	107	30	o	o	NOUN
ejpam-6270	107	31	,	,	PUNCT
ejpam-6270	107	32	α	α	NOUN
ejpam-6270	107	33	}	}	PUNCT
ejpam-6270	107	34	,	,	PUNCT
ejpam-6270	107	35	then	then	ADV
ejpam-6270	107	36	clb(m)⊙β	clb(m)⊙β	NOUN
ejpam-6270	107	37	=	=	SYM
ejpam-6270	107	38	{	{	PUNCT
ejpam-6270	107	39	0	0	NUM
ejpam-6270	107	40	}	}	PUNCT
ejpam-6270	107	41	and	and	CCONJ
ejpam-6270	107	42	cl(m⊙β	cl(m⊙β	NOUN
ejpam-6270	107	43	)	)	PUNCT
ejpam-6270	107	44	=	=	SYM
ejpam-6270	107	45	{	{	PUNCT
ejpam-6270	107	46	0	0	NUM
ejpam-6270	107	47	,	,	PUNCT
ejpam-6270	107	48	β	β	NOUN
ejpam-6270	107	49	}	}	PUNCT
ejpam-6270	107	50	,	,	PUNCT
ejpam-6270	107	51	so	so	SCONJ
ejpam-6270	107	52	clb(m)⊙β	clb(m)⊙β	PROPN
ejpam-6270	107	53	̸=	̸=	PROPN
ejpam-6270	107	54	cl(m	cl(m	PROPN
ejpam-6270	107	55	⊙	⊙	PROPN
ejpam-6270	107	56	β	β	PROPN
ejpam-6270	107	57	)	)	PUNCT
ejpam-6270	107	58	.	.	PUNCT
ejpam-6270	108	1	proposition	proposition	NOUN
ejpam-6270	108	2	2	2	NUM
ejpam-6270	108	3	.	.	PUNCT
ejpam-6270	109	1	if	if	SCONJ
ejpam-6270	109	2	m	m	NOUN
ejpam-6270	109	3	is	be	AUX
ejpam-6270	109	4	any	any	DET
ejpam-6270	109	5	subset	subset	NOUN
ejpam-6270	109	6	of	of	ADP
ejpam-6270	109	7	a	a	DET
ejpam-6270	109	8	tbd	tbd	NOUN
ejpam-6270	109	9	-	-	PUNCT
ejpam-6270	109	10	algebra	algebra	NOUN
ejpam-6270	109	11	w	w	NOUN
ejpam-6270	109	12	and	and	CCONJ
ejpam-6270	109	13	any	any	DET
ejpam-6270	109	14	element	element	NOUN
ejpam-6270	109	15	ζ	ζ	NOUN
ejpam-6270	109	16	∈	∈	PROPN
ejpam-6270	109	17	w	w	PROPN
ejpam-6270	109	18	,	,	PUNCT
ejpam-6270	109	19	,	,	PUNCT
ejpam-6270	109	20	the	the	DET
ejpam-6270	109	21	statements	statement	NOUN
ejpam-6270	109	22	listed	list	VERB
ejpam-6270	109	23	below	below	ADV
ejpam-6270	109	24	are	be	AUX
ejpam-6270	109	25	accurate	accurate	ADJ
ejpam-6270	109	26	:	:	PUNCT
ejpam-6270	109	27	(	(	PUNCT
ejpam-6270	109	28	i	i	NOUN
ejpam-6270	109	29	)	)	PUNCT
ejpam-6270	109	30	ζ	ζ	PROPN
ejpam-6270	109	31	⊙	⊙	PROPN
ejpam-6270	109	32	clb(m	clb(m	PROPN
ejpam-6270	109	33	)	)	PUNCT
ejpam-6270	109	34	⊆	⊆	NUM
ejpam-6270	109	35	cl(ζ	cl(ζ	NOUN
ejpam-6270	109	36	⊙m	⊙m	NOUN
ejpam-6270	109	37	)	)	PUNCT
ejpam-6270	109	38	.	.	PUNCT
ejpam-6270	110	1	(	(	PUNCT
ejpam-6270	110	2	ii	ii	X
ejpam-6270	110	3	)	)	PUNCT
ejpam-6270	110	4	if	if	SCONJ
ejpam-6270	110	5	ζ	ζ	PROPN
ejpam-6270	110	6	⊙	⊙	NOUN
ejpam-6270	110	7	clb(m	clb(m	PROPN
ejpam-6270	110	8	)	)	PUNCT
ejpam-6270	110	9	is	be	AUX
ejpam-6270	110	10	closed	close	VERB
ejpam-6270	110	11	,	,	PUNCT
ejpam-6270	110	12	then	then	ADV
ejpam-6270	110	13	ζ	ζ	PROPN
ejpam-6270	110	14	⊙	⊙	NOUN
ejpam-6270	110	15	clb(m	clb(m	PROPN
ejpam-6270	110	16	)	)	PUNCT
ejpam-6270	110	17	=	=	NOUN
ejpam-6270	110	18	cl(ζ	cl(ζ	NUM
ejpam-6270	110	19	⊙m	⊙m	NOUN
ejpam-6270	110	20	)	)	PUNCT
ejpam-6270	110	21	.	.	PUNCT
ejpam-6270	111	1	proof	proof	NOUN
ejpam-6270	111	2	.	.	PUNCT
ejpam-6270	112	1	(	(	PUNCT
ejpam-6270	112	2	i	i	NOUN
ejpam-6270	112	3	)	)	PUNCT
ejpam-6270	112	4	suppose	suppose	VERB
ejpam-6270	112	5	that	that	SCONJ
ejpam-6270	112	6	η	η	PROPN
ejpam-6270	112	7	∈	∈	PROPN
ejpam-6270	112	8	w	w	PROPN
ejpam-6270	112	9	⊙clb(m	⊙clb(m	PROPN
ejpam-6270	112	10	)	)	PUNCT
ejpam-6270	112	11	and	and	CCONJ
ejpam-6270	112	12	u	u	PRON
ejpam-6270	112	13	be	be	VERB
ejpam-6270	112	14	any	any	DET
ejpam-6270	112	15	open	open	ADJ
ejpam-6270	112	16	set	set	NOUN
ejpam-6270	112	17	having	have	VERB
ejpam-6270	112	18	η	η	PROPN
ejpam-6270	112	19	.	.	PROPN
ejpam-6270	113	1	so	so	PROPN
ejpam-6270	113	2	η	η	PROPN
ejpam-6270	113	3	=	=	PROPN
ejpam-6270	113	4	ζ	ζ	PROPN
ejpam-6270	113	5	⊙α	⊙α	PROPN
ejpam-6270	113	6	where	where	SCONJ
ejpam-6270	113	7	α	α	PROPN
ejpam-6270	113	8	∈	∈	PROPN
ejpam-6270	113	9	clb(m	clb(m	PROPN
ejpam-6270	113	10	)	)	PUNCT
ejpam-6270	113	11	.	.	PUNCT
ejpam-6270	114	1	since	since	SCONJ
ejpam-6270	114	2	w	w	PROPN
ejpam-6270	114	3	is	be	AUX
ejpam-6270	114	4	a	a	DET
ejpam-6270	114	5	tbd	tbd	NOUN
ejpam-6270	114	6	-	-	PUNCT
ejpam-6270	114	7	algebra	algebra	NOUN
ejpam-6270	114	8	,	,	PUNCT
ejpam-6270	114	9	there	there	PRON
ejpam-6270	114	10	exist	exist	VERB
ejpam-6270	114	11	open	open	ADJ
ejpam-6270	114	12	sets	set	NOUN
ejpam-6270	114	13	v	v	ADP
ejpam-6270	114	14	having	have	VERB
ejpam-6270	114	15	ζ	ζ	NOUN
ejpam-6270	114	16	and	and	CCONJ
ejpam-6270	114	17	g	g	NOUN
ejpam-6270	114	18	having	have	VERB
ejpam-6270	114	19	α	α	PRON
ejpam-6270	114	20	such	such	ADJ
ejpam-6270	114	21	that	that	DET
ejpam-6270	114	22	v	v	NOUN
ejpam-6270	114	23	⊙g	⊙g	PROPN
ejpam-6270	114	24	⊆	⊆	NUM
ejpam-6270	114	25	u	u	NOUN
ejpam-6270	114	26	.	.	PUNCT
ejpam-6270	115	1	also	also	ADV
ejpam-6270	115	2	,	,	PUNCT
ejpam-6270	115	3	we	we	PRON
ejpam-6270	115	4	have	have	AUX
ejpam-6270	115	5	α	α	NUM
ejpam-6270	115	6	∈	∈	PROPN
ejpam-6270	115	7	clb(m	clb(m	PROPN
ejpam-6270	115	8	)	)	PUNCT
ejpam-6270	115	9	implies	imply	VERB
ejpam-6270	115	10	that	that	SCONJ
ejpam-6270	115	11	m	m	AUX
ejpam-6270	115	12	∩g	∩g	ADJ
ejpam-6270	115	13	̸=	̸=	PROPN
ejpam-6270	115	14	ϕ.	ϕ.	PROPN
ejpam-6270	115	15	now	now	ADV
ejpam-6270	115	16	assume	assume	VERB
ejpam-6270	115	17	that	that	SCONJ
ejpam-6270	115	18	θ	θ	PROPN
ejpam-6270	115	19	∈	∈	PROPN
ejpam-6270	115	20	m	m	VERB
ejpam-6270	115	21	∩g	∩g	ADJ
ejpam-6270	115	22	,	,	PUNCT
ejpam-6270	116	1	so	so	ADV
ejpam-6270	116	2	ζ	ζ	NOUN
ejpam-6270	116	3	⊙	⊙	NOUN
ejpam-6270	116	4	θ	θ	PROPN
ejpam-6270	116	5	∈	∈	PROPN
ejpam-6270	116	6	w	w	PROPN
ejpam-6270	116	7	⊙m	⊙m	PROPN
ejpam-6270	116	8	and	and	CCONJ
ejpam-6270	116	9	ζ	ζ	NOUN
ejpam-6270	116	10	⊙	⊙	NOUN
ejpam-6270	116	11	θ	θ	PROPN
ejpam-6270	116	12	∈	∈	PROPN
ejpam-6270	117	1	w	w	ADP
ejpam-6270	117	2	⊙g	⊙g	ADJ
ejpam-6270	117	3	⊆	⊆	NUM
ejpam-6270	117	4	v	v	NOUN
ejpam-6270	117	5	⊙g	⊙g	ADJ
ejpam-6270	117	6	⊆	⊆	NUM
ejpam-6270	117	7	u	u	NOUN
ejpam-6270	117	8	.	.	PUNCT
ejpam-6270	118	1	hence	hence	ADV
ejpam-6270	118	2	we	we	PRON
ejpam-6270	118	3	obtain	obtain	VERB
ejpam-6270	118	4	that	that	SCONJ
ejpam-6270	118	5	η	η	PROPN
ejpam-6270	118	6	∈	∈	PROPN
ejpam-6270	118	7	cl(m	cl(m	PROPN
ejpam-6270	118	8	⊙	⊙	PROPN
ejpam-6270	118	9	ζ	ζ	PROPN
ejpam-6270	118	10	)	)	PUNCT
ejpam-6270	118	11	.	.	PUNCT
ejpam-6270	119	1	m.	m.	NOUN
ejpam-6270	119	2	w.	w.	PROPN
ejpam-6270	119	3	abdulqader	abdulqader	PROPN
ejpam-6270	119	4	,	,	PUNCT
ejpam-6270	119	5	a.	a.	PROPN
ejpam-6270	119	6	b.	b.	PROPN
ejpam-6270	119	7	khalaf	khalaf	PROPN
ejpam-6270	119	8	/	/	SYM
ejpam-6270	119	9	eur	eur	PROPN
ejpam-6270	119	10	.	.	PUNCT
ejpam-6270	120	1	j.	j.	PROPN
ejpam-6270	120	2	pure	pure	PROPN
ejpam-6270	120	3	appl	appl	PROPN
ejpam-6270	120	4	.	.	PROPN
ejpam-6270	120	5	math	math	PROPN
ejpam-6270	120	6	,	,	PUNCT
ejpam-6270	120	7	18	18	NUM
ejpam-6270	120	8	(	(	PUNCT
ejpam-6270	120	9	3	3	NUM
ejpam-6270	120	10	)	)	PUNCT
ejpam-6270	120	11	(	(	PUNCT
ejpam-6270	120	12	2025	2025	NUM
ejpam-6270	120	13	)	)	PUNCT
ejpam-6270	120	14	,	,	PUNCT
ejpam-6270	120	15	6270	6270	NUM
ejpam-6270	120	16	6	6	NUM
ejpam-6270	120	17	of	of	ADP
ejpam-6270	120	18	17	17	NUM
ejpam-6270	120	19	(	(	PUNCT
ejpam-6270	120	20	ii	ii	NOUN
ejpam-6270	120	21	)	)	PUNCT
ejpam-6270	120	22	assume	assume	VERB
ejpam-6270	120	23	that	that	SCONJ
ejpam-6270	120	24	ζ	ζ	PROPN
ejpam-6270	120	25	⊙	⊙	PROPN
ejpam-6270	120	26	clb(m	clb(m	PROPN
ejpam-6270	120	27	)	)	PUNCT
ejpam-6270	120	28	is	be	AUX
ejpam-6270	120	29	closed	close	VERB
ejpam-6270	120	30	and	and	CCONJ
ejpam-6270	120	31	let	let	VERB
ejpam-6270	120	32	ζ	ζ	NOUN
ejpam-6270	120	33	⊙m	⊙m	PROPN
ejpam-6270	120	34	⊆	⊆	NUM
ejpam-6270	120	35	ζ	ζ	PROPN
ejpam-6270	120	36	⊙	⊙	PROPN
ejpam-6270	120	37	clb(m	clb(m	PROPN
ejpam-6270	120	38	)	)	PUNCT
ejpam-6270	120	39	.	.	PUNCT
ejpam-6270	121	1	therefore	therefore	ADV
ejpam-6270	121	2	,	,	PUNCT
ejpam-6270	121	3	cl(ζ	cl(ζ	PUNCT
ejpam-6270	121	4	⊙	⊙	PROPN
ejpam-6270	121	5	m	m	PROPN
ejpam-6270	121	6	)	)	PUNCT
ejpam-6270	122	1	⊆	⊆	NUM
ejpam-6270	122	2	ζ	ζ	PROPN
ejpam-6270	122	3	⊙	⊙	PROPN
ejpam-6270	122	4	clb(m	clb(m	PROPN
ejpam-6270	122	5	)	)	PUNCT
ejpam-6270	122	6	.	.	PUNCT
ejpam-6270	123	1	from	from	ADP
ejpam-6270	123	2	(	(	PUNCT
ejpam-6270	123	3	1	1	NUM
ejpam-6270	123	4	)	)	PUNCT
ejpam-6270	123	5	,	,	PUNCT
ejpam-6270	123	6	we	we	PRON
ejpam-6270	123	7	get	get	VERB
ejpam-6270	123	8	ζ	ζ	ADJ
ejpam-6270	123	9	⊙	⊙	X
ejpam-6270	123	10	clb(m	clb(m	PROPN
ejpam-6270	123	11	)	)	PUNCT
ejpam-6270	123	12	=	=	NOUN
ejpam-6270	123	13	cl(ζ	cl(ζ	NUM
ejpam-6270	123	14	⊙m	⊙m	NOUN
ejpam-6270	123	15	)	)	PUNCT
ejpam-6270	123	16	.	.	PUNCT
ejpam-6270	124	1	in	in	ADP
ejpam-6270	124	2	general	general	ADJ
ejpam-6270	124	3	the	the	DET
ejpam-6270	124	4	inclusion	inclusion	NOUN
ejpam-6270	124	5	in	in	ADP
ejpam-6270	124	6	(	(	PUNCT
ejpam-6270	124	7	i	i	NOUN
ejpam-6270	124	8	)	)	PUNCT
ejpam-6270	124	9	can	can	AUX
ejpam-6270	124	10	not	not	PART
ejpam-6270	124	11	be	be	AUX
ejpam-6270	124	12	replaced	replace	VERB
ejpam-6270	124	13	by	by	ADP
ejpam-6270	124	14	equality	equality	NOUN
ejpam-6270	124	15	,	,	PUNCT
ejpam-6270	124	16	as	as	SCONJ
ejpam-6270	124	17	shown	show	VERB
ejpam-6270	124	18	in	in	ADP
ejpam-6270	124	19	example	example	NOUN
ejpam-6270	124	20	1	1	NUM
ejpam-6270	124	21	,	,	PUNCT
ejpam-6270	124	22	if	if	SCONJ
ejpam-6270	124	23	we	we	PRON
ejpam-6270	124	24	take	take	VERB
ejpam-6270	124	25	m	m	VERB
ejpam-6270	124	26	=	=	PUNCT
ejpam-6270	124	27	{	{	PUNCT
ejpam-6270	124	28	o	o	NOUN
ejpam-6270	124	29	,	,	PUNCT
ejpam-6270	124	30	α	α	NOUN
ejpam-6270	124	31	}	}	PUNCT
ejpam-6270	124	32	,	,	PUNCT
ejpam-6270	124	33	then	then	ADV
ejpam-6270	124	34	β⊙clb(m	β⊙clb(m	PROPN
ejpam-6270	124	35	)	)	PUNCT
ejpam-6270	124	36	=	=	PRON
ejpam-6270	125	1	{	{	PUNCT
ejpam-6270	125	2	β	β	NOUN
ejpam-6270	125	3	}	}	PUNCT
ejpam-6270	125	4	and	and	CCONJ
ejpam-6270	125	5	cl(β⊙m	cl(β⊙m	NOUN
ejpam-6270	125	6	)	)	PUNCT
ejpam-6270	125	7	=	=	SYM
ejpam-6270	125	8	{	{	PUNCT
ejpam-6270	125	9	0	0	NUM
ejpam-6270	125	10	,	,	PUNCT
ejpam-6270	125	11	β	β	NOUN
ejpam-6270	125	12	}	}	PUNCT
ejpam-6270	125	13	,	,	PUNCT
ejpam-6270	125	14	so	so	ADV
ejpam-6270	125	15	β⊙clb(m	β⊙clb(m	PROPN
ejpam-6270	125	16	)	)	PUNCT
ejpam-6270	125	17	̸=	̸=	PROPN
ejpam-6270	125	18	cl(β	cl(β	X
ejpam-6270	125	19	⊙m	⊙m	NOUN
ejpam-6270	125	20	)	)	PUNCT
ejpam-6270	125	21	.	.	PUNCT
ejpam-6270	126	1	proposition	proposition	NOUN
ejpam-6270	126	2	3	3	NUM
ejpam-6270	126	3	.	.	PUNCT
ejpam-6270	127	1	for	for	ADP
ejpam-6270	127	2	each	each	DET
ejpam-6270	127	3	subsets	subset	NOUN
ejpam-6270	127	4	m	m	PROPN
ejpam-6270	127	5	and	and	CCONJ
ejpam-6270	127	6	n	n	PROPN
ejpam-6270	127	7	of	of	ADP
ejpam-6270	127	8	a	a	DET
ejpam-6270	127	9	tbd	tbd	NOUN
ejpam-6270	127	10	-	-	PUNCT
ejpam-6270	127	11	algebra	algebra	NOUN
ejpam-6270	127	12	w	w	NOUN
ejpam-6270	127	13	,	,	PUNCT
ejpam-6270	127	14	the	the	DET
ejpam-6270	127	15	statements	statement	NOUN
ejpam-6270	127	16	listed	list	VERB
ejpam-6270	127	17	below	below	ADV
ejpam-6270	127	18	are	be	AUX
ejpam-6270	127	19	accurate	accurate	ADJ
ejpam-6270	127	20	.	.	PUNCT
ejpam-6270	128	1	:	:	PUNCT
ejpam-6270	128	2	(	(	PUNCT
ejpam-6270	128	3	i	i	NOUN
ejpam-6270	128	4	)	)	PUNCT
ejpam-6270	128	5	clb(m)⊙	clb(m)⊙	PROPN
ejpam-6270	128	6	clb(n	clb(n	NOUN
ejpam-6270	128	7	)	)	PUNCT
ejpam-6270	128	8	⊆	⊆	NUM
ejpam-6270	128	9	cl(m	cl(m	X
ejpam-6270	128	10	⊙n	⊙n	PROPN
ejpam-6270	128	11	)	)	PUNCT
ejpam-6270	128	12	.	.	PUNCT
ejpam-6270	129	1	(	(	PUNCT
ejpam-6270	129	2	ii	ii	NOUN
ejpam-6270	129	3	)	)	PUNCT
ejpam-6270	129	4	if	if	SCONJ
ejpam-6270	129	5	clb(m)⊙	clb(m)⊙	NOUN
ejpam-6270	129	6	clb(n	clb(n	NOUN
ejpam-6270	129	7	)	)	PUNCT
ejpam-6270	129	8	is	be	AUX
ejpam-6270	129	9	closed	close	VERB
ejpam-6270	129	10	,	,	PUNCT
ejpam-6270	129	11	then	then	ADV
ejpam-6270	129	12	clb(m)⊙	clb(m)⊙	PROPN
ejpam-6270	129	13	clb(n	clb(n	NOUN
ejpam-6270	129	14	)	)	PUNCT
ejpam-6270	129	15	=	=	SYM
ejpam-6270	129	16	cl(m	cl(m	X
ejpam-6270	129	17	⊙n	⊙n	PROPN
ejpam-6270	129	18	)	)	PUNCT
ejpam-6270	129	19	.	.	PUNCT
ejpam-6270	130	1	proof	proof	NOUN
ejpam-6270	130	2	.	.	PUNCT
ejpam-6270	131	1	(	(	PUNCT
ejpam-6270	131	2	i	i	NOUN
ejpam-6270	131	3	)	)	PUNCT
ejpam-6270	131	4	let	let	VERB
ejpam-6270	131	5	ζ	ζ	NOUN
ejpam-6270	131	6	=	=	SYM
ejpam-6270	131	7	α	α	PROPN
ejpam-6270	131	8	⊙	⊙	NOUN
ejpam-6270	131	9	β	β	PROPN
ejpam-6270	131	10	∈	∈	PROPN
ejpam-6270	131	11	clb(m	clb(m	PROPN
ejpam-6270	131	12	)	)	PUNCT
ejpam-6270	131	13	⊙	⊙	NOUN
ejpam-6270	131	14	clb(n	clb(n	PROPN
ejpam-6270	131	15	)	)	PUNCT
ejpam-6270	131	16	and	and	CCONJ
ejpam-6270	131	17	u	u	PRON
ejpam-6270	131	18	be	be	VERB
ejpam-6270	131	19	any	any	DET
ejpam-6270	131	20	open	open	ADJ
ejpam-6270	131	21	set	set	NOUN
ejpam-6270	131	22	having	have	VERB
ejpam-6270	131	23	ζ	ζ	NOUN
ejpam-6270	131	24	.	.	PUNCT
ejpam-6270	132	1	since	since	SCONJ
ejpam-6270	132	2	w	w	PROPN
ejpam-6270	132	3	is	be	AUX
ejpam-6270	132	4	a	a	DET
ejpam-6270	132	5	tbd	tbd	NOUN
ejpam-6270	132	6	-	-	PUNCT
ejpam-6270	132	7	algebra	algebra	NOUN
ejpam-6270	132	8	,	,	PUNCT
ejpam-6270	132	9	so	so	SCONJ
ejpam-6270	132	10	there	there	PRON
ejpam-6270	132	11	exist	exist	VERB
ejpam-6270	132	12	open	open	ADJ
ejpam-6270	132	13	sets	set	NOUN
ejpam-6270	132	14	v	v	ADP
ejpam-6270	132	15	having	have	VERB
ejpam-6270	132	16	α	α	NOUN
ejpam-6270	132	17	and	and	CCONJ
ejpam-6270	132	18	g	g	NOUN
ejpam-6270	132	19	having	have	VERB
ejpam-6270	132	20	β	β	NOUN
ejpam-6270	132	21	such	such	ADJ
ejpam-6270	132	22	that	that	DET
ejpam-6270	132	23	v	v	NOUN
ejpam-6270	132	24	⊙	⊙	NOUN
ejpam-6270	132	25	g	g	PROPN
ejpam-6270	132	26	⊆	⊆	NUM
ejpam-6270	132	27	u	u	NOUN
ejpam-6270	132	28	.	.	PUNCT
ejpam-6270	133	1	also	also	ADV
ejpam-6270	133	2	,	,	PUNCT
ejpam-6270	133	3	we	we	PRON
ejpam-6270	133	4	have	have	VERB
ejpam-6270	133	5	α	α	NUM
ejpam-6270	133	6	∈	∈	PROPN
ejpam-6270	133	7	clb(m	clb(m	PROPN
ejpam-6270	133	8	)	)	PUNCT
ejpam-6270	133	9	and	and	CCONJ
ejpam-6270	133	10	β	β	X
ejpam-6270	133	11	∈	∈	PROPN
ejpam-6270	133	12	clb(n	clb(n	PROPN
ejpam-6270	133	13	)	)	PUNCT
ejpam-6270	133	14	,	,	PUNCT
ejpam-6270	133	15	implies	imply	VERB
ejpam-6270	133	16	that	that	SCONJ
ejpam-6270	133	17	m	m	PROPN
ejpam-6270	133	18	∩	∩	NOUN
ejpam-6270	133	19	v	v	ADP
ejpam-6270	133	20	̸=	̸=	PROPN
ejpam-6270	133	21	ϕ	ϕ	NOUN
ejpam-6270	133	22	and	and	CCONJ
ejpam-6270	133	23	n	n	PRON
ejpam-6270	133	24	∩g	∩g	NOUN
ejpam-6270	133	25	̸=	̸=	PROPN
ejpam-6270	133	26	ϕ.	ϕ.	PROPN
ejpam-6270	133	27	assume	assume	VERB
ejpam-6270	133	28	that	that	SCONJ
ejpam-6270	133	29	α1	α1	PROPN
ejpam-6270	133	30	∈	∈	PROPN
ejpam-6270	133	31	m	m	VERB
ejpam-6270	133	32	∩v	∩v	NOUN
ejpam-6270	133	33	and	and	CCONJ
ejpam-6270	133	34	β1	β1	PROPN
ejpam-6270	133	35	∈	∈	PROPN
ejpam-6270	133	36	n	n	PRON
ejpam-6270	133	37	∩g	∩g	ADJ
ejpam-6270	133	38	,	,	PUNCT
ejpam-6270	133	39	so	so	ADV
ejpam-6270	133	40	α1	α1	PROPN
ejpam-6270	133	41	⊙	⊙	PROPN
ejpam-6270	133	42	β1	β1	PROPN
ejpam-6270	133	43	∈	∈	PROPN
ejpam-6270	133	44	m	m	VERB
ejpam-6270	133	45	⊙n	⊙n	NOUN
ejpam-6270	133	46	and	and	CCONJ
ejpam-6270	133	47	α1	α1	PROPN
ejpam-6270	133	48	⊙	⊙	PROPN
ejpam-6270	133	49	β1	β1	PROPN
ejpam-6270	133	50	∈	∈	PROPN
ejpam-6270	133	51	v	v	ADP
ejpam-6270	133	52	⊙g	⊙g	ADJ
ejpam-6270	133	53	⊆	⊆	NUM
ejpam-6270	133	54	u	u	NOUN
ejpam-6270	133	55	.	.	PUNCT
ejpam-6270	134	1	hence	hence	ADV
ejpam-6270	134	2	we	we	PRON
ejpam-6270	134	3	get	get	VERB
ejpam-6270	134	4	ζ	ζ	PRON
ejpam-6270	134	5	∈	∈	PROPN
ejpam-6270	134	6	cl(m	cl(m	X
ejpam-6270	134	7	⊙n	⊙n	PROPN
ejpam-6270	134	8	)	)	PUNCT
ejpam-6270	134	9	.	.	PUNCT
ejpam-6270	135	1	(	(	PUNCT
ejpam-6270	135	2	ii	ii	NOUN
ejpam-6270	135	3	)	)	PUNCT
ejpam-6270	135	4	assume	assume	VERB
ejpam-6270	135	5	that	that	SCONJ
ejpam-6270	135	6	clb(m	clb(m	PROPN
ejpam-6270	135	7	)	)	PUNCT
ejpam-6270	135	8	⊙	⊙	NOUN
ejpam-6270	135	9	clb(n	clb(n	PROPN
ejpam-6270	135	10	)	)	PUNCT
ejpam-6270	135	11	is	be	AUX
ejpam-6270	135	12	closed	closed	ADJ
ejpam-6270	135	13	.	.	PUNCT
ejpam-6270	136	1	we	we	PRON
ejpam-6270	136	2	have	have	VERB
ejpam-6270	136	3	m	m	PROPN
ejpam-6270	136	4	⊆	⊆	NUM
ejpam-6270	136	5	clb(m	clb(m	NOUN
ejpam-6270	136	6	)	)	PUNCT
ejpam-6270	136	7	and	and	CCONJ
ejpam-6270	136	8	n	n	CCONJ
ejpam-6270	136	9	⊆	⊆	NUM
ejpam-6270	136	10	clb(n	clb(n	NOUN
ejpam-6270	136	11	)	)	PUNCT
ejpam-6270	136	12	and	and	CCONJ
ejpam-6270	136	13	hence	hence	ADV
ejpam-6270	136	14	m	m	PROPN
ejpam-6270	136	15	⊙	⊙	NOUN
ejpam-6270	136	16	n	n	CCONJ
ejpam-6270	136	17	⊆	⊆	NUM
ejpam-6270	136	18	clb(m	clb(m	PROPN
ejpam-6270	136	19	)	)	PUNCT
ejpam-6270	136	20	⊙	⊙	NOUN
ejpam-6270	136	21	clb(n	clb(n	PROPN
ejpam-6270	136	22	)	)	PUNCT
ejpam-6270	136	23	.	.	PUNCT
ejpam-6270	137	1	therefore	therefore	ADV
ejpam-6270	137	2	,	,	PUNCT
ejpam-6270	137	3	by	by	ADP
ejpam-6270	137	4	hypothesis	hypothesis	NOUN
ejpam-6270	137	5	,	,	PUNCT
ejpam-6270	137	6	cl(m	cl(m	PROPN
ejpam-6270	137	7	⊙	⊙	PROPN
ejpam-6270	137	8	n	n	CCONJ
ejpam-6270	137	9	)	)	PUNCT
ejpam-6270	137	10	⊆	⊆	NUM
ejpam-6270	137	11	clb(m)⊙	clb(m)⊙	PROPN
ejpam-6270	137	12	clb(n	clb(n	NOUN
ejpam-6270	137	13	)	)	PUNCT
ejpam-6270	137	14	.	.	PUNCT
ejpam-6270	138	1	hence	hence	ADV
ejpam-6270	138	2	,	,	PUNCT
ejpam-6270	138	3	from	from	ADP
ejpam-6270	138	4	(	(	PUNCT
ejpam-6270	138	5	i	i	NOUN
ejpam-6270	138	6	)	)	PUNCT
ejpam-6270	138	7	,	,	PUNCT
ejpam-6270	138	8	the	the	DET
ejpam-6270	138	9	equality	equality	NOUN
ejpam-6270	138	10	holds	hold	VERB
ejpam-6270	138	11	.	.	PUNCT
ejpam-6270	139	1	from	from	ADP
ejpam-6270	139	2	proposition	proposition	NOUN
ejpam-6270	139	3	1	1	NUM
ejpam-6270	139	4	and	and	CCONJ
ejpam-6270	139	5	proposition	proposition	NOUN
ejpam-6270	139	6	2	2	NUM
ejpam-6270	139	7	,	,	PUNCT
ejpam-6270	139	8	we	we	PRON
ejpam-6270	139	9	obtain	obtain	VERB
ejpam-6270	139	10	the	the	DET
ejpam-6270	139	11	following	following	ADJ
ejpam-6270	139	12	result	result	NOUN
ejpam-6270	139	13	:	:	PUNCT
ejpam-6270	139	14	corollary	corollary	ADJ
ejpam-6270	139	15	1	1	NUM
ejpam-6270	139	16	.	.	PUNCT
ejpam-6270	140	1	for	for	ADP
ejpam-6270	140	2	a	a	DET
ejpam-6270	140	3	subset	subset	NOUN
ejpam-6270	140	4	m	m	NOUN
ejpam-6270	140	5	of	of	ADP
ejpam-6270	140	6	a	a	DET
ejpam-6270	140	7	tbd	tbd	NOUN
ejpam-6270	140	8	-	-	PUNCT
ejpam-6270	140	9	algebra	algebra	NOUN
ejpam-6270	140	10	w	w	NOUN
ejpam-6270	140	11	and	and	CCONJ
ejpam-6270	140	12	an	an	DET
ejpam-6270	140	13	element	element	NOUN
ejpam-6270	140	14	ζ	ζ	NOUN
ejpam-6270	140	15	∈	∈	PROPN
ejpam-6270	140	16	w	w	PROPN
ejpam-6270	140	17	,	,	PUNCT
ejpam-6270	140	18	the	the	DET
ejpam-6270	140	19	statements	statement	NOUN
ejpam-6270	140	20	listed	list	VERB
ejpam-6270	140	21	below	below	ADV
ejpam-6270	140	22	are	be	AUX
ejpam-6270	140	23	accurate	accurate	ADJ
ejpam-6270	140	24	:	:	PUNCT
ejpam-6270	140	25	(	(	PUNCT
ejpam-6270	140	26	i	i	NOUN
ejpam-6270	140	27	)	)	PUNCT
ejpam-6270	140	28	if	if	SCONJ
ejpam-6270	140	29	m	m	PROPN
ejpam-6270	140	30	⊙	⊙	NOUN
ejpam-6270	140	31	ζ	ζ	PROPN
ejpam-6270	140	32	is	be	AUX
ejpam-6270	140	33	closed	closed	ADJ
ejpam-6270	140	34	,	,	PUNCT
ejpam-6270	140	35	then	then	ADV
ejpam-6270	140	36	clb(m)⊙	clb(m)⊙	NOUN
ejpam-6270	140	37	ζ	ζ	NOUN
ejpam-6270	140	38	=	=	PUNCT
ejpam-6270	140	39	m	m	PROPN
ejpam-6270	140	40	⊙	⊙	NOUN
ejpam-6270	140	41	ζ	ζ	X
ejpam-6270	140	42	.	.	PUNCT
ejpam-6270	141	1	(	(	PUNCT
ejpam-6270	141	2	ii	ii	NOUN
ejpam-6270	141	3	)	)	PUNCT
ejpam-6270	141	4	if	if	SCONJ
ejpam-6270	141	5	ζ	ζ	NOUN
ejpam-6270	141	6	⊙m	⊙m	PROPN
ejpam-6270	141	7	is	be	AUX
ejpam-6270	141	8	closed	closed	ADJ
ejpam-6270	141	9	,	,	PUNCT
ejpam-6270	141	10	then	then	ADV
ejpam-6270	141	11	ζ	ζ	PROPN
ejpam-6270	141	12	⊙	⊙	NOUN
ejpam-6270	141	13	clb(m	clb(m	PROPN
ejpam-6270	141	14	)	)	PUNCT
ejpam-6270	141	15	=	=	SYM
ejpam-6270	141	16	ζ	ζ	PROPN
ejpam-6270	141	17	⊙m	⊙m	PROPN
ejpam-6270	141	18	.	.	PUNCT
ejpam-6270	142	1	proof	proof	NOUN
ejpam-6270	142	2	.	.	PUNCT
ejpam-6270	143	1	(	(	PUNCT
ejpam-6270	143	2	i	i	NOUN
ejpam-6270	143	3	)	)	PUNCT
ejpam-6270	143	4	by	by	ADP
ejpam-6270	143	5	proposition	proposition	NOUN
ejpam-6270	143	6	1	1	NUM
ejpam-6270	143	7	,	,	PUNCT
ejpam-6270	143	8	we	we	PRON
ejpam-6270	143	9	have	have	VERB
ejpam-6270	143	10	clb(m	clb(m	PROPN
ejpam-6270	143	11	)	)	PUNCT
ejpam-6270	143	12	⊙	⊙	NOUN
ejpam-6270	143	13	ζ	ζ	PROPN
ejpam-6270	143	14	⊆	⊆	NUM
ejpam-6270	143	15	cl(m	cl(m	PROPN
ejpam-6270	143	16	⊙	⊙	X
ejpam-6270	143	17	ζ	ζ	PROPN
ejpam-6270	143	18	)	)	PUNCT
ejpam-6270	144	1	=	=	PUNCT
ejpam-6270	144	2	m	m	PROPN
ejpam-6270	144	3	⊙	⊙	NOUN
ejpam-6270	144	4	ζ	ζ	PROPN
ejpam-6270	144	5	and	and	CCONJ
ejpam-6270	144	6	m	m	PROPN
ejpam-6270	144	7	⊙	⊙	NOUN
ejpam-6270	144	8	ζ	ζ	VERB
ejpam-6270	144	9	⊆	⊆	NUM
ejpam-6270	144	10	clb(m)⊙	clb(m)⊙	PROPN
ejpam-6270	144	11	ζ	ζ	NOUN
ejpam-6270	144	12	.	.	PUNCT
ejpam-6270	145	1	hence	hence	ADV
ejpam-6270	145	2	,	,	PUNCT
ejpam-6270	145	3	the	the	DET
ejpam-6270	145	4	proof	proof	NOUN
ejpam-6270	145	5	.	.	PUNCT
ejpam-6270	146	1	(	(	PUNCT
ejpam-6270	146	2	ii	ii	NOUN
ejpam-6270	146	3	)	)	PUNCT
ejpam-6270	146	4	is	be	AUX
ejpam-6270	146	5	similar	similar	ADJ
ejpam-6270	146	6	.	.	PUNCT
ejpam-6270	147	1	m.	m.	NOUN
ejpam-6270	147	2	w.	w.	PROPN
ejpam-6270	147	3	abdulqader	abdulqader	PROPN
ejpam-6270	147	4	,	,	PUNCT
ejpam-6270	147	5	a.	a.	PROPN
ejpam-6270	147	6	b.	b.	PROPN
ejpam-6270	147	7	khalaf	khalaf	PROPN
ejpam-6270	147	8	/	/	SYM
ejpam-6270	147	9	eur	eur	PROPN
ejpam-6270	147	10	.	.	PUNCT
ejpam-6270	148	1	j.	j.	PROPN
ejpam-6270	148	2	pure	pure	PROPN
ejpam-6270	148	3	appl	appl	PROPN
ejpam-6270	148	4	.	.	PROPN
ejpam-6270	148	5	math	math	PROPN
ejpam-6270	148	6	,	,	PUNCT
ejpam-6270	148	7	18	18	NUM
ejpam-6270	148	8	(	(	PUNCT
ejpam-6270	148	9	3	3	NUM
ejpam-6270	148	10	)	)	PUNCT
ejpam-6270	148	11	(	(	PUNCT
ejpam-6270	148	12	2025	2025	NUM
ejpam-6270	148	13	)	)	PUNCT
ejpam-6270	148	14	,	,	PUNCT
ejpam-6270	148	15	6270	6270	NUM
ejpam-6270	148	16	7	7	NUM
ejpam-6270	148	17	of	of	ADP
ejpam-6270	148	18	17	17	NUM
ejpam-6270	148	19	definition	definition	NOUN
ejpam-6270	148	20	15	15	NUM
ejpam-6270	148	21	.	.	PUNCT
ejpam-6270	149	1	let	let	VERB
ejpam-6270	149	2	w	w	NOUN
ejpam-6270	149	3	be	be	AUX
ejpam-6270	149	4	a	a	DET
ejpam-6270	149	5	d	d	NOUN
ejpam-6270	149	6	-	-	NOUN
ejpam-6270	149	7	algebra	algebra	NOUN
ejpam-6270	149	8	,	,	PUNCT
ejpam-6270	149	9	u	u	PRON
ejpam-6270	149	10	be	be	VERB
ejpam-6270	149	11	a	a	DET
ejpam-6270	149	12	non	non	ADJ
ejpam-6270	149	13	-	-	ADJ
ejpam-6270	149	14	empty	empty	ADJ
ejpam-6270	149	15	subset	subset	NOUN
ejpam-6270	149	16	of	of	ADP
ejpam-6270	149	17	w	w	PROPN
ejpam-6270	149	18	and	and	CCONJ
ejpam-6270	149	19	α	α	PROPN
ejpam-6270	149	20	∈	∈	PROPN
ejpam-6270	149	21	w.	w.	NOUN
ejpam-6270	149	22	we	we	PRON
ejpam-6270	149	23	define	define	VERB
ejpam-6270	149	24	the	the	DET
ejpam-6270	149	25	following	follow	VERB
ejpam-6270	149	26	subsets	subset	NOUN
ejpam-6270	149	27	.	.	PUNCT
ejpam-6270	150	1	uα	uα	NOUN
ejpam-6270	150	2	and	and	CCONJ
ejpam-6270	150	3	αu	αu	INTJ
ejpam-6270	150	4	:	:	PUNCT
ejpam-6270	150	5	uα	uα	PROPN
ejpam-6270	150	6	=	=	PRON
ejpam-6270	150	7	{	{	PUNCT
ejpam-6270	150	8	ζ	ζ	NOUN
ejpam-6270	150	9	∈	∈	NOUN
ejpam-6270	150	10	w	w	NOUN
ejpam-6270	150	11	:	:	PUNCT
ejpam-6270	150	12	ζ	ζ	NOUN
ejpam-6270	150	13	⊙	⊙	NOUN
ejpam-6270	150	14	α	α	PROPN
ejpam-6270	150	15	∈	∈	PROPN
ejpam-6270	150	16	u	u	NOUN
ejpam-6270	150	17	}	}	PUNCT
ejpam-6270	150	18	and	and	CCONJ
ejpam-6270	150	19	αu	αu	NOUN
ejpam-6270	150	20	=	=	PUNCT
ejpam-6270	150	21	{	{	PUNCT
ejpam-6270	150	22	ζ	ζ	NOUN
ejpam-6270	150	23	∈	∈	PROPN
ejpam-6270	150	24	w	w	NOUN
ejpam-6270	150	25	:	:	PUNCT
ejpam-6270	150	26	α⊙	α⊙	NOUN
ejpam-6270	150	27	ζ	ζ	NOUN
ejpam-6270	150	28	∈	∈	PROPN
ejpam-6270	150	29	u	u	NOUN
ejpam-6270	150	30	}	}	PUNCT
ejpam-6270	150	31	.	.	PUNCT
ejpam-6270	151	1	also	also	ADV
ejpam-6270	151	2	if	if	SCONJ
ejpam-6270	151	3	k	k	PROPN
ejpam-6270	151	4	⊆	⊆	X
ejpam-6270	151	5	w	w	VERB
ejpam-6270	151	6	we	we	PRON
ejpam-6270	151	7	define	define	VERB
ejpam-6270	151	8	ku	ku	PROPN
ejpam-6270	152	1	=	=	PUNCT
ejpam-6270	152	2	⋃	⋃	PROPN
ejpam-6270	152	3	α∈k	α∈k	ADJ
ejpam-6270	152	4	αu	αu	PROPN
ejpam-6270	152	5	&	&	CCONJ
ejpam-6270	152	6	uk	uk	PROPN
ejpam-6270	152	7	=	=	SYM
ejpam-6270	152	8	⋃	⋃	PROPN
ejpam-6270	152	9	α∈k	α∈k	NOUN
ejpam-6270	152	10	uα	uα	PROPN
ejpam-6270	152	11	.	.	PUNCT
ejpam-6270	153	1	proposition	proposition	NOUN
ejpam-6270	153	2	4	4	NUM
ejpam-6270	153	3	.	.	PUNCT
ejpam-6270	154	1	let	let	VERB
ejpam-6270	154	2	w	w	NOUN
ejpam-6270	154	3	be	be	AUX
ejpam-6270	154	4	an	an	DET
ejpam-6270	154	5	d	d	NOUN
ejpam-6270	154	6	-	-	PUNCT
ejpam-6270	154	7	algebra	algebra	NOUN
ejpam-6270	154	8	and	and	CCONJ
ejpam-6270	154	9	m	m	PROPN
ejpam-6270	154	10	,	,	PUNCT
ejpam-6270	154	11	n	n	CCONJ
ejpam-6270	154	12	,	,	PUNCT
ejpam-6270	154	13	w	w	PROPN
ejpam-6270	154	14	,	,	PUNCT
ejpam-6270	154	15	k	k	PROPN
ejpam-6270	154	16	are	be	AUX
ejpam-6270	154	17	subsets	subset	NOUN
ejpam-6270	154	18	of	of	ADP
ejpam-6270	154	19	w	w	NOUN
ejpam-6270	154	20	then	then	ADV
ejpam-6270	154	21	:	:	PUNCT
ejpam-6270	154	22	(	(	PUNCT
ejpam-6270	154	23	i	i	NOUN
ejpam-6270	154	24	)	)	PUNCT
ejpam-6270	154	25	mw	mw	VERB
ejpam-6270	154	26	⊆	⊆	NUM
ejpam-6270	154	27	nw	nw	INTJ
ejpam-6270	154	28	,	,	PUNCT
ejpam-6270	154	29	if	if	SCONJ
ejpam-6270	154	30	m	m	PROPN
ejpam-6270	154	31	⊆	⊆	NUM
ejpam-6270	154	32	n	n	NOUN
ejpam-6270	154	33	.	.	PUNCT
ejpam-6270	155	1	(	(	PUNCT
ejpam-6270	155	2	ii	ii	NOUN
ejpam-6270	155	3	)	)	PUNCT
ejpam-6270	155	4	mw	mw	VERB
ejpam-6270	155	5	⊆	⊆	NUM
ejpam-6270	155	6	mk	mk	NOUN
ejpam-6270	155	7	,	,	PUNCT
ejpam-6270	155	8	if	if	SCONJ
ejpam-6270	155	9	w	w	PROPN
ejpam-6270	155	10	⊆	⊆	NUM
ejpam-6270	155	11	k.	k.	PROPN
ejpam-6270	155	12	(	(	PUNCT
ejpam-6270	155	13	iii	iii	NOUN
ejpam-6270	155	14	)	)	PUNCT
ejpam-6270	155	15	(	(	PUNCT
ejpam-6270	155	16	fα	fα	NOUN
ejpam-6270	155	17	)	)	PUNCT
ejpam-6270	155	18	c	c	NOUN
ejpam-6270	156	1	=	=	SYM
ejpam-6270	156	2	(	(	PUNCT
ejpam-6270	156	3	f	f	PROPN
ejpam-6270	156	4	c)α	c)α	NOUN
ejpam-6270	156	5	and	and	CCONJ
ejpam-6270	156	6	(	(	PUNCT
ejpam-6270	156	7	αf	αf	NOUN
ejpam-6270	156	8	)	)	PUNCT
ejpam-6270	156	9	c	c	NOUN
ejpam-6270	157	1	=	=	SYM
ejpam-6270	157	2	α	α	PROPN
ejpam-6270	157	3	(	(	PUNCT
ejpam-6270	157	4	f	f	NOUN
ejpam-6270	157	5	c	c	NOUN
ejpam-6270	157	6	)	)	PUNCT
ejpam-6270	157	7	for	for	ADP
ejpam-6270	157	8	each	each	DET
ejpam-6270	157	9	α	α	NOUN
ejpam-6270	157	10	∈	∈	PROPN
ejpam-6270	157	11	w	w	NOUN
ejpam-6270	157	12	,	,	PUNCT
ejpam-6270	157	13	if	if	SCONJ
ejpam-6270	157	14	f	f	PROPN
ejpam-6270	157	15	⊆	⊆	NUM
ejpam-6270	157	16	w.	w.	NOUN
ejpam-6270	157	17	proof	proof	NOUN
ejpam-6270	157	18	.	.	PUNCT
ejpam-6270	158	1	these	these	DET
ejpam-6270	158	2	results	result	NOUN
ejpam-6270	158	3	follow	follow	VERB
ejpam-6270	158	4	from	from	ADP
ejpam-6270	158	5	definition	definition	NOUN
ejpam-6270	158	6	15	15	NUM
ejpam-6270	158	7	.	.	PUNCT
ejpam-6270	159	1	proposition	proposition	NOUN
ejpam-6270	159	2	5	5	NUM
ejpam-6270	159	3	.	.	PUNCT
ejpam-6270	160	1	let	let	VERB
ejpam-6270	160	2	w	w	NOUN
ejpam-6270	160	3	be	be	AUX
ejpam-6270	160	4	a	a	DET
ejpam-6270	160	5	tbd	tbd	NOUN
ejpam-6270	160	6	-	-	PUNCT
ejpam-6270	160	7	algebra	algebra	NOUN
ejpam-6270	160	8	and	and	CCONJ
ejpam-6270	160	9	α	α	PRON
ejpam-6270	160	10	∈	∈	PROPN
ejpam-6270	160	11	w	w	NOUN
ejpam-6270	160	12	and	and	CCONJ
ejpam-6270	160	13	u	u	NOUN
ejpam-6270	160	14	be	be	VERB
ejpam-6270	160	15	any	any	DET
ejpam-6270	160	16	nonempty	nonempty	NOUN
ejpam-6270	160	17	subset	subset	NOUN
ejpam-6270	160	18	of	of	ADP
ejpam-6270	160	19	w	w	PROPN
ejpam-6270	160	20	,	,	PUNCT
ejpam-6270	160	21	,	,	PUNCT
ejpam-6270	160	22	then	then	ADV
ejpam-6270	160	23	the	the	DET
ejpam-6270	160	24	statements	statement	NOUN
ejpam-6270	160	25	listed	list	VERB
ejpam-6270	160	26	below	below	ADV
ejpam-6270	160	27	are	be	AUX
ejpam-6270	160	28	accurate	accurate	ADJ
ejpam-6270	160	29	:	:	PUNCT
ejpam-6270	160	30	(	(	PUNCT
ejpam-6270	160	31	i	i	NOUN
ejpam-6270	160	32	)	)	PUNCT
ejpam-6270	160	33	uα	uα	PROPN
ejpam-6270	160	34	and	and	CCONJ
ejpam-6270	160	35	αu	αu	PROPN
ejpam-6270	160	36	are	be	AUX
ejpam-6270	160	37	b	b	ADJ
ejpam-6270	160	38	-	-	PUNCT
ejpam-6270	160	39	open	open	ADJ
ejpam-6270	160	40	sets	set	NOUN
ejpam-6270	160	41	,	,	PUNCT
ejpam-6270	160	42	if	if	SCONJ
ejpam-6270	160	43	u	u	NOUN
ejpam-6270	160	44	is	be	AUX
ejpam-6270	160	45	an	an	DET
ejpam-6270	160	46	open	open	ADJ
ejpam-6270	160	47	set	set	NOUN
ejpam-6270	160	48	.	.	PUNCT
ejpam-6270	161	1	(	(	PUNCT
ejpam-6270	161	2	ii	ii	NOUN
ejpam-6270	161	3	)	)	PUNCT
ejpam-6270	161	4	fα	fα	NOUN
ejpam-6270	161	5	and	and	CCONJ
ejpam-6270	161	6	αf	αf	VERB
ejpam-6270	161	7	are	be	AUX
ejpam-6270	161	8	b	b	NOUN
ejpam-6270	161	9	-	-	PUNCT
ejpam-6270	161	10	closed	closed	ADJ
ejpam-6270	161	11	sets	set	NOUN
ejpam-6270	161	12	,	,	PUNCT
ejpam-6270	161	13	if	if	SCONJ
ejpam-6270	161	14	f	f	PROPN
ejpam-6270	161	15	is	be	AUX
ejpam-6270	161	16	closed	close	VERB
ejpam-6270	161	17	set	set	VERB
ejpam-6270	161	18	.	.	PUNCT
ejpam-6270	162	1	(	(	PUNCT
ejpam-6270	162	2	iii	iii	X
ejpam-6270	162	3	)	)	PUNCT
ejpam-6270	162	4	if	if	SCONJ
ejpam-6270	162	5	u	u	NOUN
ejpam-6270	162	6	is	be	AUX
ejpam-6270	162	7	open	open	ADJ
ejpam-6270	162	8	,	,	PUNCT
ejpam-6270	162	9	then	then	ADV
ejpam-6270	162	10	ku	ku	PROPN
ejpam-6270	162	11	and	and	CCONJ
ejpam-6270	162	12	uk	uk	PROPN
ejpam-6270	162	13	are	be	AUX
ejpam-6270	162	14	b	b	ADJ
ejpam-6270	162	15	-	-	PUNCT
ejpam-6270	162	16	open	open	ADJ
ejpam-6270	162	17	sets	set	NOUN
ejpam-6270	162	18	for	for	ADP
ejpam-6270	162	19	every	every	DET
ejpam-6270	162	20	subset	subset	NOUN
ejpam-6270	162	21	k	k	PROPN
ejpam-6270	162	22	of	of	ADP
ejpam-6270	162	23	w.	w.	PROPN
ejpam-6270	162	24	proof	proof	NOUN
ejpam-6270	162	25	.	.	PUNCT
ejpam-6270	163	1	(	(	PUNCT
ejpam-6270	163	2	i	i	NOUN
ejpam-6270	163	3	)	)	PUNCT
ejpam-6270	163	4	let	let	VERB
ejpam-6270	163	5	ζ	ζ	NOUN
ejpam-6270	163	6	∈	∈	PROPN
ejpam-6270	163	7	uα	uα	NOUN
ejpam-6270	163	8	,	,	PUNCT
ejpam-6270	163	9	so	so	ADV
ejpam-6270	163	10	ζ	ζ	NOUN
ejpam-6270	163	11	⊙	⊙	NOUN
ejpam-6270	163	12	α	α	PROPN
ejpam-6270	163	13	∈	∈	PROPN
ejpam-6270	163	14	u	u	PROPN
ejpam-6270	163	15	.	.	PUNCT
ejpam-6270	164	1	since	since	SCONJ
ejpam-6270	164	2	w	w	PROPN
ejpam-6270	164	3	is	be	AUX
ejpam-6270	164	4	tbd	tbd	NOUN
ejpam-6270	164	5	-	-	PUNCT
ejpam-6270	164	6	algebra	algebra	NOUN
ejpam-6270	164	7	and	and	CCONJ
ejpam-6270	164	8	u	u	NOUN
ejpam-6270	164	9	is	be	AUX
ejpam-6270	164	10	open	open	ADJ
ejpam-6270	164	11	,	,	PUNCT
ejpam-6270	164	12	so	so	SCONJ
ejpam-6270	164	13	there	there	PRON
ejpam-6270	164	14	exists	exist	VERB
ejpam-6270	164	15	a	a	DET
ejpam-6270	164	16	b	b	NOUN
ejpam-6270	164	17	-	-	PUNCT
ejpam-6270	164	18	open	open	ADJ
ejpam-6270	164	19	set	set	NOUN
ejpam-6270	164	20	g	g	NOUN
ejpam-6270	164	21	having	have	VERB
ejpam-6270	164	22	ζ	ζ	NOUN
ejpam-6270	164	23	such	such	ADJ
ejpam-6270	164	24	that	that	SCONJ
ejpam-6270	164	25	g	g	PROPN
ejpam-6270	164	26	⊙	⊙	PROPN
ejpam-6270	164	27	α	α	PROPN
ejpam-6270	164	28	⊆	⊆	NUM
ejpam-6270	164	29	u	u	NOUN
ejpam-6270	164	30	,	,	PUNCT
ejpam-6270	164	31	ζ	ζ	PROPN
ejpam-6270	164	32	⊙	⊙	NOUN
ejpam-6270	164	33	α	α	PROPN
ejpam-6270	164	34	∈	∈	PROPN
ejpam-6270	165	1	g	g	PROPN
ejpam-6270	165	2	⊙	⊙	PROPN
ejpam-6270	165	3	α	α	PROPN
ejpam-6270	165	4	⊆	⊆	NUM
ejpam-6270	165	5	u	u	NOUN
ejpam-6270	165	6	.	.	PUNCT
ejpam-6270	166	1	therefore	therefore	ADV
ejpam-6270	166	2	,	,	PUNCT
ejpam-6270	166	3	for	for	ADP
ejpam-6270	166	4	every	every	DET
ejpam-6270	166	5	θ	θ	PROPN
ejpam-6270	166	6	∈	∈	PROPN
ejpam-6270	166	7	g	g	PROPN
ejpam-6270	166	8	,	,	PUNCT
ejpam-6270	166	9	we	we	PRON
ejpam-6270	166	10	have	have	VERB
ejpam-6270	166	11	θ	θ	PROPN
ejpam-6270	166	12	⊙	⊙	PROPN
ejpam-6270	167	1	α	α	PROPN
ejpam-6270	167	2	⊆	⊆	NUM
ejpam-6270	167	3	u	u	NOUN
ejpam-6270	167	4	implies	imply	VERB
ejpam-6270	167	5	that	that	SCONJ
ejpam-6270	167	6	θ	θ	PROPN
ejpam-6270	167	7	∈	∈	PROPN
ejpam-6270	167	8	uα	uα	PROPN
ejpam-6270	167	9	.	.	PUNCT
ejpam-6270	168	1	hence	hence	ADV
ejpam-6270	168	2	,	,	PUNCT
ejpam-6270	168	3	g	g	PROPN
ejpam-6270	168	4	⊆	⊆	NUM
ejpam-6270	168	5	uα	uα	PROPN
ejpam-6270	168	6	implies	imply	VERB
ejpam-6270	168	7	that	that	SCONJ
ejpam-6270	168	8	uα	uα	PROPN
ejpam-6270	168	9	is	be	AUX
ejpam-6270	168	10	b	b	NOUN
ejpam-6270	168	11	-	-	ADV
ejpam-6270	168	12	open	open	ADJ
ejpam-6270	168	13	.	.	PUNCT
ejpam-6270	169	1	to	to	PART
ejpam-6270	169	2	show	show	VERB
ejpam-6270	169	3	that	that	SCONJ
ejpam-6270	169	4	αu	αu	PROPN
ejpam-6270	169	5	is	be	AUX
ejpam-6270	169	6	b	b	NOUN
ejpam-6270	169	7	-	-	ADJ
ejpam-6270	169	8	open	open	ADJ
ejpam-6270	169	9	,	,	PUNCT
ejpam-6270	169	10	let	let	VERB
ejpam-6270	169	11	ζ	ζ	PRON
ejpam-6270	169	12	∈	∈	NOUN
ejpam-6270	169	13	αu	αu	NOUN
ejpam-6270	169	14	implies	imply	VERB
ejpam-6270	169	15	that	that	SCONJ
ejpam-6270	169	16	α	α	PROPN
ejpam-6270	169	17	⊙	⊙	VERB
ejpam-6270	169	18	ζ	ζ	PROPN
ejpam-6270	169	19	∈	∈	PROPN
ejpam-6270	169	20	u	u	PROPN
ejpam-6270	169	21	.	.	PUNCT
ejpam-6270	170	1	since	since	SCONJ
ejpam-6270	170	2	w	w	PROPN
ejpam-6270	170	3	is	be	AUX
ejpam-6270	170	4	tbdalgebra	tbdalgebra	NOUN
ejpam-6270	170	5	,	,	PUNCT
ejpam-6270	170	6	then	then	ADV
ejpam-6270	170	7	there	there	PRON
ejpam-6270	170	8	exists	exist	VERB
ejpam-6270	170	9	a	a	DET
ejpam-6270	170	10	b	b	NOUN
ejpam-6270	170	11	-	-	PUNCT
ejpam-6270	170	12	open	open	ADJ
ejpam-6270	170	13	set	set	ADJ
ejpam-6270	170	14	h	h	NOUN
ejpam-6270	170	15	that	that	PRON
ejpam-6270	170	16	has	have	VERB
ejpam-6270	170	17	ζ	ζ	NOUN
ejpam-6270	170	18	such	such	ADJ
ejpam-6270	170	19	that	that	SCONJ
ejpam-6270	170	20	α	α	PROPN
ejpam-6270	170	21	⊙	⊙	PROPN
ejpam-6270	170	22	h	h	PROPN
ejpam-6270	171	1	⊆	⊆	NUM
ejpam-6270	171	2	u	u	NOUN
ejpam-6270	171	3	,	,	PUNCT
ejpam-6270	171	4	so	so	ADV
ejpam-6270	171	5	for	for	ADP
ejpam-6270	171	6	each	each	DET
ejpam-6270	171	7	θ	θ	PROPN
ejpam-6270	171	8	∈	∈	PROPN
ejpam-6270	171	9	h	h	NOUN
ejpam-6270	171	10	,	,	PUNCT
ejpam-6270	171	11	we	we	PRON
ejpam-6270	171	12	have	have	VERB
ejpam-6270	171	13	α⊙	α⊙	NOUN
ejpam-6270	171	14	θ	θ	PROPN
ejpam-6270	171	15	∈	∈	PROPN
ejpam-6270	171	16	u	u	NOUN
ejpam-6270	171	17	.	.	PUNCT
ejpam-6270	172	1	hence	hence	ADV
ejpam-6270	172	2	,	,	PUNCT
ejpam-6270	172	3	θ	θ	PROPN
ejpam-6270	172	4	∈	∈	PROPN
ejpam-6270	172	5	h	h	NOUN
ejpam-6270	172	6	⊆	⊆	NUM
ejpam-6270	172	7	αu	αu	NOUN
ejpam-6270	172	8	.	.	PUNCT
ejpam-6270	173	1	therefore	therefore	ADV
ejpam-6270	173	2	,	,	PUNCT
ejpam-6270	173	3	αu	αu	PROPN
ejpam-6270	173	4	is	be	AUX
ejpam-6270	173	5	a	a	DET
ejpam-6270	173	6	b	b	NOUN
ejpam-6270	173	7	-	-	PUNCT
ejpam-6270	173	8	open	open	ADJ
ejpam-6270	173	9	set	set	NOUN
ejpam-6270	173	10	.	.	PUNCT
ejpam-6270	174	1	(	(	PUNCT
ejpam-6270	174	2	ii	ii	NOUN
ejpam-6270	174	3	)	)	PUNCT
ejpam-6270	174	4	assuming	assume	VERB
ejpam-6270	174	5	f	f	PRON
ejpam-6270	174	6	be	be	AUX
ejpam-6270	174	7	a	a	DET
ejpam-6270	174	8	closed	closed	ADJ
ejpam-6270	174	9	set	set	NOUN
ejpam-6270	174	10	,	,	PUNCT
ejpam-6270	174	11	then	then	ADV
ejpam-6270	174	12	f	f	PROPN
ejpam-6270	174	13	c	c	PROPN
ejpam-6270	174	14	is	be	AUX
ejpam-6270	174	15	open	open	ADJ
ejpam-6270	174	16	.	.	PUNCT
ejpam-6270	175	1	hence	hence	ADV
ejpam-6270	175	2	,	,	PUNCT
ejpam-6270	175	3	according	accord	VERB
ejpam-6270	175	4	(	(	PUNCT
ejpam-6270	175	5	1	1	NUM
ejpam-6270	175	6	)	)	PUNCT
ejpam-6270	175	7	,	,	PUNCT
ejpam-6270	175	8	(	(	PUNCT
ejpam-6270	175	9	f	f	PROPN
ejpam-6270	175	10	c)α	c)α	NOUN
ejpam-6270	175	11	and	and	CCONJ
ejpam-6270	175	12	α(f	α(f	PROPN
ejpam-6270	175	13	c	c	X
ejpam-6270	175	14	)	)	PUNCT
ejpam-6270	175	15	are	be	AUX
ejpam-6270	175	16	b	b	NOUN
ejpam-6270	175	17	-	-	ADJ
ejpam-6270	175	18	open	open	ADJ
ejpam-6270	175	19	.	.	PUNCT
ejpam-6270	176	1	using	use	VERB
ejpam-6270	176	2	proposition	proposition	NOUN
ejpam-6270	176	3	4	4	NUM
ejpam-6270	176	4	,	,	PUNCT
ejpam-6270	176	5	(	(	PUNCT
ejpam-6270	176	6	fα	fα	NOUN
ejpam-6270	176	7	)	)	PUNCT
ejpam-6270	176	8	c	c	NOUN
ejpam-6270	177	1	=	=	SYM
ejpam-6270	177	2	(	(	PUNCT
ejpam-6270	177	3	f	f	PROPN
ejpam-6270	177	4	c)α	c)α	NOUN
ejpam-6270	177	5	and	and	CCONJ
ejpam-6270	177	6	(	(	PUNCT
ejpam-6270	177	7	αf	αf	NOUN
ejpam-6270	177	8	)	)	PUNCT
ejpam-6270	177	9	c	c	NOUN
ejpam-6270	178	1	=	=	SYM
ejpam-6270	178	2	α	α	PROPN
ejpam-6270	178	3	(	(	PUNCT
ejpam-6270	178	4	f	f	NOUN
ejpam-6270	178	5	c	c	NOUN
ejpam-6270	178	6	)	)	PUNCT
ejpam-6270	178	7	.	.	PUNCT
ejpam-6270	179	1	hence	hence	ADV
ejpam-6270	179	2	,	,	PUNCT
ejpam-6270	179	3	(	(	PUNCT
ejpam-6270	179	4	fα	fα	NOUN
ejpam-6270	179	5	)	)	PUNCT
ejpam-6270	179	6	c	c	NOUN
ejpam-6270	179	7	and	and	CCONJ
ejpam-6270	179	8	(	(	PUNCT
ejpam-6270	179	9	αf	αf	NOUN
ejpam-6270	179	10	)	)	PUNCT
ejpam-6270	179	11	c	c	NOUN
ejpam-6270	179	12	are	be	AUX
ejpam-6270	179	13	b	b	NOUN
ejpam-6270	179	14	-	-	ADJ
ejpam-6270	179	15	open	open	ADJ
ejpam-6270	179	16	.	.	PUNCT
ejpam-6270	180	1	consequently	consequently	ADV
ejpam-6270	180	2	,	,	PUNCT
ejpam-6270	180	3	fα	fα	ADP
ejpam-6270	180	4	and	and	CCONJ
ejpam-6270	180	5	αf	αf	VERB
ejpam-6270	180	6	are	be	AUX
ejpam-6270	180	7	b	b	NOUN
ejpam-6270	180	8	-	-	PUNCT
ejpam-6270	180	9	closed	closed	ADJ
ejpam-6270	180	10	.	.	PUNCT
ejpam-6270	181	1	(	(	PUNCT
ejpam-6270	181	2	iii	iii	NOUN
ejpam-6270	181	3	)	)	PUNCT
ejpam-6270	181	4	follows	follow	VERB
ejpam-6270	181	5	from	from	ADP
ejpam-6270	181	6	(	(	PUNCT
ejpam-6270	181	7	i	i	NOUN
ejpam-6270	181	8	)	)	PUNCT
ejpam-6270	181	9	and	and	CCONJ
ejpam-6270	181	10	the	the	DET
ejpam-6270	181	11	fact	fact	NOUN
ejpam-6270	181	12	that	that	SCONJ
ejpam-6270	181	13	arbitrary	arbitrary	ADJ
ejpam-6270	181	14	union	union	NOUN
ejpam-6270	181	15	of	of	ADP
ejpam-6270	181	16	b	b	NOUN
ejpam-6270	181	17	-	-	PUNCT
ejpam-6270	181	18	open	open	ADJ
ejpam-6270	181	19	sets	set	NOUN
ejpam-6270	181	20	is	be	AUX
ejpam-6270	181	21	b	b	NOUN
ejpam-6270	181	22	-	-	ADV
ejpam-6270	181	23	open	open	ADJ
ejpam-6270	181	24	.	.	PUNCT
ejpam-6270	182	1	m.	m.	NOUN
ejpam-6270	182	2	w.	w.	PROPN
ejpam-6270	182	3	abdulqader	abdulqader	PROPN
ejpam-6270	182	4	,	,	PUNCT
ejpam-6270	182	5	a.	a.	PROPN
ejpam-6270	182	6	b.	b.	PROPN
ejpam-6270	182	7	khalaf	khalaf	PROPN
ejpam-6270	182	8	/	/	SYM
ejpam-6270	182	9	eur	eur	PROPN
ejpam-6270	182	10	.	.	PUNCT
ejpam-6270	183	1	j.	j.	PROPN
ejpam-6270	183	2	pure	pure	PROPN
ejpam-6270	183	3	appl	appl	PROPN
ejpam-6270	183	4	.	.	PROPN
ejpam-6270	183	5	math	math	PROPN
ejpam-6270	183	6	,	,	PUNCT
ejpam-6270	183	7	18	18	NUM
ejpam-6270	183	8	(	(	PUNCT
ejpam-6270	183	9	3	3	NUM
ejpam-6270	183	10	)	)	PUNCT
ejpam-6270	183	11	(	(	PUNCT
ejpam-6270	183	12	2025	2025	NUM
ejpam-6270	183	13	)	)	PUNCT
ejpam-6270	183	14	,	,	PUNCT
ejpam-6270	183	15	6270	6270	NUM
ejpam-6270	183	16	8	8	NUM
ejpam-6270	183	17	of	of	ADP
ejpam-6270	183	18	17	17	NUM
ejpam-6270	183	19	corollary	corollary	ADJ
ejpam-6270	183	20	2	2	NUM
ejpam-6270	183	21	.	.	PUNCT
ejpam-6270	184	1	let	let	VERB
ejpam-6270	184	2	w	w	NOUN
ejpam-6270	184	3	be	be	AUX
ejpam-6270	184	4	tbd	tbd	NOUN
ejpam-6270	184	5	–	–	PUNCT
ejpam-6270	184	6	algebra	algebra	NOUN
ejpam-6270	184	7	,	,	PUNCT
ejpam-6270	184	8	u	u	NOUN
ejpam-6270	184	9	and	and	CCONJ
ejpam-6270	184	10	m	m	VERB
ejpam-6270	184	11	be	be	VERB
ejpam-6270	184	12	two	two	NUM
ejpam-6270	184	13	non	non	ADJ
ejpam-6270	184	14	–	–	ADJ
ejpam-6270	184	15	empty	empty	ADJ
ejpam-6270	184	16	subset	subset	NOUN
ejpam-6270	184	17	of	of	ADP
ejpam-6270	184	18	w	w	PROPN
ejpam-6270	184	19	,	,	PUNCT
ejpam-6270	184	20	then	then	ADV
ejpam-6270	184	21	the	the	DET
ejpam-6270	184	22	statements	statement	NOUN
ejpam-6270	184	23	listed	list	VERB
ejpam-6270	184	24	below	below	ADV
ejpam-6270	184	25	are	be	AUX
ejpam-6270	184	26	accurate	accurate	ADJ
ejpam-6270	184	27	:	:	PUNCT
ejpam-6270	184	28	i	i	X
ejpam-6270	184	29	)	)	PUNCT
ejpam-6270	184	30	the	the	PRON
ejpam-6270	184	31	sets	set	VERB
ejpam-6270	184	32	mu	mu	NOUN
ejpam-6270	184	33	and	and	CCONJ
ejpam-6270	184	34	um	um	INTJ
ejpam-6270	184	35	are	be	AUX
ejpam-6270	184	36	b	b	ADJ
ejpam-6270	184	37	-	-	PUNCT
ejpam-6270	184	38	open	open	ADJ
ejpam-6270	184	39	sets	set	NOUN
ejpam-6270	184	40	if	if	SCONJ
ejpam-6270	184	41	u	u	NOUN
ejpam-6270	184	42	is	be	AUX
ejpam-6270	184	43	open	open	ADJ
ejpam-6270	184	44	.	.	PUNCT
ejpam-6270	185	1	ii)the	ii)the	PRON
ejpam-6270	185	2	sets	set	VERB
ejpam-6270	185	3	mu	mu	NOUN
ejpam-6270	185	4	and	and	CCONJ
ejpam-6270	185	5	um	um	INTJ
ejpam-6270	185	6	are	be	AUX
ejpam-6270	185	7	closed	close	VERB
ejpam-6270	185	8	sets	set	NOUN
ejpam-6270	185	9	if	if	SCONJ
ejpam-6270	185	10	u	u	NOUN
ejpam-6270	185	11	is	be	AUX
ejpam-6270	185	12	closed	close	VERB
ejpam-6270	185	13	set	set	VERB
ejpam-6270	185	14	and	and	CCONJ
ejpam-6270	185	15	m	m	NOUN
ejpam-6270	185	16	is	be	AUX
ejpam-6270	185	17	finite	finite	ADJ
ejpam-6270	185	18	.	.	PUNCT
ejpam-6270	185	19	example	example	NOUN
ejpam-6270	186	1	2	2	NUM
ejpam-6270	186	2	.	.	X
ejpam-6270	186	3	in	in	ADP
ejpam-6270	186	4	example	example	NOUN
ejpam-6270	186	5	1	1	NUM
ejpam-6270	186	6	,	,	PUNCT
ejpam-6270	186	7	we	we	PRON
ejpam-6270	186	8	have	have	VERB
ejpam-6270	186	9	u	u	NOUN
ejpam-6270	186	10	=	=	NOUN
ejpam-6270	186	11	{	{	PUNCT
ejpam-6270	186	12	α	α	PROPN
ejpam-6270	186	13	,	,	PUNCT
ejpam-6270	186	14	γ	γ	NOUN
ejpam-6270	186	15	}	}	PUNCT
ejpam-6270	186	16	∈	∈	PROPN
ejpam-6270	186	17	ω	ω	NOUN
ejpam-6270	186	18	and	and	CCONJ
ejpam-6270	186	19	by	by	ADP
ejpam-6270	186	20	simple	simple	ADJ
ejpam-6270	186	21	calculation	calculation	NOUN
ejpam-6270	186	22	we	we	PRON
ejpam-6270	186	23	can	can	AUX
ejpam-6270	186	24	see	see	VERB
ejpam-6270	186	25	that	that	DET
ejpam-6270	186	26	mu	mu	PROPN
ejpam-6270	186	27	and	and	CCONJ
ejpam-6270	186	28	um	um	INTJ
ejpam-6270	186	29	are	be	AUX
ejpam-6270	186	30	b	b	ADJ
ejpam-6270	186	31	-	-	PUNCT
ejpam-6270	186	32	open	open	ADJ
ejpam-6270	186	33	sets	set	NOUN
ejpam-6270	186	34	for	for	ADP
ejpam-6270	186	35	any	any	DET
ejpam-6270	186	36	subset	subset	NOUN
ejpam-6270	186	37	m	m	NOUN
ejpam-6270	186	38	of	of	ADP
ejpam-6270	186	39	w.	w.	PROPN
ejpam-6270	186	40	proposition	proposition	PROPN
ejpam-6270	186	41	6	6	NUM
ejpam-6270	186	42	.	.	PUNCT
ejpam-6270	187	1	let	let	VERB
ejpam-6270	187	2	w	w	NOUN
ejpam-6270	187	3	be	be	AUX
ejpam-6270	187	4	tbd	tbd	NOUN
ejpam-6270	187	5	–	–	PUNCT
ejpam-6270	187	6	algebra	algebra	NOUN
ejpam-6270	187	7	and	and	CCONJ
ejpam-6270	187	8	w	w	NOUN
ejpam-6270	187	9	be	be	AUX
ejpam-6270	187	10	t2	t2	PROPN
ejpam-6270	187	11	b	b	X
ejpam-6270	187	12	-	-	ADJ
ejpam-6270	187	13	compact	compact	ADJ
ejpam-6270	187	14	space	space	NOUN
ejpam-6270	187	15	.	.	PUNCT
ejpam-6270	188	1	if	if	SCONJ
ejpam-6270	188	2	s	s	NOUN
ejpam-6270	188	3	is	be	AUX
ejpam-6270	188	4	a	a	DET
ejpam-6270	188	5	compact	compact	ADJ
ejpam-6270	188	6	subset	subset	NOUN
ejpam-6270	188	7	of	of	ADP
ejpam-6270	188	8	w	w	PROPN
ejpam-6270	188	9	,	,	PUNCT
ejpam-6270	188	10	then	then	ADV
ejpam-6270	188	11	sα	sα	ADV
ejpam-6270	188	12	and	and	CCONJ
ejpam-6270	188	13	αs	αs	INTJ
ejpam-6270	188	14	are	be	AUX
ejpam-6270	188	15	b	b	ADJ
ejpam-6270	188	16	-	-	ADJ
ejpam-6270	188	17	compact	compact	ADJ
ejpam-6270	188	18	sets	set	NOUN
ejpam-6270	188	19	for	for	ADP
ejpam-6270	188	20	all	all	DET
ejpam-6270	188	21	α	α	PRON
ejpam-6270	188	22	∈	∈	PROPN
ejpam-6270	188	23	w.	w.	NOUN
ejpam-6270	188	24	proof	proof	NOUN
ejpam-6270	188	25	.	.	PUNCT
ejpam-6270	189	1	let	let	VERB
ejpam-6270	189	2	s	s	PRON
ejpam-6270	189	3	be	be	AUX
ejpam-6270	189	4	a	a	DET
ejpam-6270	189	5	compact	compact	ADJ
ejpam-6270	189	6	subset	subset	NOUN
ejpam-6270	189	7	of	of	ADP
ejpam-6270	189	8	w.	w.	PROPN
ejpam-6270	189	9	since	since	SCONJ
ejpam-6270	189	10	w	w	PROPN
ejpam-6270	189	11	is	be	AUX
ejpam-6270	189	12	t2	t2	NOUN
ejpam-6270	189	13	,	,	PUNCT
ejpam-6270	189	14	then	then	ADV
ejpam-6270	189	15	s	s	VERB
ejpam-6270	189	16	is	be	AUX
ejpam-6270	189	17	closed	close	VERB
ejpam-6270	189	18	set	set	VERB
ejpam-6270	189	19	in	in	ADP
ejpam-6270	189	20	w.	w.	NOUN
ejpam-6270	189	21	thus	thus	ADV
ejpam-6270	189	22	by	by	ADP
ejpam-6270	189	23	proposition	proposition	NOUN
ejpam-6270	189	24	5	5	NUM
ejpam-6270	189	25	sα	sα	ADV
ejpam-6270	189	26	and	and	CCONJ
ejpam-6270	189	27	αs	αs	INTJ
ejpam-6270	189	28	are	be	AUX
ejpam-6270	189	29	b	b	NOUN
ejpam-6270	189	30	-	-	PUNCT
ejpam-6270	189	31	closed	closed	ADJ
ejpam-6270	189	32	sets	set	NOUN
ejpam-6270	189	33	in	in	ADP
ejpam-6270	189	34	w	w	NOUN
ejpam-6270	189	35	for	for	ADP
ejpam-6270	189	36	all	all	DET
ejpam-6270	189	37	ζ	ζ	PROPN
ejpam-6270	189	38	∈	∈	PROPN
ejpam-6270	189	39	w.	w.	NOUN
ejpam-6270	189	40	then	then	ADV
ejpam-6270	189	41	,	,	PUNCT
ejpam-6270	189	42	by	by	ADP
ejpam-6270	189	43	lemma	lemma	PROPN
ejpam-6270	189	44	5	5	NUM
ejpam-6270	189	45	,	,	PUNCT
ejpam-6270	189	46	sα	sα	ADJ
ejpam-6270	189	47	and	and	CCONJ
ejpam-6270	189	48	αs	αs	INTJ
ejpam-6270	189	49	are	be	AUX
ejpam-6270	189	50	b	b	ADJ
ejpam-6270	189	51	-	-	ADJ
ejpam-6270	189	52	compact	compact	ADJ
ejpam-6270	189	53	sets	set	NOUN
ejpam-6270	189	54	in	in	ADP
ejpam-6270	189	55	w	w	NOUN
ejpam-6270	189	56	for	for	ADP
ejpam-6270	189	57	all	all	DET
ejpam-6270	189	58	ζ	ζ	PROPN
ejpam-6270	189	59	∈	∈	PROPN
ejpam-6270	189	60	w.	w.	NOUN
ejpam-6270	189	61	in	in	ADP
ejpam-6270	189	62	the	the	DET
ejpam-6270	189	63	following	follow	VERB
ejpam-6270	189	64	example	example	NOUN
ejpam-6270	189	65	,	,	PUNCT
ejpam-6270	189	66	we	we	PRON
ejpam-6270	189	67	see	see	VERB
ejpam-6270	189	68	that	that	SCONJ
ejpam-6270	189	69	sα	sα	ADV
ejpam-6270	189	70	and	and	CCONJ
ejpam-6270	189	71	αs	αs	INTJ
ejpam-6270	189	72	are	be	AUX
ejpam-6270	189	73	b	b	ADJ
ejpam-6270	189	74	-	-	ADJ
ejpam-6270	189	75	compact	compact	ADJ
ejpam-6270	189	76	sets	set	NOUN
ejpam-6270	189	77	while	while	SCONJ
ejpam-6270	189	78	s	s	NOUN
ejpam-6270	189	79	is	be	AUX
ejpam-6270	189	80	no	no	DET
ejpam-6270	189	81	compact	compact	ADJ
ejpam-6270	189	82	.	.	PUNCT
ejpam-6270	190	1	example	example	NOUN
ejpam-6270	191	1	3	3	X
ejpam-6270	191	2	.	.	X
ejpam-6270	191	3	consider	consider	VERB
ejpam-6270	191	4	the	the	DET
ejpam-6270	191	5	set	set	NOUN
ejpam-6270	191	6	of	of	ADP
ejpam-6270	191	7	real	real	ADJ
ejpam-6270	191	8	numbers	number	NOUN
ejpam-6270	191	9	r	r	NOUN
ejpam-6270	191	10	and	and	CCONJ
ejpam-6270	191	11	an	an	DET
ejpam-6270	191	12	operation	operation	NOUN
ejpam-6270	191	13	⊙	⊙	NOUN
ejpam-6270	191	14	defined	define	VERB
ejpam-6270	191	15	as	as	ADP
ejpam-6270	191	16	:	:	PUNCT
ejpam-6270	191	17	x⊙	x⊙	PROPN
ejpam-6270	191	18	y=	y=	PROPN
ejpam-6270	191	19	{	{	PUNCT
ejpam-6270	191	20	0	0	NUM
ejpam-6270	191	21	if	if	SCONJ
ejpam-6270	191	22	x	x	PROPN
ejpam-6270	191	23	≤	≤	NUM
ejpam-6270	191	24	y	y	NOUN
ejpam-6270	191	25	1	1	NUM
ejpam-6270	191	26	otherwise	otherwise	ADV
ejpam-6270	191	27	.	.	PUNCT
ejpam-6270	192	1	then	then	ADV
ejpam-6270	192	2	,	,	PUNCT
ejpam-6270	192	3	(	(	PUNCT
ejpam-6270	192	4	r,⊙	r,⊙	PROPN
ejpam-6270	192	5	,	,	PUNCT
ejpam-6270	192	6	τ	τ	X
ejpam-6270	192	7	)	)	PUNCT
ejpam-6270	192	8	is	be	AUX
ejpam-6270	192	9	a	a	DET
ejpam-6270	192	10	tbd	tbd	PROPN
ejpam-6270	192	11	–	–	PUNCT
ejpam-6270	192	12	algebra	algebra	NOUN
ejpam-6270	192	13	t2	t2	NOUN
ejpam-6270	192	14	-	-	PUNCT
ejpam-6270	192	15	space	space	NOUN
ejpam-6270	192	16	where	where	SCONJ
ejpam-6270	192	17	τ	τ	PROPN
ejpam-6270	192	18	is	be	AUX
ejpam-6270	192	19	the	the	DET
ejpam-6270	192	20	discrete	discrete	ADJ
ejpam-6270	192	21	topology	topology	NOUN
ejpam-6270	192	22	.	.	PUNCT
ejpam-6270	193	1	suppose	suppose	VERB
ejpam-6270	193	2	that	that	SCONJ
ejpam-6270	193	3	s	s	VERB
ejpam-6270	193	4	=	=	X
ejpam-6270	193	5	(	(	PUNCT
ejpam-6270	193	6	1	1	NUM
ejpam-6270	193	7	,	,	PUNCT
ejpam-6270	193	8	5	5	NUM
ejpam-6270	193	9	)	)	PUNCT
ejpam-6270	193	10	,	,	PUNCT
ejpam-6270	193	11	then	then	ADV
ejpam-6270	193	12	obviously	obviously	ADV
ejpam-6270	193	13	,	,	PUNCT
ejpam-6270	193	14	s	s	VERB
ejpam-6270	193	15	is	be	AUX
ejpam-6270	193	16	not	not	PART
ejpam-6270	193	17	compact	compact	ADJ
ejpam-6270	193	18	,	,	PUNCT
ejpam-6270	193	19	but	but	CCONJ
ejpam-6270	193	20	we	we	PRON
ejpam-6270	193	21	have	have	AUX
ejpam-6270	193	22	sα	sα	ADV
ejpam-6270	193	23	and	and	CCONJ
ejpam-6270	193	24	αs	αs	INTJ
ejpam-6270	193	25	are	be	AUX
ejpam-6270	193	26	empty	empty	ADJ
ejpam-6270	193	27	sets	set	NOUN
ejpam-6270	193	28	for	for	ADP
ejpam-6270	193	29	every	every	DET
ejpam-6270	193	30	α	α	NOUN
ejpam-6270	193	31	∈	∈	NOUN
ejpam-6270	193	32	r	r	NOUN
ejpam-6270	193	33	and	and	CCONJ
ejpam-6270	193	34	hence	hence	ADV
ejpam-6270	193	35	they	they	PRON
ejpam-6270	193	36	are	be	AUX
ejpam-6270	193	37	b	b	ADJ
ejpam-6270	193	38	-	-	ADJ
ejpam-6270	193	39	compact	compact	ADJ
ejpam-6270	193	40	.	.	PUNCT
ejpam-6270	194	1	proposition	proposition	NOUN
ejpam-6270	194	2	7	7	NUM
ejpam-6270	194	3	.	.	PUNCT
ejpam-6270	195	1	if	if	SCONJ
ejpam-6270	195	2	{	{	PUNCT
ejpam-6270	195	3	0	0	X
ejpam-6270	195	4	}	}	PUNCT
ejpam-6270	195	5	is	be	AUX
ejpam-6270	195	6	open	open	ADJ
ejpam-6270	195	7	in	in	ADP
ejpam-6270	195	8	a	a	DET
ejpam-6270	195	9	tbd	tbd	NOUN
ejpam-6270	195	10	-	-	PUNCT
ejpam-6270	195	11	algebra	algebra	NOUN
ejpam-6270	195	12	w	w	NOUN
ejpam-6270	195	13	,	,	PUNCT
ejpam-6270	195	14	then	then	ADV
ejpam-6270	195	15	it	it	PRON
ejpam-6270	195	16	is	be	AUX
ejpam-6270	195	17	b	b	NOUN
ejpam-6270	195	18	-	-	PUNCT
ejpam-6270	195	19	t1	t1	NOUN
ejpam-6270	195	20	.	.	PUNCT
ejpam-6270	196	1	proof	proof	NOUN
ejpam-6270	196	2	.	.	PUNCT
ejpam-6270	197	1	assume	assume	VERB
ejpam-6270	197	2	that	that	SCONJ
ejpam-6270	197	3	{	{	PUNCT
ejpam-6270	197	4	0	0	X
ejpam-6270	197	5	}	}	PUNCT
ejpam-6270	197	6	is	be	AUX
ejpam-6270	197	7	open	open	ADJ
ejpam-6270	197	8	and	and	CCONJ
ejpam-6270	197	9	ζ	ζ	NOUN
ejpam-6270	197	10	,	,	PUNCT
ejpam-6270	197	11	η	η	PROPN
ejpam-6270	197	12	∈	∈	PROPN
ejpam-6270	197	13	w	w	NOUN
ejpam-6270	197	14	be	be	AUX
ejpam-6270	197	15	any	any	DET
ejpam-6270	197	16	two	two	NUM
ejpam-6270	197	17	distinct	distinct	ADJ
ejpam-6270	197	18	points	point	NOUN
ejpam-6270	197	19	.	.	PUNCT
ejpam-6270	198	1	since	since	SCONJ
ejpam-6270	198	2	ζ	ζ	PROPN
ejpam-6270	198	3	⊙	⊙	X
ejpam-6270	198	4	ζ	ζ	NOUN
ejpam-6270	198	5	=	=	NOUN
ejpam-6270	198	6	0	0	NUM
ejpam-6270	198	7	for	for	ADP
ejpam-6270	198	8	all	all	DET
ejpam-6270	198	9	ζ	ζ	PROPN
ejpam-6270	198	10	∈	∈	PROPN
ejpam-6270	198	11	w	w	NOUN
ejpam-6270	198	12	and	and	CCONJ
ejpam-6270	198	13	w	w	PROPN
ejpam-6270	198	14	is	be	AUX
ejpam-6270	198	15	tbd	tbd	NOUN
ejpam-6270	198	16	-	-	PUNCT
ejpam-6270	198	17	algebra	algebra	NOUN
ejpam-6270	198	18	,	,	PUNCT
ejpam-6270	198	19	then	then	ADV
ejpam-6270	198	20	there	there	PRON
ejpam-6270	198	21	exist	exist	VERB
ejpam-6270	198	22	b	b	X
ejpam-6270	198	23	-	-	PUNCT
ejpam-6270	198	24	open	open	ADJ
ejpam-6270	198	25	sets	set	NOUN
ejpam-6270	198	26	h	h	NOUN
ejpam-6270	198	27	and	and	CCONJ
ejpam-6270	198	28	g	g	NOUN
ejpam-6270	198	29	containing	contain	VERB
ejpam-6270	198	30	ζ	ζ	NOUN
ejpam-6270	198	31	such	such	DET
ejpam-6270	198	32	that	that	SCONJ
ejpam-6270	198	33	h	h	NOUN
ejpam-6270	198	34	⊙	⊙	VERB
ejpam-6270	198	35	g	g	PROPN
ejpam-6270	198	36	⊆	⊆	NUM
ejpam-6270	198	37	{	{	PUNCT
ejpam-6270	198	38	0	0	NUM
ejpam-6270	198	39	}	}	PUNCT
ejpam-6270	198	40	.	.	PUNCT
ejpam-6270	199	1	hence	hence	ADV
ejpam-6270	199	2	,	,	PUNCT
ejpam-6270	199	3	either	either	CCONJ
ejpam-6270	199	4	η	η	PROPN
ejpam-6270	199	5	/∈	/∈	PROPN
ejpam-6270	199	6	h	h	PROPN
ejpam-6270	199	7	or	or	CCONJ
ejpam-6270	199	8	η	η	PROPN
ejpam-6270	199	9	/∈	/∈	PROPN
ejpam-6270	199	10	g.	g.	PROPN
ejpam-6270	199	11	also	also	ADV
ejpam-6270	199	12	,	,	PUNCT
ejpam-6270	199	13	we	we	PRON
ejpam-6270	199	14	have	have	VERB
ejpam-6270	199	15	η	η	PROPN
ejpam-6270	199	16	⊙	⊙	PROPN
ejpam-6270	199	17	η	η	PROPN
ejpam-6270	199	18	=	=	PROPN
ejpam-6270	199	19	0	0	PROPN
ejpam-6270	199	20	,	,	PUNCT
ejpam-6270	199	21	so	so	ADV
ejpam-6270	199	22	the	the	DET
ejpam-6270	199	23	exist	exist	VERB
ejpam-6270	199	24	two	two	NUM
ejpam-6270	199	25	b	b	X
ejpam-6270	199	26	-	-	PUNCT
ejpam-6270	199	27	open	open	ADJ
ejpam-6270	199	28	sets	set	NOUN
ejpam-6270	199	29	u	u	NOUN
ejpam-6270	199	30	,	,	PUNCT
ejpam-6270	199	31	v	v	ADP
ejpam-6270	199	32	containing	contain	VERB
ejpam-6270	199	33	η	η	PROPN
ejpam-6270	199	34	such	such	ADJ
ejpam-6270	199	35	that	that	SCONJ
ejpam-6270	199	36	u	u	PROPN
ejpam-6270	199	37	⊙	⊙	VERB
ejpam-6270	199	38	v	v	ADP
ejpam-6270	199	39	⊆	⊆	NUM
ejpam-6270	199	40	{	{	PUNCT
ejpam-6270	199	41	0	0	NUM
ejpam-6270	199	42	}	}	PUNCT
ejpam-6270	199	43	.	.	PUNCT
ejpam-6270	200	1	hence	hence	ADV
ejpam-6270	200	2	,	,	PUNCT
ejpam-6270	200	3	either	either	CCONJ
ejpam-6270	200	4	ζ	ζ	NOUN
ejpam-6270	200	5	/∈	/∈	SYM
ejpam-6270	200	6	u	u	NOUN
ejpam-6270	200	7	or	or	CCONJ
ejpam-6270	200	8	ζ	ζ	NOUN
ejpam-6270	200	9	/∈	/∈	NOUN
ejpam-6270	200	10	v	v	NOUN
ejpam-6270	200	11	.therefore	.therefore	NOUN
ejpam-6270	200	12	,	,	PUNCT
ejpam-6270	200	13	we	we	PRON
ejpam-6270	200	14	obtain	obtain	VERB
ejpam-6270	200	15	that	that	SCONJ
ejpam-6270	200	16	a	a	DET
ejpam-6270	200	17	b	b	NOUN
ejpam-6270	200	18	-	-	PUNCT
ejpam-6270	200	19	open	open	ADJ
ejpam-6270	200	20	set	set	NOUN
ejpam-6270	200	21	containing	contain	VERB
ejpam-6270	200	22	ζ	ζ	NOUN
ejpam-6270	200	23	but	but	CCONJ
ejpam-6270	200	24	not	not	PART
ejpam-6270	200	25	η	η	PROPN
ejpam-6270	200	26	and	and	CCONJ
ejpam-6270	200	27	a	a	DET
ejpam-6270	200	28	b	b	NOUN
ejpam-6270	200	29	-	-	PUNCT
ejpam-6270	200	30	open	open	ADJ
ejpam-6270	200	31	set	set	NOUN
ejpam-6270	200	32	containing	contain	VERB
ejpam-6270	200	33	η	η	PROPN
ejpam-6270	200	34	but	but	CCONJ
ejpam-6270	200	35	not	not	PART
ejpam-6270	200	36	ζ	ζ	NOUN
ejpam-6270	200	37	.	.	PUNCT
ejpam-6270	201	1	therefore	therefore	ADV
ejpam-6270	201	2	,	,	PUNCT
ejpam-6270	201	3	w	w	PROPN
ejpam-6270	201	4	is	be	AUX
ejpam-6270	201	5	a	a	DET
ejpam-6270	201	6	b	b	PROPN
ejpam-6270	201	7	-	-	PUNCT
ejpam-6270	201	8	t1	t1	NOUN
ejpam-6270	201	9	-	-	PUNCT
ejpam-6270	201	10	space	space	NOUN
ejpam-6270	201	11	.	.	PUNCT
ejpam-6270	202	1	remark	remark	PROPN
ejpam-6270	202	2	1	1	NUM
ejpam-6270	202	3	.	.	PUNCT
ejpam-6270	203	1	the	the	DET
ejpam-6270	203	2	space	space	NOUN
ejpam-6270	203	3	(	(	PUNCT
ejpam-6270	203	4	w	w	PROPN
ejpam-6270	203	5	,	,	PUNCT
ejpam-6270	203	6	ω	ω	NOUN
ejpam-6270	203	7	)	)	PUNCT
ejpam-6270	203	8	in	in	ADP
ejpam-6270	203	9	example	example	NOUN
ejpam-6270	203	10	1	1	NUM
ejpam-6270	203	11	is	be	AUX
ejpam-6270	203	12	b	b	NOUN
ejpam-6270	203	13	-	-	PUNCT
ejpam-6270	203	14	t1	t1	NOUN
ejpam-6270	203	15	but	but	CCONJ
ejpam-6270	203	16	{	{	PUNCT
ejpam-6270	203	17	0	0	NUM
ejpam-6270	203	18	}	}	PUNCT
ejpam-6270	203	19	is	be	AUX
ejpam-6270	203	20	not	not	PART
ejpam-6270	203	21	b	b	NOUN
ejpam-6270	203	22	-	-	PUNCT
ejpam-6270	203	23	open	open	ADJ
ejpam-6270	203	24	.	.	PUNCT
ejpam-6270	204	1	corollary	corollary	ADJ
ejpam-6270	204	2	3	3	X
ejpam-6270	204	3	.	.	PUNCT
ejpam-6270	205	1	if	if	SCONJ
ejpam-6270	205	2	{	{	PUNCT
ejpam-6270	205	3	0	0	X
ejpam-6270	205	4	}	}	PUNCT
ejpam-6270	205	5	is	be	AUX
ejpam-6270	205	6	an	an	DET
ejpam-6270	205	7	open	open	ADJ
ejpam-6270	205	8	set	set	NOUN
ejpam-6270	205	9	in	in	ADP
ejpam-6270	205	10	a	a	DET
ejpam-6270	205	11	tbd	tbd	NOUN
ejpam-6270	205	12	-	-	PUNCT
ejpam-6270	205	13	algebra	algebra	NOUN
ejpam-6270	205	14	w	w	NOUN
ejpam-6270	205	15	,	,	PUNCT
ejpam-6270	205	16	then	then	ADV
ejpam-6270	205	17	every	every	DET
ejpam-6270	205	18	open	open	ADJ
ejpam-6270	205	19	singular	singular	NOUN
ejpam-6270	205	20	set	set	NOUN
ejpam-6270	205	21	is	be	AUX
ejpam-6270	205	22	regular	regular	ADJ
ejpam-6270	205	23	open	open	ADJ
ejpam-6270	205	24	.	.	PUNCT
ejpam-6270	206	1	proof	proof	NOUN
ejpam-6270	206	2	.	.	PUNCT
ejpam-6270	207	1	from	from	ADP
ejpam-6270	207	2	proposition	proposition	NOUN
ejpam-6270	207	3	7	7	NUM
ejpam-6270	207	4	,	,	PUNCT
ejpam-6270	207	5	we	we	PRON
ejpam-6270	207	6	have	have	VERB
ejpam-6270	207	7	w	w	PROPN
ejpam-6270	207	8	is	be	AUX
ejpam-6270	207	9	b	b	NOUN
ejpam-6270	207	10	-	-	PUNCT
ejpam-6270	207	11	t1	t1	NOUN
ejpam-6270	207	12	.	.	PUNCT
ejpam-6270	208	1	hence	hence	ADV
ejpam-6270	208	2	,	,	PUNCT
ejpam-6270	208	3	every	every	DET
ejpam-6270	208	4	singleton	singleton	NOUN
ejpam-6270	208	5	set	set	NOUN
ejpam-6270	208	6	is	be	AUX
ejpam-6270	208	7	b	b	NOUN
ejpam-6270	208	8	-	-	PUNCT
ejpam-6270	208	9	closed	closed	ADJ
ejpam-6270	208	10	.	.	PUNCT
ejpam-6270	209	1	if	if	SCONJ
ejpam-6270	209	2	{	{	PUNCT
ejpam-6270	209	3	ζ	ζ	NOUN
ejpam-6270	209	4	}	}	PUNCT
ejpam-6270	209	5	is	be	AUX
ejpam-6270	209	6	an	an	DET
ejpam-6270	209	7	open	open	ADJ
ejpam-6270	209	8	set	set	NOUN
ejpam-6270	209	9	,	,	PUNCT
ejpam-6270	209	10	so	so	SCONJ
ejpam-6270	209	11	we	we	PRON
ejpam-6270	209	12	have	have	VERB
ejpam-6270	209	13	int(cl({ζ	int(cl({ζ	NOUN
ejpam-6270	209	14	}	}	PUNCT
ejpam-6270	209	15	⊆	⊆	NUM
ejpam-6270	209	16	{	{	PUNCT
ejpam-6270	209	17	ζ	ζ	NOUN
ejpam-6270	209	18	}	}	PUNCT
ejpam-6270	209	19	⊆	⊆	NUM
ejpam-6270	209	20	int(cl({ζ	int(cl({ζ	NOUN
ejpam-6270	209	21	}	}	PUNCT
ejpam-6270	209	22	which	which	PRON
ejpam-6270	209	23	implies	imply	VERB
ejpam-6270	209	24	that	that	SCONJ
ejpam-6270	209	25	{	{	PUNCT
ejpam-6270	209	26	ζ	ζ	NOUN
ejpam-6270	209	27	}	}	PUNCT
ejpam-6270	209	28	is	be	AUX
ejpam-6270	209	29	regular	regular	ADJ
ejpam-6270	209	30	open	open	ADJ
ejpam-6270	209	31	.	.	PUNCT
ejpam-6270	210	1	corollary	corollary	ADJ
ejpam-6270	210	2	4	4	NUM
ejpam-6270	210	3	.	.	PUNCT
ejpam-6270	210	4	suppose	suppose	VERB
ejpam-6270	210	5	that	that	SCONJ
ejpam-6270	210	6	{	{	PUNCT
ejpam-6270	210	7	0	0	X
ejpam-6270	210	8	}	}	PUNCT
ejpam-6270	210	9	is	be	AUX
ejpam-6270	210	10	an	an	DET
ejpam-6270	210	11	open	open	ADJ
ejpam-6270	210	12	set	set	NOUN
ejpam-6270	210	13	in	in	ADP
ejpam-6270	210	14	a	a	DET
ejpam-6270	210	15	tbd	tbd	NOUN
ejpam-6270	210	16	-	-	PUNCT
ejpam-6270	210	17	algebra	algebra	NOUN
ejpam-6270	210	18	w.	w.	NOUN
ejpam-6270	210	19	if	if	SCONJ
ejpam-6270	210	20	w	w	PROPN
ejpam-6270	210	21	is	be	AUX
ejpam-6270	210	22	a	a	DET
ejpam-6270	210	23	door	door	NOUN
ejpam-6270	210	24	space	space	NOUN
ejpam-6270	210	25	,	,	PUNCT
ejpam-6270	210	26	then	then	ADV
ejpam-6270	210	27	every	every	DET
ejpam-6270	210	28	singular	singular	NOUN
ejpam-6270	210	29	set	set	NOUN
ejpam-6270	210	30	is	be	AUX
ejpam-6270	210	31	either	either	CCONJ
ejpam-6270	210	32	closed	closed	ADJ
ejpam-6270	210	33	or	or	CCONJ
ejpam-6270	210	34	regular	regular	ADJ
ejpam-6270	210	35	open	open	ADJ
ejpam-6270	210	36	.	.	PUNCT
ejpam-6270	211	1	m.	m.	NOUN
ejpam-6270	211	2	w.	w.	PROPN
ejpam-6270	211	3	abdulqader	abdulqader	PROPN
ejpam-6270	211	4	,	,	PUNCT
ejpam-6270	211	5	a.	a.	PROPN
ejpam-6270	211	6	b.	b.	PROPN
ejpam-6270	211	7	khalaf	khalaf	PROPN
ejpam-6270	211	8	/	/	SYM
ejpam-6270	211	9	eur	eur	PROPN
ejpam-6270	211	10	.	.	PUNCT
ejpam-6270	212	1	j.	j.	PROPN
ejpam-6270	212	2	pure	pure	PROPN
ejpam-6270	212	3	appl	appl	PROPN
ejpam-6270	212	4	.	.	PROPN
ejpam-6270	212	5	math	math	PROPN
ejpam-6270	212	6	,	,	PUNCT
ejpam-6270	212	7	18	18	NUM
ejpam-6270	212	8	(	(	PUNCT
ejpam-6270	212	9	3	3	NUM
ejpam-6270	212	10	)	)	PUNCT
ejpam-6270	212	11	(	(	PUNCT
ejpam-6270	212	12	2025	2025	NUM
ejpam-6270	212	13	)	)	PUNCT
ejpam-6270	212	14	,	,	PUNCT
ejpam-6270	212	15	6270	6270	NUM
ejpam-6270	212	16	9	9	NUM
ejpam-6270	212	17	of	of	ADP
ejpam-6270	212	18	17	17	NUM
ejpam-6270	212	19	proof	proof	NOUN
ejpam-6270	212	20	.	.	PUNCT
ejpam-6270	212	21	follows	follow	VERB
ejpam-6270	212	22	from	from	ADP
ejpam-6270	212	23	corollary	corollary	ADJ
ejpam-6270	212	24	3	3	NUM
ejpam-6270	212	25	and	and	CCONJ
ejpam-6270	212	26	the	the	DET
ejpam-6270	212	27	definition	definition	NOUN
ejpam-6270	212	28	of	of	ADP
ejpam-6270	212	29	door	door	NOUN
ejpam-6270	212	30	space	space	NOUN
ejpam-6270	212	31	.	.	PUNCT
ejpam-6270	213	1	proposition	proposition	NOUN
ejpam-6270	213	2	8	8	NUM
ejpam-6270	213	3	.	.	PUNCT
ejpam-6270	214	1	in	in	ADP
ejpam-6270	214	2	a	a	DET
ejpam-6270	214	3	tbd	tbd	NOUN
ejpam-6270	214	4	-	-	PUNCT
ejpam-6270	214	5	algebra	algebra	NOUN
ejpam-6270	214	6	w	w	NOUN
ejpam-6270	214	7	which	which	PRON
ejpam-6270	214	8	is	be	AUX
ejpam-6270	214	9	both	both	PRON
ejpam-6270	214	10	submaximal	submaximal	ADJ
ejpam-6270	214	11	and	and	CCONJ
ejpam-6270	214	12	extremally	extremally	ADV
ejpam-6270	214	13	disconnected	disconnected	ADJ
ejpam-6270	214	14	space	space	NOUN
ejpam-6270	214	15	.	.	PUNCT
ejpam-6270	215	1	if	if	SCONJ
ejpam-6270	215	2	{	{	PUNCT
ejpam-6270	215	3	0	0	X
ejpam-6270	215	4	}	}	PUNCT
ejpam-6270	215	5	is	be	AUX
ejpam-6270	215	6	open	open	ADJ
ejpam-6270	215	7	,	,	PUNCT
ejpam-6270	215	8	then	then	ADV
ejpam-6270	215	9	the	the	DET
ejpam-6270	215	10	space	space	NOUN
ejpam-6270	215	11	is	be	AUX
ejpam-6270	215	12	discrete	discrete	ADJ
ejpam-6270	215	13	.	.	PUNCT
ejpam-6270	216	1	proof	proof	NOUN
ejpam-6270	216	2	.	.	PUNCT
ejpam-6270	217	1	assume	assume	VERB
ejpam-6270	217	2	that	that	SCONJ
ejpam-6270	217	3	{	{	PUNCT
ejpam-6270	217	4	0	0	X
ejpam-6270	217	5	}	}	PUNCT
ejpam-6270	217	6	is	be	AUX
ejpam-6270	217	7	open	open	ADJ
ejpam-6270	217	8	and	and	CCONJ
ejpam-6270	217	9	let	let	VERB
ejpam-6270	217	10	ζ	ζ	NOUN
ejpam-6270	217	11	be	be	AUX
ejpam-6270	217	12	any	any	DET
ejpam-6270	217	13	point	point	NOUN
ejpam-6270	217	14	in	in	ADP
ejpam-6270	217	15	w.	w.	NOUN
ejpam-6270	217	16	since	since	SCONJ
ejpam-6270	217	17	ζ	ζ	PROPN
ejpam-6270	217	18	⊙	⊙	X
ejpam-6270	217	19	ζ	ζ	NOUN
ejpam-6270	217	20	=	=	NOUN
ejpam-6270	217	21	0	0	NUM
ejpam-6270	217	22	for	for	SCONJ
ejpam-6270	217	23	all	all	DET
ejpam-6270	217	24	ζ	ζ	PROPN
ejpam-6270	217	25	∈	∈	PROPN
ejpam-6270	217	26	w	w	NOUN
ejpam-6270	217	27	and	and	CCONJ
ejpam-6270	217	28	w	w	PROPN
ejpam-6270	217	29	is	be	AUX
ejpam-6270	217	30	tbd	tbd	NOUN
ejpam-6270	217	31	-	-	PUNCT
ejpam-6270	217	32	algebra	algebra	NOUN
ejpam-6270	217	33	,	,	PUNCT
ejpam-6270	217	34	so	so	SCONJ
ejpam-6270	217	35	there	there	PRON
ejpam-6270	217	36	exist	exist	VERB
ejpam-6270	217	37	b	b	X
ejpam-6270	217	38	-	-	PUNCT
ejpam-6270	217	39	open	open	ADJ
ejpam-6270	217	40	sets	set	NOUN
ejpam-6270	217	41	u	u	NOUN
ejpam-6270	217	42	and	and	CCONJ
ejpam-6270	217	43	v	v	ADP
ejpam-6270	217	44	having	have	VERB
ejpam-6270	217	45	ζ	ζ	NOUN
ejpam-6270	217	46	such	such	ADJ
ejpam-6270	217	47	that	that	SCONJ
ejpam-6270	217	48	u⊙v	u⊙v	NOUN
ejpam-6270	217	49	⊆	⊆	NUM
ejpam-6270	217	50	{	{	PUNCT
ejpam-6270	217	51	0	0	NUM
ejpam-6270	217	52	}	}	PUNCT
ejpam-6270	217	53	.	.	PUNCT
ejpam-6270	218	1	since	since	SCONJ
ejpam-6270	218	2	w	w	PROPN
ejpam-6270	218	3	is	be	AUX
ejpam-6270	218	4	extremally	extremally	ADV
ejpam-6270	218	5	disconnected	disconnect	VERB
ejpam-6270	218	6	,	,	PUNCT
ejpam-6270	218	7	so	so	CCONJ
ejpam-6270	218	8	by	by	ADP
ejpam-6270	218	9	using	use	VERB
ejpam-6270	218	10	lemma	lemma	PROPN
ejpam-6270	218	11	4	4	NUM
ejpam-6270	218	12	,	,	PUNCT
ejpam-6270	218	13	u	u	NOUN
ejpam-6270	218	14	,	,	PUNCT
ejpam-6270	218	15	v	v	NOUN
ejpam-6270	218	16	are	be	AUX
ejpam-6270	218	17	pre	pre	ADJ
ejpam-6270	218	18	-	-	ADJ
ejpam-6270	218	19	open	open	ADJ
ejpam-6270	218	20	sets	set	NOUN
ejpam-6270	218	21	.	.	PUNCT
ejpam-6270	219	1	also	also	ADV
ejpam-6270	219	2	,	,	PUNCT
ejpam-6270	219	3	w	w	NOUN
ejpam-6270	219	4	is	be	AUX
ejpam-6270	219	5	submaximal	submaximal	ADJ
ejpam-6270	219	6	,	,	PUNCT
ejpam-6270	219	7	so	so	ADV
ejpam-6270	219	8	by	by	ADP
ejpam-6270	219	9	lemma	lemma	PROPN
ejpam-6270	219	10	3	3	NUM
ejpam-6270	219	11	,	,	PUNCT
ejpam-6270	219	12	u	u	NOUN
ejpam-6270	219	13	,	,	PUNCT
ejpam-6270	219	14	v	v	NOUN
ejpam-6270	219	15	are	be	AUX
ejpam-6270	219	16	open	open	ADJ
ejpam-6270	219	17	.	.	PUNCT
ejpam-6270	220	1	hence	hence	ADV
ejpam-6270	220	2	w	w	PROPN
ejpam-6270	220	3	=	=	PUNCT
ejpam-6270	220	4	u	u	NOUN
ejpam-6270	220	5	∩v	∩v	NOUN
ejpam-6270	220	6	is	be	AUX
ejpam-6270	220	7	an	an	DET
ejpam-6270	220	8	open	open	ADJ
ejpam-6270	220	9	set	set	NOUN
ejpam-6270	220	10	having	have	VERB
ejpam-6270	220	11	ζ	ζ	NOUN
ejpam-6270	220	12	.	.	PUNCT
ejpam-6270	221	1	now	now	ADV
ejpam-6270	221	2	if	if	SCONJ
ejpam-6270	221	3	w	w	ADP
ejpam-6270	221	4	having	have	VERB
ejpam-6270	221	5	another	another	DET
ejpam-6270	221	6	point	point	NOUN
ejpam-6270	221	7	η	η	PROPN
ejpam-6270	221	8	,	,	PUNCT
ejpam-6270	221	9	then	then	ADV
ejpam-6270	221	10	we	we	PRON
ejpam-6270	221	11	obtain	obtain	VERB
ejpam-6270	221	12	ζ	ζ	PROPN
ejpam-6270	221	13	⊙	⊙	PROPN
ejpam-6270	221	14	η	η	PROPN
ejpam-6270	221	15	=	=	PROPN
ejpam-6270	221	16	0	0	NUM
ejpam-6270	221	17	and	and	CCONJ
ejpam-6270	221	18	η	η	PROPN
ejpam-6270	221	19	⊙	⊙	PROPN
ejpam-6270	221	20	ζ	ζ	PROPN
ejpam-6270	221	21	=	=	SYM
ejpam-6270	221	22	0	0	NUM
ejpam-6270	221	23	which	which	PRON
ejpam-6270	221	24	is	be	AUX
ejpam-6270	221	25	a	a	DET
ejpam-6270	221	26	contradiction	contradiction	NOUN
ejpam-6270	221	27	.	.	PUNCT
ejpam-6270	222	1	hence	hence	ADV
ejpam-6270	222	2	w	w	PROPN
ejpam-6270	222	3	is	be	AUX
ejpam-6270	222	4	an	an	DET
ejpam-6270	222	5	open	open	ADJ
ejpam-6270	222	6	set	set	NOUN
ejpam-6270	222	7	having	have	VERB
ejpam-6270	222	8	ζ	ζ	NOUN
ejpam-6270	222	9	only	only	ADV
ejpam-6270	222	10	.	.	PUNCT
ejpam-6270	223	1	therefore	therefore	ADV
ejpam-6270	223	2	,	,	PUNCT
ejpam-6270	223	3	{	{	PUNCT
ejpam-6270	223	4	ζ	ζ	NOUN
ejpam-6270	223	5	}	}	PUNCT
ejpam-6270	223	6	is	be	AUX
ejpam-6270	223	7	open	open	ADJ
ejpam-6270	223	8	for	for	SCONJ
ejpam-6270	223	9	each	each	DET
ejpam-6270	223	10	ζ	ζ	PROPN
ejpam-6270	223	11	∈	∈	PROPN
ejpam-6270	223	12	w.	w.	NOUN
ejpam-6270	223	13	thus	thus	ADV
ejpam-6270	223	14	,	,	PUNCT
ejpam-6270	223	15	the	the	DET
ejpam-6270	223	16	space	space	NOUN
ejpam-6270	223	17	w	w	NOUN
ejpam-6270	223	18	is	be	AUX
ejpam-6270	223	19	discrete	discrete	ADJ
ejpam-6270	223	20	.	.	PUNCT
ejpam-6270	224	1	proposition	proposition	NOUN
ejpam-6270	224	2	9	9	NUM
ejpam-6270	224	3	.	.	PUNCT
ejpam-6270	225	1	in	in	ADP
ejpam-6270	225	2	a	a	DET
ejpam-6270	225	3	tbd	tbd	NOUN
ejpam-6270	225	4	-	-	PUNCT
ejpam-6270	225	5	algebra	algebra	NOUN
ejpam-6270	225	6	(	(	PUNCT
ejpam-6270	225	7	w,⊙,ω	w,⊙,ω	PROPN
ejpam-6270	225	8	)	)	PUNCT
ejpam-6270	225	9	.	.	PUNCT
ejpam-6270	226	1	if	if	SCONJ
ejpam-6270	226	2	w	w	NOUN
ejpam-6270	226	3	is	be	AUX
ejpam-6270	226	4	an	an	DET
ejpam-6270	226	5	open	open	ADJ
ejpam-6270	226	6	set	set	NOUN
ejpam-6270	226	7	not	not	PART
ejpam-6270	226	8	containing	contain	VERB
ejpam-6270	226	9	0	0	NUM
ejpam-6270	226	10	,	,	PUNCT
ejpam-6270	226	11	then	then	ADV
ejpam-6270	226	12	for	for	ADP
ejpam-6270	226	13	each	each	DET
ejpam-6270	226	14	distinct	distinct	ADJ
ejpam-6270	226	15	elements	element	NOUN
ejpam-6270	226	16	ζ	ζ	NOUN
ejpam-6270	226	17	,	,	PUNCT
ejpam-6270	226	18	η	η	PROPN
ejpam-6270	226	19	∈	∈	PROPN
ejpam-6270	226	20	w	w	NOUN
ejpam-6270	226	21	with	with	ADP
ejpam-6270	226	22	ζ	ζ	PROPN
ejpam-6270	226	23	⊙	⊙	PROPN
ejpam-6270	226	24	η	η	PROPN
ejpam-6270	226	25	∈	∈	PROPN
ejpam-6270	226	26	w	w	NOUN
ejpam-6270	226	27	there	there	PRON
ejpam-6270	226	28	exist	exist	VERB
ejpam-6270	226	29	two	two	NUM
ejpam-6270	226	30	disjoint	disjoint	NOUN
ejpam-6270	226	31	b	b	X
ejpam-6270	226	32	-	-	PUNCT
ejpam-6270	226	33	open	open	ADJ
ejpam-6270	226	34	sets	set	NOUN
ejpam-6270	226	35	containing	contain	VERB
ejpam-6270	226	36	ζ	ζ	NOUN
ejpam-6270	226	37	and	and	CCONJ
ejpam-6270	226	38	η	η	PROPN
ejpam-6270	226	39	.	.	PROPN
ejpam-6270	226	40	proof	proof	NOUN
ejpam-6270	226	41	.	.	PUNCT
ejpam-6270	227	1	let	let	VERB
ejpam-6270	227	2	ζ	ζ	PROPN
ejpam-6270	227	3	⊙	⊙	PROPN
ejpam-6270	227	4	η	η	PROPN
ejpam-6270	227	5	∈	∈	PROPN
ejpam-6270	227	6	w	w	PROPN
ejpam-6270	227	7	,	,	PUNCT
ejpam-6270	227	8	since	since	SCONJ
ejpam-6270	227	9	(	(	PUNCT
ejpam-6270	227	10	w,⊙,ω	w,⊙,ω	PROPN
ejpam-6270	227	11	)	)	PUNCT
ejpam-6270	227	12	is	be	AUX
ejpam-6270	227	13	a	a	DET
ejpam-6270	227	14	tbd	tbd	NOUN
ejpam-6270	227	15	-	-	PUNCT
ejpam-6270	227	16	algebra	algebra	NOUN
ejpam-6270	227	17	,	,	PUNCT
ejpam-6270	227	18	then	then	ADV
ejpam-6270	227	19	there	there	PRON
ejpam-6270	227	20	exist	exist	VERB
ejpam-6270	227	21	b	b	NOUN
ejpam-6270	227	22	-	-	PUNCT
ejpam-6270	227	23	open	open	ADJ
ejpam-6270	227	24	sets	set	NOUN
ejpam-6270	227	25	u	u	NOUN
ejpam-6270	227	26	and	and	CCONJ
ejpam-6270	227	27	v	v	NOUN
ejpam-6270	227	28	of	of	ADP
ejpam-6270	227	29	containing	contain	VERB
ejpam-6270	227	30	ζ	ζ	NOUN
ejpam-6270	227	31	and	and	CCONJ
ejpam-6270	227	32	η	η	PROPN
ejpam-6270	227	33	such	such	ADJ
ejpam-6270	227	34	that	that	SCONJ
ejpam-6270	227	35	u	u	PROPN
ejpam-6270	227	36	⊙	⊙	VERB
ejpam-6270	227	37	v	v	ADP
ejpam-6270	227	38	⊆	⊆	NUM
ejpam-6270	227	39	w	w	NOUN
ejpam-6270	227	40	.	.	PUNCT
ejpam-6270	228	1	if	if	SCONJ
ejpam-6270	228	2	u	u	PROPN
ejpam-6270	228	3	∩	∩	NOUN
ejpam-6270	228	4	v	v	ADP
ejpam-6270	228	5	̸=	̸=	PROPN
ejpam-6270	228	6	ϕ	ϕ	NOUN
ejpam-6270	228	7	,	,	PUNCT
ejpam-6270	228	8	then	then	ADV
ejpam-6270	228	9	there	there	PRON
ejpam-6270	228	10	is	be	VERB
ejpam-6270	228	11	a	a	DET
ejpam-6270	228	12	point	point	NOUN
ejpam-6270	228	13	θ	θ	NOUN
ejpam-6270	228	14	∈	∈	PROPN
ejpam-6270	228	15	u	u	NOUN
ejpam-6270	228	16	∩	∩	NOUN
ejpam-6270	228	17	v	v	NUM
ejpam-6270	228	18	which	which	PRON
ejpam-6270	228	19	implies	imply	VERB
ejpam-6270	228	20	0	0	NUM
ejpam-6270	228	21	=	=	SYM
ejpam-6270	228	22	θ	θ	NOUN
ejpam-6270	228	23	⊙	⊙	NOUN
ejpam-6270	228	24	θ	θ	PROPN
ejpam-6270	228	25	∈	∈	PROPN
ejpam-6270	228	26	u	u	NOUN
ejpam-6270	228	27	⊙	⊙	VERB
ejpam-6270	228	28	v	v	ADP
ejpam-6270	228	29	⊆	⊆	NUM
ejpam-6270	228	30	w	w	ADP
ejpam-6270	228	31	which	which	PRON
ejpam-6270	228	32	contradicts	contradict	VERB
ejpam-6270	228	33	itself.therefore	itself.therefore	NOUN
ejpam-6270	228	34	,	,	PUNCT
ejpam-6270	228	35	u	u	NOUN
ejpam-6270	228	36	∩	∩	NOUN
ejpam-6270	228	37	v	v	NOUN
ejpam-6270	228	38	=	=	PUNCT
ejpam-6270	228	39	ϕ.	ϕ.	NOUN
ejpam-6270	228	40	proposition	proposition	NOUN
ejpam-6270	228	41	10	10	NUM
ejpam-6270	228	42	.	.	PUNCT
ejpam-6270	229	1	in	in	ADP
ejpam-6270	229	2	a	a	DET
ejpam-6270	229	3	tbd	tbd	NOUN
ejpam-6270	229	4	-	-	PUNCT
ejpam-6270	229	5	algebra	algebra	NOUN
ejpam-6270	229	6	w	w	NOUN
ejpam-6270	229	7	,	,	PUNCT
ejpam-6270	229	8	if	if	SCONJ
ejpam-6270	229	9	{	{	PUNCT
ejpam-6270	229	10	0	0	NUM
ejpam-6270	229	11	}	}	PUNCT
ejpam-6270	229	12	is	be	AUX
ejpam-6270	229	13	closed	closed	ADJ
ejpam-6270	229	14	,	,	PUNCT
ejpam-6270	229	15	then	then	ADV
ejpam-6270	229	16	w	w	PROPN
ejpam-6270	229	17	is	be	AUX
ejpam-6270	229	18	b	b	NOUN
ejpam-6270	229	19	-	-	PUNCT
ejpam-6270	229	20	t2	t2	NOUN
ejpam-6270	229	21	.	.	PUNCT
ejpam-6270	230	1	proof	proof	NOUN
ejpam-6270	230	2	.	.	PUNCT
ejpam-6270	231	1	let	let	AUX
ejpam-6270	231	2	{	{	PUNCT
ejpam-6270	231	3	0	0	NUM
ejpam-6270	231	4	}	}	PUNCT
ejpam-6270	231	5	is	be	AUX
ejpam-6270	231	6	closed	close	VERB
ejpam-6270	231	7	and	and	CCONJ
ejpam-6270	231	8	let	let	VERB
ejpam-6270	231	9	ζ	ζ	NOUN
ejpam-6270	231	10	and	and	CCONJ
ejpam-6270	231	11	η	η	PROPN
ejpam-6270	231	12	be	be	VERB
ejpam-6270	231	13	any	any	DET
ejpam-6270	231	14	two	two	NUM
ejpam-6270	231	15	distinct	distinct	ADJ
ejpam-6270	231	16	points	point	NOUN
ejpam-6270	231	17	in	in	ADP
ejpam-6270	231	18	w	w	NOUN
ejpam-6270	231	19	,	,	PUNCT
ejpam-6270	231	20	then	then	ADV
ejpam-6270	231	21	either	either	CCONJ
ejpam-6270	231	22	ζ⊙	ζ⊙	PROPN
ejpam-6270	231	23	η	η	PROPN
ejpam-6270	231	24	̸=	̸=	PROPN
ejpam-6270	231	25	0	0	NUM
ejpam-6270	231	26	or	or	CCONJ
ejpam-6270	231	27	η⊙	η⊙	VERB
ejpam-6270	231	28	ζ	ζ	NOUN
ejpam-6270	231	29	̸=	̸=	PROPN
ejpam-6270	231	30	0	0	NUM
ejpam-6270	231	31	without	without	ADP
ejpam-6270	231	32	loss	loss	NOUN
ejpam-6270	231	33	of	of	ADP
ejpam-6270	231	34	generality	generality	NOUN
ejpam-6270	231	35	assume	assume	VERB
ejpam-6270	231	36	that	that	SCONJ
ejpam-6270	231	37	ζ⊙	ζ⊙	PROPN
ejpam-6270	231	38	η	η	PROPN
ejpam-6270	231	39	̸=	̸=	PROPN
ejpam-6270	231	40	0	0	NUM
ejpam-6270	231	41	.	.	PUNCT
ejpam-6270	232	1	hence	hence	ADV
ejpam-6270	232	2	,	,	PUNCT
ejpam-6270	232	3	there	there	PRON
ejpam-6270	232	4	exist	exist	VERB
ejpam-6270	232	5	b	b	X
ejpam-6270	232	6	-	-	PUNCT
ejpam-6270	232	7	open	open	ADJ
ejpam-6270	232	8	sets	set	NOUN
ejpam-6270	232	9	u	u	NOUN
ejpam-6270	232	10	and	and	CCONJ
ejpam-6270	232	11	v	v	ADP
ejpam-6270	232	12	having	have	VERB
ejpam-6270	232	13	ζ	ζ	NOUN
ejpam-6270	232	14	and	and	CCONJ
ejpam-6270	232	15	η	η	NOUN
ejpam-6270	232	16	respectively	respectively	ADV
ejpam-6270	232	17	such	such	ADJ
ejpam-6270	232	18	that	that	SCONJ
ejpam-6270	232	19	u	u	PROPN
ejpam-6270	232	20	⊙	⊙	VERB
ejpam-6270	232	21	v	v	ADP
ejpam-6270	232	22	⊆	⊆	NUM
ejpam-6270	232	23	ζ	ζ	NOUN
ejpam-6270	232	24	\	\	NOUN
ejpam-6270	232	25	{	{	PUNCT
ejpam-6270	232	26	0	0	NUM
ejpam-6270	232	27	}	}	PUNCT
ejpam-6270	232	28	and	and	CCONJ
ejpam-6270	232	29	hence	hence	ADV
ejpam-6270	232	30	u	u	NOUN
ejpam-6270	232	31	∩	∩	NOUN
ejpam-6270	232	32	v	v	NOUN
ejpam-6270	232	33	=	=	SYM
ejpam-6270	232	34	ϕ.	ϕ.	PROPN
ejpam-6270	232	35	therefore	therefore	ADV
ejpam-6270	232	36	,	,	PUNCT
ejpam-6270	232	37	w	w	PROPN
ejpam-6270	232	38	is	be	AUX
ejpam-6270	232	39	b	b	NOUN
ejpam-6270	232	40	-	-	PUNCT
ejpam-6270	232	41	t2	t2	NOUN
ejpam-6270	232	42	.	.	PUNCT
ejpam-6270	233	1	example	example	NOUN
ejpam-6270	234	1	4	4	NUM
ejpam-6270	234	2	.	.	X
ejpam-6270	234	3	consider	consider	VERB
ejpam-6270	234	4	any	any	DET
ejpam-6270	234	5	infinite	infinite	ADJ
ejpam-6270	234	6	d	d	NOUN
ejpam-6270	234	7	-	-	PUNCT
ejpam-6270	234	8	algebra	algebra	NOUN
ejpam-6270	234	9	(	(	PUNCT
ejpam-6270	234	10	w,⊙,ω	w,⊙,ω	PROPN
ejpam-6270	234	11	)	)	PUNCT
ejpam-6270	234	12	where	where	SCONJ
ejpam-6270	234	13	ω	ω	PROPN
ejpam-6270	234	14	is	be	AUX
ejpam-6270	234	15	the	the	DET
ejpam-6270	234	16	indescrete	indescrete	ADJ
ejpam-6270	234	17	topology	topology	NOUN
ejpam-6270	234	18	on	on	ADP
ejpam-6270	234	19	w.	w.	PROPN
ejpam-6270	234	20	then	then	ADV
ejpam-6270	234	21	,	,	PUNCT
ejpam-6270	234	22	bo(w	bo(w	NOUN
ejpam-6270	234	23	,	,	PUNCT
ejpam-6270	234	24	ω	ω	NOUN
ejpam-6270	234	25	)	)	PUNCT
ejpam-6270	234	26	=	=	SYM
ejpam-6270	234	27	p	p	X
ejpam-6270	234	28	(	(	PUNCT
ejpam-6270	234	29	w	w	NOUN
ejpam-6270	234	30	)	)	PUNCT
ejpam-6270	234	31	and	and	CCONJ
ejpam-6270	234	32	hence	hence	ADV
ejpam-6270	234	33	(	(	PUNCT
ejpam-6270	234	34	w	w	PROPN
ejpam-6270	234	35	,	,	PUNCT
ejpam-6270	234	36	ω	ω	NOUN
ejpam-6270	234	37	)	)	PUNCT
ejpam-6270	234	38	is	be	AUX
ejpam-6270	234	39	a	a	DET
ejpam-6270	234	40	b	b	PROPN
ejpam-6270	234	41	-	-	PUNCT
ejpam-6270	234	42	t2	t2	NOUN
ejpam-6270	234	43	-	-	PUNCT
ejpam-6270	234	44	space	space	NOUN
ejpam-6270	234	45	but	but	CCONJ
ejpam-6270	234	46	{	{	PUNCT
ejpam-6270	234	47	0	0	X
ejpam-6270	234	48	}	}	PUNCT
ejpam-6270	234	49	is	be	AUX
ejpam-6270	234	50	not	not	PART
ejpam-6270	234	51	closed	closed	ADJ
ejpam-6270	234	52	.	.	PUNCT
ejpam-6270	235	1	corollary	corollary	ADJ
ejpam-6270	235	2	5	5	NUM
ejpam-6270	235	3	.	.	PUNCT
ejpam-6270	236	1	if	if	SCONJ
ejpam-6270	236	2	a	a	DET
ejpam-6270	236	3	tbd	tbd	NOUN
ejpam-6270	236	4	-	-	PUNCT
ejpam-6270	236	5	algebra	algebra	NOUN
ejpam-6270	236	6	(	(	PUNCT
ejpam-6270	236	7	w,⊙,ω	w,⊙,ω	PROPN
ejpam-6270	236	8	)	)	PUNCT
ejpam-6270	236	9	is	be	AUX
ejpam-6270	236	10	t1	t1	NOUN
ejpam-6270	236	11	,	,	PUNCT
ejpam-6270	236	12	then	then	ADV
ejpam-6270	236	13	it	it	PRON
ejpam-6270	236	14	is	be	AUX
ejpam-6270	236	15	b	b	NOUN
ejpam-6270	236	16	-	-	PUNCT
ejpam-6270	236	17	t2	t2	NOUN
ejpam-6270	236	18	.	.	PUNCT
ejpam-6270	237	1	proof	proof	NOUN
ejpam-6270	237	2	.	.	PUNCT
ejpam-6270	238	1	since	since	SCONJ
ejpam-6270	238	2	(	(	PUNCT
ejpam-6270	238	3	w,⊙,ω	w,⊙,ω	PROPN
ejpam-6270	238	4	)	)	PUNCT
ejpam-6270	238	5	is	be	AUX
ejpam-6270	238	6	t1	t1	NOUN
ejpam-6270	238	7	,	,	PUNCT
ejpam-6270	238	8	so	so	CCONJ
ejpam-6270	238	9	{	{	PUNCT
ejpam-6270	238	10	0	0	NUM
ejpam-6270	238	11	}	}	PUNCT
ejpam-6270	238	12	is	be	AUX
ejpam-6270	238	13	closed	close	VERB
ejpam-6270	238	14	.	.	PUNCT
ejpam-6270	239	1	hence	hence	ADV
ejpam-6270	239	2	,	,	PUNCT
ejpam-6270	239	3	by	by	ADP
ejpam-6270	239	4	proposition	proposition	NOUN
ejpam-6270	239	5	10	10	NUM
ejpam-6270	239	6	,	,	PUNCT
ejpam-6270	239	7	(	(	PUNCT
ejpam-6270	239	8	w,⊙,ω	w,⊙,ω	PROPN
ejpam-6270	239	9	)	)	PUNCT
ejpam-6270	239	10	is	be	AUX
ejpam-6270	239	11	b−	b−	PROPN
ejpam-6270	239	12	t2	t2	NOUN
ejpam-6270	239	13	.	.	PUNCT
ejpam-6270	240	1	proposition	proposition	NOUN
ejpam-6270	240	2	11	11	NUM
ejpam-6270	240	3	.	.	PUNCT
ejpam-6270	241	1	if	if	SCONJ
ejpam-6270	241	2	a	a	DET
ejpam-6270	241	3	tbd	tbd	NOUN
ejpam-6270	241	4	-	-	PUNCT
ejpam-6270	241	5	algebra	algebra	NOUN
ejpam-6270	241	6	(	(	PUNCT
ejpam-6270	241	7	w,⊙,ω	w,⊙,ω	PROPN
ejpam-6270	241	8	)	)	PUNCT
ejpam-6270	241	9	is	be	AUX
ejpam-6270	241	10	t0	t0	NOUN
ejpam-6270	241	11	,	,	PUNCT
ejpam-6270	241	12	then	then	ADV
ejpam-6270	241	13	it	it	PRON
ejpam-6270	241	14	is	be	AUX
ejpam-6270	241	15	b	b	NOUN
ejpam-6270	241	16	-	-	PUNCT
ejpam-6270	241	17	t1	t1	NOUN
ejpam-6270	241	18	.	.	PUNCT
ejpam-6270	242	1	proof	proof	NOUN
ejpam-6270	242	2	.	.	PUNCT
ejpam-6270	243	1	suppose	suppose	VERB
ejpam-6270	243	2	that	that	SCONJ
ejpam-6270	243	3	ζ	ζ	NOUN
ejpam-6270	243	4	,	,	PUNCT
ejpam-6270	243	5	η	η	PROPN
ejpam-6270	243	6	∈	∈	PROPN
ejpam-6270	243	7	w	w	PROPN
ejpam-6270	243	8	and	and	CCONJ
ejpam-6270	243	9	ζ	ζ	PROPN
ejpam-6270	243	10	̸=	̸=	PROPN
ejpam-6270	243	11	η	η	PROPN
ejpam-6270	243	12	.	.	PROPN
ejpam-6270	243	13	then	then	ADV
ejpam-6270	243	14	either	either	CCONJ
ejpam-6270	243	15	ζ	ζ	PROPN
ejpam-6270	243	16	⊙	⊙	PROPN
ejpam-6270	243	17	η	η	PROPN
ejpam-6270	243	18	̸=	̸=	PROPN
ejpam-6270	243	19	0	0	NUM
ejpam-6270	243	20	or	or	CCONJ
ejpam-6270	243	21	η	η	PROPN
ejpam-6270	243	22	⊙	⊙	PROPN
ejpam-6270	243	23	ζ	ζ	PROPN
ejpam-6270	243	24	̸=	̸=	PROPN
ejpam-6270	243	25	0	0	NUM
ejpam-6270	243	26	.	.	PUNCT
ejpam-6270	244	1	now	now	ADV
ejpam-6270	244	2	let	let	VERB
ejpam-6270	244	3	ζ	ζ	PROPN
ejpam-6270	244	4	⊙	⊙	PROPN
ejpam-6270	244	5	η	η	PROPN
ejpam-6270	244	6	̸=	̸=	PROPN
ejpam-6270	244	7	0	0	NUM
ejpam-6270	244	8	.	.	PUNCT
ejpam-6270	245	1	since	since	SCONJ
ejpam-6270	245	2	w	w	PROPN
ejpam-6270	245	3	is	be	AUX
ejpam-6270	245	4	t0	t0	PROPN
ejpam-6270	245	5	space	space	NOUN
ejpam-6270	245	6	,	,	PUNCT
ejpam-6270	245	7	then	then	ADV
ejpam-6270	245	8	there	there	PRON
ejpam-6270	245	9	is	be	VERB
ejpam-6270	245	10	an	an	DET
ejpam-6270	245	11	open	open	ADJ
ejpam-6270	245	12	set	set	NOUN
ejpam-6270	245	13	w	w	NOUN
ejpam-6270	245	14	that	that	PRON
ejpam-6270	245	15	contains	contain	VERB
ejpam-6270	245	16	one	one	NUM
ejpam-6270	245	17	of	of	ADP
ejpam-6270	245	18	them	they	PRON
ejpam-6270	245	19	but	but	CCONJ
ejpam-6270	245	20	not	not	PART
ejpam-6270	245	21	the	the	DET
ejpam-6270	245	22	other	other	ADJ
ejpam-6270	245	23	.	.	PUNCT
ejpam-6270	246	1	case	case	NOUN
ejpam-6270	246	2	1	1	X
ejpam-6270	246	3	.	.	X
ejpam-6270	246	4	assume	assume	VERB
ejpam-6270	246	5	that	that	SCONJ
ejpam-6270	246	6	w	w	NOUN
ejpam-6270	246	7	contains	contain	VERB
ejpam-6270	246	8	ζ	ζ	PROPN
ejpam-6270	246	9	⊙	⊙	PROPN
ejpam-6270	246	10	η	η	PROPN
ejpam-6270	246	11	and	and	CCONJ
ejpam-6270	246	12	0	0	NUM
ejpam-6270	246	13	/∈	/∈	INTJ
ejpam-6270	247	1	w	w	INTJ
ejpam-6270	247	2	.	.	PUNCT
ejpam-6270	248	1	since	since	SCONJ
ejpam-6270	248	2	(	(	PUNCT
ejpam-6270	248	3	w,⊙,ω	w,⊙,ω	PROPN
ejpam-6270	248	4	)	)	PUNCT
ejpam-6270	248	5	is	be	AUX
ejpam-6270	248	6	a	a	DET
ejpam-6270	248	7	tbd	tbd	NOUN
ejpam-6270	248	8	-	-	PUNCT
ejpam-6270	248	9	algebra	algebra	NOUN
ejpam-6270	248	10	,	,	PUNCT
ejpam-6270	248	11	then	then	ADV
ejpam-6270	248	12	there	there	PRON
ejpam-6270	248	13	exist	exist	VERB
ejpam-6270	248	14	b	b	NOUN
ejpam-6270	248	15	-	-	PUNCT
ejpam-6270	248	16	open	open	ADJ
ejpam-6270	248	17	sets	set	VERB
ejpam-6270	248	18	u	u	NOUN
ejpam-6270	248	19	of	of	ADP
ejpam-6270	248	20	ζ	ζ	NOUN
ejpam-6270	248	21	and	and	CCONJ
ejpam-6270	248	22	v	v	NOUN
ejpam-6270	248	23	of	of	ADP
ejpam-6270	248	24	η	η	PROPN
ejpam-6270	248	25	such	such	ADJ
ejpam-6270	248	26	that	that	DET
ejpam-6270	248	27	m.	m.	NOUN
ejpam-6270	248	28	w.	w.	PROPN
ejpam-6270	248	29	abdulqader	abdulqader	PROPN
ejpam-6270	248	30	,	,	PUNCT
ejpam-6270	248	31	a.	a.	PROPN
ejpam-6270	248	32	b.	b.	PROPN
ejpam-6270	248	33	khalaf	khalaf	PROPN
ejpam-6270	248	34	/	/	SYM
ejpam-6270	248	35	eur	eur	PROPN
ejpam-6270	248	36	.	.	PUNCT
ejpam-6270	249	1	j.	j.	PROPN
ejpam-6270	249	2	pure	pure	PROPN
ejpam-6270	249	3	appl	appl	PROPN
ejpam-6270	249	4	.	.	PROPN
ejpam-6270	249	5	math	math	PROPN
ejpam-6270	249	6	,	,	PUNCT
ejpam-6270	249	7	18	18	NUM
ejpam-6270	249	8	(	(	PUNCT
ejpam-6270	249	9	3	3	NUM
ejpam-6270	249	10	)	)	PUNCT
ejpam-6270	249	11	(	(	PUNCT
ejpam-6270	249	12	2025	2025	NUM
ejpam-6270	249	13	)	)	PUNCT
ejpam-6270	249	14	,	,	PUNCT
ejpam-6270	249	15	6270	6270	NUM
ejpam-6270	249	16	10	10	NUM
ejpam-6270	249	17	of	of	ADP
ejpam-6270	249	18	17	17	NUM
ejpam-6270	249	19	u	u	NOUN
ejpam-6270	249	20	⊙	⊙	NOUN
ejpam-6270	249	21	v	v	ADP
ejpam-6270	249	22	⊆	⊆	NUM
ejpam-6270	249	23	w	w	NOUN
ejpam-6270	249	24	.	.	PUNCT
ejpam-6270	250	1	then	then	ADV
ejpam-6270	250	2	u	u	PROPN
ejpam-6270	250	3	is	be	AUX
ejpam-6270	250	4	a	a	DET
ejpam-6270	250	5	b	b	NOUN
ejpam-6270	250	6	-	-	PUNCT
ejpam-6270	250	7	open	open	ADJ
ejpam-6270	250	8	set	set	NOUN
ejpam-6270	250	9	and	and	CCONJ
ejpam-6270	250	10	v	v	NOUN
ejpam-6270	250	11	is	be	AUX
ejpam-6270	250	12	a	a	DET
ejpam-6270	250	13	b	b	NOUN
ejpam-6270	250	14	-	-	PUNCT
ejpam-6270	250	15	open	open	ADJ
ejpam-6270	250	16	set	set	NOUN
ejpam-6270	250	17	having	have	VERB
ejpam-6270	250	18	η	η	PROPN
ejpam-6270	250	19	.	.	PUNCT
ejpam-6270	251	1	if	if	SCONJ
ejpam-6270	251	2	u	u	PROPN
ejpam-6270	251	3	∩	∩	NOUN
ejpam-6270	251	4	v	v	ADP
ejpam-6270	251	5	̸=	̸=	PROPN
ejpam-6270	251	6	ϕ	ϕ	NOUN
ejpam-6270	251	7	,	,	PUNCT
ejpam-6270	251	8	that	that	PRON
ejpam-6270	251	9	is	is	ADV
ejpam-6270	251	10	mean	mean	VERB
ejpam-6270	251	11	there	there	PRON
ejpam-6270	251	12	is	be	VERB
ejpam-6270	251	13	a	a	DET
ejpam-6270	251	14	point	point	NOUN
ejpam-6270	251	15	θ	θ	X
ejpam-6270	251	16	∈	∈	PROPN
ejpam-6270	251	17	u	u	NOUN
ejpam-6270	251	18	∩v	∩v	NOUN
ejpam-6270	251	19	.	.	PUNCT
ejpam-6270	252	1	thus	thus	ADV
ejpam-6270	252	2	0	0	X
ejpam-6270	252	3	=	=	SYM
ejpam-6270	252	4	η⊙	η⊙	NUM
ejpam-6270	252	5	θ	θ	NOUN
ejpam-6270	252	6	∈	∈	NOUN
ejpam-6270	252	7	u	u	NOUN
ejpam-6270	252	8	⊙v	⊙v	NOUN
ejpam-6270	252	9	⊆	⊆	NUM
ejpam-6270	252	10	w	w	NOUN
ejpam-6270	252	11	that	that	PRON
ejpam-6270	252	12	is	be	AUX
ejpam-6270	252	13	a	a	DET
ejpam-6270	252	14	contradiction	contradiction	NOUN
ejpam-6270	252	15	.	.	PUNCT
ejpam-6270	253	1	case	case	NOUN
ejpam-6270	253	2	2	2	NUM
ejpam-6270	253	3	.	.	PUNCT
ejpam-6270	254	1	now	now	ADV
ejpam-6270	254	2	if	if	SCONJ
ejpam-6270	254	3	0	0	NUM
ejpam-6270	254	4	∈	∈	PROPN
ejpam-6270	254	5	w	w	NOUN
ejpam-6270	254	6	and	and	CCONJ
ejpam-6270	254	7	ζ⊙η	ζ⊙η	NOUN
ejpam-6270	254	8	/∈	/∈	PUNCT
ejpam-6270	255	1	w	w	INTJ
ejpam-6270	255	2	.	.	PUNCT
ejpam-6270	256	1	then	then	ADV
ejpam-6270	256	2	we	we	PRON
ejpam-6270	256	3	have	have	AUX
ejpam-6270	256	4	,	,	PUNCT
ejpam-6270	256	5	ζ⊙	ζ⊙	ADJ
ejpam-6270	256	6	ζ	ζ	NOUN
ejpam-6270	256	7	=	=	SYM
ejpam-6270	256	8	0	0	NUM
ejpam-6270	256	9	∈	∈	PROPN
ejpam-6270	256	10	w	w	NOUN
ejpam-6270	256	11	,	,	PUNCT
ejpam-6270	256	12	so	so	SCONJ
ejpam-6270	256	13	there	there	PRON
ejpam-6270	256	14	exist	exist	VERB
ejpam-6270	256	15	b	b	X
ejpam-6270	256	16	-	-	PUNCT
ejpam-6270	256	17	open	open	ADJ
ejpam-6270	256	18	sets	set	NOUN
ejpam-6270	256	19	u1	u1	NOUN
ejpam-6270	256	20	,	,	PUNCT
ejpam-6270	256	21	u2	u2	PROPN
ejpam-6270	256	22	having	have	VERB
ejpam-6270	256	23	ζ	ζ	NOUN
ejpam-6270	256	24	such	such	ADJ
ejpam-6270	256	25	that	that	DET
ejpam-6270	256	26	u1	u1	NOUN
ejpam-6270	256	27	⊙	⊙	PROPN
ejpam-6270	256	28	u2	u2	PROPN
ejpam-6270	256	29	∈	∈	PROPN
ejpam-6270	256	30	w	w	PROPN
ejpam-6270	256	31	.	.	PUNCT
ejpam-6270	257	1	obviously	obviously	ADV
ejpam-6270	257	2	,	,	PUNCT
ejpam-6270	257	3	u2	u2	PROPN
ejpam-6270	257	4	is	be	AUX
ejpam-6270	257	5	a	a	DET
ejpam-6270	257	6	b	b	NOUN
ejpam-6270	257	7	-	-	PUNCT
ejpam-6270	257	8	open	open	ADJ
ejpam-6270	257	9	set	set	NOUN
ejpam-6270	257	10	containing	contain	VERB
ejpam-6270	257	11	ζ	ζ	NOUN
ejpam-6270	257	12	and	and	CCONJ
ejpam-6270	257	13	does	do	AUX
ejpam-6270	257	14	not	not	PART
ejpam-6270	257	15	contains	contain	VERB
ejpam-6270	257	16	η	η	PROPN
ejpam-6270	257	17	.	.	PROPN
ejpam-6270	257	18	again	again	PROPN
ejpam-6270	257	19	η	η	PROPN
ejpam-6270	257	20	⊙	⊙	PROPN
ejpam-6270	257	21	η	η	PROPN
ejpam-6270	257	22	=	=	PROPN
ejpam-6270	257	23	0	0	NUM
ejpam-6270	257	24	∈	∈	PROPN
ejpam-6270	257	25	w	w	NOUN
ejpam-6270	257	26	,	,	PUNCT
ejpam-6270	257	27	so	so	SCONJ
ejpam-6270	257	28	there	there	PRON
ejpam-6270	257	29	exist	exist	VERB
ejpam-6270	257	30	b	b	X
ejpam-6270	257	31	-	-	PUNCT
ejpam-6270	257	32	open	open	ADJ
ejpam-6270	257	33	sets	set	NOUN
ejpam-6270	257	34	uη	uη	ADJ
ejpam-6270	257	35	and	and	CCONJ
ejpam-6270	257	36	vη	vη	PRON
ejpam-6270	257	37	containing	contain	VERB
ejpam-6270	257	38	η	η	PROPN
ejpam-6270	257	39	such	such	ADJ
ejpam-6270	257	40	that	that	SCONJ
ejpam-6270	257	41	uη	uη	ADP
ejpam-6270	257	42	⊙	⊙	PROPN
ejpam-6270	257	43	vη	vη	VERB
ejpam-6270	257	44	⊆	⊆	NUM
ejpam-6270	257	45	w	w	NOUN
ejpam-6270	257	46	.	.	PUNCT
ejpam-6270	258	1	hence	hence	ADV
ejpam-6270	258	2	,	,	PUNCT
ejpam-6270	258	3	uη	uη	PROPN
ejpam-6270	258	4	is	be	AUX
ejpam-6270	258	5	a	a	DET
ejpam-6270	258	6	b	b	NOUN
ejpam-6270	258	7	-	-	PUNCT
ejpam-6270	258	8	open	open	ADJ
ejpam-6270	258	9	set	set	NOUN
ejpam-6270	258	10	containing	contain	VERB
ejpam-6270	258	11	η	η	PROPN
ejpam-6270	258	12	but	but	CCONJ
ejpam-6270	258	13	not	not	PART
ejpam-6270	258	14	ζ	ζ	NOUN
ejpam-6270	258	15	.	.	PUNCT
ejpam-6270	259	1	therefore	therefore	ADV
ejpam-6270	259	2	,	,	PUNCT
ejpam-6270	259	3	(	(	PUNCT
ejpam-6270	259	4	w,⊙,ω	w,⊙,ω	PROPN
ejpam-6270	259	5	)	)	PUNCT
ejpam-6270	259	6	is	be	AUX
ejpam-6270	259	7	a	a	DET
ejpam-6270	259	8	b	b	PROPN
ejpam-6270	259	9	-	-	PUNCT
ejpam-6270	259	10	t1	t1	NOUN
ejpam-6270	259	11	space	space	NOUN
ejpam-6270	259	12	.	.	PUNCT
ejpam-6270	260	1	remark	remark	PROPN
ejpam-6270	260	2	2	2	NUM
ejpam-6270	260	3	.	.	PUNCT
ejpam-6270	261	1	the	the	DET
ejpam-6270	261	2	space	space	NOUN
ejpam-6270	261	3	(	(	PUNCT
ejpam-6270	261	4	w,⊙,ω	w,⊙,ω	PROPN
ejpam-6270	261	5	)	)	PUNCT
ejpam-6270	261	6	in	in	ADP
ejpam-6270	261	7	example	example	NOUN
ejpam-6270	261	8	4	4	NUM
ejpam-6270	261	9	is	be	AUX
ejpam-6270	261	10	a	a	DET
ejpam-6270	261	11	b	b	PROPN
ejpam-6270	261	12	-	-	PUNCT
ejpam-6270	261	13	t1	t1	NOUN
ejpam-6270	261	14	-	-	PUNCT
ejpam-6270	261	15	space	space	NOUN
ejpam-6270	261	16	which	which	PRON
ejpam-6270	261	17	is	be	AUX
ejpam-6270	261	18	not	not	PART
ejpam-6270	261	19	t0	t0	NOUN
ejpam-6270	261	20	.	.	PUNCT
ejpam-6270	262	1	definition	definition	NOUN
ejpam-6270	262	2	16	16	NUM
ejpam-6270	262	3	.	.	PUNCT
ejpam-6270	263	1	we	we	PRON
ejpam-6270	263	2	say	say	VERB
ejpam-6270	263	3	that	that	SCONJ
ejpam-6270	263	4	a	a	DET
ejpam-6270	263	5	topological	topological	ADJ
ejpam-6270	263	6	space	space	NOUN
ejpam-6270	263	7	(	(	PUNCT
ejpam-6270	263	8	w	w	PROPN
ejpam-6270	263	9	,	,	PUNCT
ejpam-6270	263	10	ω	ω	NOUN
ejpam-6270	263	11	)	)	PUNCT
ejpam-6270	263	12	is	be	AUX
ejpam-6270	263	13	bζ	bζ	NOUN
ejpam-6270	263	14	-	-	NOUN
ejpam-6270	263	15	space	space	NOUN
ejpam-6270	263	16	if	if	SCONJ
ejpam-6270	263	17	u1	u1	NOUN
ejpam-6270	263	18	,	,	PUNCT
ejpam-6270	263	19	u2	u2	PROPN
ejpam-6270	263	20	are	be	AUX
ejpam-6270	263	21	any	any	DET
ejpam-6270	263	22	b	b	NOUN
ejpam-6270	263	23	-	-	PUNCT
ejpam-6270	263	24	open	open	ADJ
ejpam-6270	263	25	subsets	subset	NOUN
ejpam-6270	263	26	of	of	ADP
ejpam-6270	263	27	w	w	NOUN
ejpam-6270	263	28	containing	contain	VERB
ejpam-6270	263	29	ζ	ζ	NOUN
ejpam-6270	263	30	,	,	PUNCT
ejpam-6270	263	31	then	then	ADV
ejpam-6270	263	32	there	there	PRON
ejpam-6270	263	33	exists	exist	VERB
ejpam-6270	263	34	a	a	DET
ejpam-6270	263	35	b	b	NOUN
ejpam-6270	263	36	-	-	PUNCT
ejpam-6270	263	37	open	open	ADJ
ejpam-6270	263	38	set	set	NOUN
ejpam-6270	263	39	u	u	PRON
ejpam-6270	263	40	such	such	ADJ
ejpam-6270	263	41	that	that	SCONJ
ejpam-6270	263	42	ζ	ζ	PROPN
ejpam-6270	263	43	∈	∈	PROPN
ejpam-6270	263	44	u	u	NOUN
ejpam-6270	263	45	⊆	⊆	NUM
ejpam-6270	263	46	u1	u1	NOUN
ejpam-6270	263	47	∩	∩	ADJ
ejpam-6270	263	48	u2	u2	PROPN
ejpam-6270	263	49	.	.	PUNCT
ejpam-6270	263	50	proposition	proposition	NOUN
ejpam-6270	263	51	12	12	NUM
ejpam-6270	263	52	.	.	PUNCT
ejpam-6270	264	1	in	in	ADP
ejpam-6270	264	2	a	a	DET
ejpam-6270	264	3	bζ	bζ	NOUN
ejpam-6270	264	4	tbd	tbd	NOUN
ejpam-6270	264	5	-	-	PUNCT
ejpam-6270	264	6	algebra	algebra	NOUN
ejpam-6270	264	7	(	(	PUNCT
ejpam-6270	264	8	w,⊙,ω	w,⊙,ω	PROPN
ejpam-6270	264	9	)	)	PUNCT
ejpam-6270	264	10	.	.	PUNCT
ejpam-6270	265	1	if	if	SCONJ
ejpam-6270	265	2	w	w	NOUN
ejpam-6270	265	3	is	be	AUX
ejpam-6270	265	4	an	an	DET
ejpam-6270	265	5	open	open	ADJ
ejpam-6270	265	6	set	set	NOUN
ejpam-6270	265	7	having	have	VERB
ejpam-6270	265	8	0	0	NUM
ejpam-6270	265	9	,	,	PUNCT
ejpam-6270	265	10	then	then	ADV
ejpam-6270	265	11	for	for	ADP
ejpam-6270	265	12	all	all	PRON
ejpam-6270	265	13	ζ	ζ	NOUN
ejpam-6270	265	14	∈	∈	NOUN
ejpam-6270	265	15	w	w	NOUN
ejpam-6270	265	16	there	there	PRON
ejpam-6270	265	17	exists	exist	VERB
ejpam-6270	265	18	a	a	DET
ejpam-6270	265	19	b	b	NOUN
ejpam-6270	265	20	-	-	PUNCT
ejpam-6270	265	21	open	open	ADJ
ejpam-6270	265	22	set	set	NOUN
ejpam-6270	265	23	u	u	NOUN
ejpam-6270	265	24	having	have	VERB
ejpam-6270	265	25	ζ	ζ	NOUN
ejpam-6270	265	26	such	such	ADJ
ejpam-6270	265	27	that	that	SCONJ
ejpam-6270	265	28	u	u	PROPN
ejpam-6270	265	29	⊙	⊙	VERB
ejpam-6270	265	30	u	u	NOUN
ejpam-6270	265	31	⊆	⊆	NUM
ejpam-6270	265	32	w	w	NOUN
ejpam-6270	265	33	.	.	PUNCT
ejpam-6270	266	1	proof	proof	NOUN
ejpam-6270	266	2	.	.	PUNCT
ejpam-6270	267	1	let	let	VERB
ejpam-6270	267	2	w	w	NOUN
ejpam-6270	267	3	be	be	AUX
ejpam-6270	267	4	an	an	DET
ejpam-6270	267	5	open	open	ADJ
ejpam-6270	267	6	set	set	NOUN
ejpam-6270	267	7	having	have	VERB
ejpam-6270	267	8	0	0	NUM
ejpam-6270	267	9	.	.	PUNCT
ejpam-6270	268	1	we	we	PRON
ejpam-6270	268	2	have	have	VERB
ejpam-6270	268	3	ζ	ζ	NOUN
ejpam-6270	268	4	⊙	⊙	X
ejpam-6270	268	5	ζ	ζ	X
ejpam-6270	268	6	=	=	SYM
ejpam-6270	268	7	0	0	NUM
ejpam-6270	268	8	for	for	SCONJ
ejpam-6270	268	9	all	all	DET
ejpam-6270	268	10	ζ	ζ	PROPN
ejpam-6270	268	11	∈	∈	PROPN
ejpam-6270	268	12	w	w	NOUN
ejpam-6270	268	13	and	and	CCONJ
ejpam-6270	268	14	w	w	PROPN
ejpam-6270	268	15	is	be	AUX
ejpam-6270	268	16	tbd	tbd	NOUN
ejpam-6270	268	17	-	-	PUNCT
ejpam-6270	268	18	algebra	algebra	NOUN
ejpam-6270	268	19	,	,	PUNCT
ejpam-6270	268	20	so	so	SCONJ
ejpam-6270	268	21	there	there	PRON
ejpam-6270	268	22	exist	exist	VERB
ejpam-6270	268	23	b	b	X
ejpam-6270	268	24	-	-	PUNCT
ejpam-6270	268	25	open	open	ADJ
ejpam-6270	268	26	sets	set	NOUN
ejpam-6270	268	27	u1	u1	NOUN
ejpam-6270	268	28	,	,	PUNCT
ejpam-6270	268	29	u2	u2	PROPN
ejpam-6270	268	30	having	have	VERB
ejpam-6270	268	31	ζ	ζ	NOUN
ejpam-6270	268	32	such	such	ADJ
ejpam-6270	268	33	that	that	DET
ejpam-6270	268	34	u1	u1	NOUN
ejpam-6270	268	35	⊙	⊙	PROPN
ejpam-6270	268	36	u2	u2	PROPN
ejpam-6270	268	37	⊆	⊆	NUM
ejpam-6270	268	38	w	w	NOUN
ejpam-6270	268	39	.	.	PUNCT
ejpam-6270	269	1	since	since	SCONJ
ejpam-6270	269	2	w	w	PROPN
ejpam-6270	269	3	is	be	AUX
ejpam-6270	269	4	a	a	DET
ejpam-6270	269	5	bζ	bζ	NOUN
ejpam-6270	269	6	space	space	NOUN
ejpam-6270	269	7	,	,	PUNCT
ejpam-6270	269	8	so	so	SCONJ
ejpam-6270	269	9	there	there	PRON
ejpam-6270	269	10	exists	exist	VERB
ejpam-6270	269	11	a	a	DET
ejpam-6270	269	12	b	b	NOUN
ejpam-6270	269	13	-	-	PUNCT
ejpam-6270	269	14	open	open	ADJ
ejpam-6270	269	15	set	set	NOUN
ejpam-6270	269	16	u	u	NOUN
ejpam-6270	269	17	⊆	⊆	NUM
ejpam-6270	269	18	u1	u1	NOUN
ejpam-6270	269	19	∩	∩	NOUN
ejpam-6270	269	20	u2	u2	NOUN
ejpam-6270	269	21	.	.	PUNCT
ejpam-6270	270	1	therefore	therefore	ADV
ejpam-6270	270	2	,	,	PUNCT
ejpam-6270	270	3	we	we	PRON
ejpam-6270	270	4	obtain	obtain	VERB
ejpam-6270	270	5	that	that	SCONJ
ejpam-6270	270	6	u	u	PROPN
ejpam-6270	270	7	⊙	⊙	NOUN
ejpam-6270	270	8	u	u	NOUN
ejpam-6270	270	9	⊆	⊆	NUM
ejpam-6270	270	10	w	w	NOUN
ejpam-6270	270	11	.	.	PUNCT
ejpam-6270	271	1	proposition	proposition	NOUN
ejpam-6270	271	2	13	13	NUM
ejpam-6270	271	3	.	.	PUNCT
ejpam-6270	272	1	in	in	ADP
ejpam-6270	272	2	a	a	DET
ejpam-6270	272	3	bζ	bζ	NOUN
ejpam-6270	272	4	tbd	tbd	NOUN
ejpam-6270	272	5	-	-	PUNCT
ejpam-6270	272	6	algebra	algebra	NOUN
ejpam-6270	272	7	,	,	PUNCT
ejpam-6270	272	8	if	if	SCONJ
ejpam-6270	272	9	(	(	PUNCT
ejpam-6270	272	10	w,⊙,ω	w,⊙,ω	PROPN
ejpam-6270	272	11	)	)	PUNCT
ejpam-6270	272	12	is	be	AUX
ejpam-6270	272	13	an	an	DET
ejpam-6270	272	14	extremally	extremally	ADV
ejpam-6270	272	15	disconnected	disconnect	VERB
ejpam-6270	272	16	submaximal	submaximal	ADJ
ejpam-6270	272	17	t0	t0	PROPN
ejpam-6270	272	18	space	space	NOUN
ejpam-6270	272	19	,	,	PUNCT
ejpam-6270	272	20	then	then	ADV
ejpam-6270	272	21	it	it	PRON
ejpam-6270	272	22	is	be	AUX
ejpam-6270	272	23	b	b	NOUN
ejpam-6270	272	24	-	-	PUNCT
ejpam-6270	272	25	t2	t2	NOUN
ejpam-6270	272	26	.	.	PUNCT
ejpam-6270	273	1	proof	proof	NOUN
ejpam-6270	273	2	.	.	PUNCT
ejpam-6270	274	1	let	let	VERB
ejpam-6270	274	2	ζ	ζ	NOUN
ejpam-6270	274	3	,	,	PUNCT
ejpam-6270	274	4	η	η	PROPN
ejpam-6270	274	5	∈	∈	PROPN
ejpam-6270	274	6	w	w	PROPN
ejpam-6270	274	7	,	,	PUNCT
ejpam-6270	274	8	so	so	CCONJ
ejpam-6270	274	9	either	either	CCONJ
ejpam-6270	274	10	ζ⊙	ζ⊙	PROPN
ejpam-6270	274	11	η	η	PROPN
ejpam-6270	274	12	̸=	̸=	PROPN
ejpam-6270	274	13	0	0	NUM
ejpam-6270	274	14	or	or	CCONJ
ejpam-6270	274	15	η⊙	η⊙	VERB
ejpam-6270	274	16	ζ	ζ	NOUN
ejpam-6270	274	17	̸=	̸=	PROPN
ejpam-6270	274	18	0	0	NUM
ejpam-6270	274	19	.	.	PUNCT
ejpam-6270	275	1	assume	assume	VERB
ejpam-6270	275	2	that	that	SCONJ
ejpam-6270	275	3	ζ⊙	ζ⊙	NOUN
ejpam-6270	275	4	y	y	PROPN
ejpam-6270	275	5	̸=	̸=	PROPN
ejpam-6270	275	6	0	0	NUM
ejpam-6270	275	7	.	.	PUNCT
ejpam-6270	276	1	since	since	SCONJ
ejpam-6270	276	2	w	w	PROPN
ejpam-6270	276	3	is	be	AUX
ejpam-6270	276	4	t0	t0	NOUN
ejpam-6270	276	5	,	,	PUNCT
ejpam-6270	276	6	so	so	SCONJ
ejpam-6270	276	7	there	there	PRON
ejpam-6270	276	8	exists	exist	VERB
ejpam-6270	276	9	an	an	DET
ejpam-6270	276	10	open	open	ADJ
ejpam-6270	276	11	set	set	NOUN
ejpam-6270	276	12	w	w	ADP
ejpam-6270	276	13	having	have	VERB
ejpam-6270	276	14	either	either	CCONJ
ejpam-6270	276	15	ζ	ζ	PROPN
ejpam-6270	276	16	⊙	⊙	PROPN
ejpam-6270	276	17	η	η	PROPN
ejpam-6270	276	18	and	and	CCONJ
ejpam-6270	276	19	not	not	PART
ejpam-6270	276	20	having	have	VERB
ejpam-6270	276	21	0	0	NUM
ejpam-6270	276	22	or	or	CCONJ
ejpam-6270	276	23	conversely	conversely	ADV
ejpam-6270	276	24	.	.	PUNCT
ejpam-6270	277	1	if	if	SCONJ
ejpam-6270	277	2	ζ⊙	ζ⊙	PROPN
ejpam-6270	277	3	η	η	PROPN
ejpam-6270	277	4	∈	∈	PROPN
ejpam-6270	277	5	w	w	PROPN
ejpam-6270	277	6	and	and	CCONJ
ejpam-6270	277	7	0	0	NUM
ejpam-6270	277	8	/∈	/∈	PUNCT
ejpam-6270	278	1	w	w	INTJ
ejpam-6270	278	2	,	,	PUNCT
ejpam-6270	278	3	so	so	ADV
ejpam-6270	278	4	by	by	ADP
ejpam-6270	278	5	proposition	proposition	NOUN
ejpam-6270	278	6	9	9	NUM
ejpam-6270	278	7	,	,	PUNCT
ejpam-6270	278	8	there	there	PRON
ejpam-6270	278	9	exist	exist	VERB
ejpam-6270	278	10	two	two	NUM
ejpam-6270	278	11	disjoint	disjoint	NOUN
ejpam-6270	278	12	b	b	X
ejpam-6270	278	13	-	-	PUNCT
ejpam-6270	278	14	open	open	ADJ
ejpam-6270	278	15	sets	set	NOUN
ejpam-6270	278	16	containing	contain	VERB
ejpam-6270	278	17	ζ	ζ	NOUN
ejpam-6270	278	18	and	and	CCONJ
ejpam-6270	278	19	η	η	PROPN
ejpam-6270	278	20	.	.	PROPN
ejpam-6270	279	1	if	if	SCONJ
ejpam-6270	279	2	ζ	ζ	PROPN
ejpam-6270	279	3	⊙	⊙	PROPN
ejpam-6270	279	4	η	η	PROPN
ejpam-6270	279	5	/∈	/∈	PROPN
ejpam-6270	279	6	w	w	PROPN
ejpam-6270	279	7	and	and	CCONJ
ejpam-6270	279	8	0	0	NUM
ejpam-6270	279	9	∈	∈	PROPN
ejpam-6270	279	10	w	w	NOUN
ejpam-6270	279	11	,	,	PUNCT
ejpam-6270	279	12	then	then	ADV
ejpam-6270	279	13	we	we	PRON
ejpam-6270	279	14	have	have	VERB
ejpam-6270	279	15	,	,	PUNCT
ejpam-6270	279	16	ζ	ζ	PROPN
ejpam-6270	279	17	⊙	⊙	X
ejpam-6270	279	18	ζ	ζ	NOUN
ejpam-6270	279	19	=	=	SYM
ejpam-6270	279	20	0	0	NUM
ejpam-6270	279	21	∈	∈	PROPN
ejpam-6270	279	22	w	w	NOUN
ejpam-6270	279	23	,	,	PUNCT
ejpam-6270	279	24	so	so	SCONJ
ejpam-6270	279	25	there	there	PRON
ejpam-6270	279	26	exist	exist	VERB
ejpam-6270	279	27	b	b	X
ejpam-6270	279	28	-	-	PUNCT
ejpam-6270	279	29	open	open	ADJ
ejpam-6270	279	30	sets	set	NOUN
ejpam-6270	279	31	u1	u1	NOUN
ejpam-6270	279	32	,	,	PUNCT
ejpam-6270	279	33	u2	u2	NOUN
ejpam-6270	279	34	containing	contain	VERB
ejpam-6270	279	35	ζ	ζ	PROPN
ejpam-6270	280	1	such	such	DET
ejpam-6270	280	2	that	that	DET
ejpam-6270	280	3	u1	u1	NOUN
ejpam-6270	280	4	⊙	⊙	PROPN
ejpam-6270	280	5	u2	u2	PROPN
ejpam-6270	280	6	∈	∈	PROPN
ejpam-6270	280	7	w	w	PROPN
ejpam-6270	280	8	.	.	PUNCT
ejpam-6270	281	1	since	since	SCONJ
ejpam-6270	281	2	w	w	PROPN
ejpam-6270	281	3	is	be	AUX
ejpam-6270	281	4	a	a	DET
ejpam-6270	281	5	bζ	bζ	NOUN
ejpam-6270	281	6	space	space	NOUN
ejpam-6270	281	7	,	,	PUNCT
ejpam-6270	281	8	so	so	SCONJ
ejpam-6270	281	9	there	there	PRON
ejpam-6270	281	10	exists	exist	VERB
ejpam-6270	281	11	a	a	DET
ejpam-6270	281	12	b	b	NOUN
ejpam-6270	281	13	-	-	PUNCT
ejpam-6270	281	14	open	open	ADJ
ejpam-6270	281	15	set	set	NOUN
ejpam-6270	281	16	u	u	PRON
ejpam-6270	281	17	such	such	ADJ
ejpam-6270	281	18	that	that	SCONJ
ejpam-6270	281	19	ζ	ζ	PROPN
ejpam-6270	281	20	∈	∈	PROPN
ejpam-6270	281	21	u	u	NOUN
ejpam-6270	281	22	⊆	⊆	NUM
ejpam-6270	281	23	u1	u1	NOUN
ejpam-6270	281	24	∩	∩	ADJ
ejpam-6270	281	25	u2	u2	NOUN
ejpam-6270	281	26	implies	imply	VERB
ejpam-6270	281	27	that	that	SCONJ
ejpam-6270	281	28	u	u	NOUN
ejpam-6270	281	29	is	be	AUX
ejpam-6270	281	30	a	a	DET
ejpam-6270	281	31	b	b	NOUN
ejpam-6270	281	32	-	-	PUNCT
ejpam-6270	281	33	open	open	ADJ
ejpam-6270	281	34	set	set	NOUN
ejpam-6270	281	35	containing	contain	VERB
ejpam-6270	281	36	ζ	ζ	PROPN
ejpam-6270	281	37	such	such	DET
ejpam-6270	281	38	that	that	SCONJ
ejpam-6270	281	39	u	u	PROPN
ejpam-6270	281	40	⊙	⊙	VERB
ejpam-6270	281	41	u	u	NOUN
ejpam-6270	281	42	⊆	⊆	NUM
ejpam-6270	281	43	w	w	NOUN
ejpam-6270	281	44	.	.	PUNCT
ejpam-6270	282	1	again	again	ADV
ejpam-6270	282	2	η	η	PROPN
ejpam-6270	282	3	⊙	⊙	PROPN
ejpam-6270	282	4	η	η	PROPN
ejpam-6270	282	5	=	=	PROPN
ejpam-6270	282	6	0	0	NUM
ejpam-6270	282	7	∈	∈	PROPN
ejpam-6270	282	8	w	w	NOUN
ejpam-6270	282	9	,	,	PUNCT
ejpam-6270	282	10	so	so	SCONJ
ejpam-6270	282	11	there	there	PRON
ejpam-6270	282	12	exists	exist	VERB
ejpam-6270	282	13	a	a	DET
ejpam-6270	282	14	b	b	NOUN
ejpam-6270	282	15	-	-	PUNCT
ejpam-6270	282	16	open	open	ADJ
ejpam-6270	282	17	setv	setv	NOUN
ejpam-6270	282	18	containing	contain	VERB
ejpam-6270	282	19	η	η	PROPN
ejpam-6270	282	20	such	such	ADJ
ejpam-6270	282	21	that	that	DET
ejpam-6270	282	22	v	v	NOUN
ejpam-6270	282	23	⊙	⊙	NOUN
ejpam-6270	282	24	v	v	ADP
ejpam-6270	282	25	⊆	⊆	NUM
ejpam-6270	282	26	w	w	NOUN
ejpam-6270	282	27	.	.	PUNCT
ejpam-6270	283	1	hence	hence	ADV
ejpam-6270	283	2	,	,	PUNCT
ejpam-6270	283	3	we	we	PRON
ejpam-6270	283	4	have	have	VERB
ejpam-6270	283	5	η	η	PROPN
ejpam-6270	283	6	/∈	/∈	PROPN
ejpam-6270	283	7	u	u	PROPN
ejpam-6270	283	8	and	and	CCONJ
ejpam-6270	283	9	ζ	ζ	NOUN
ejpam-6270	283	10	/∈	/∈	NOUN
ejpam-6270	283	11	v	v	NOUN
ejpam-6270	283	12	because	because	SCONJ
ejpam-6270	283	13	we	we	PRON
ejpam-6270	283	14	get	get	VERB
ejpam-6270	283	15	a	a	DET
ejpam-6270	283	16	contradiction	contradiction	NOUN
ejpam-6270	283	17	.	.	PUNCT
ejpam-6270	284	1	since	since	SCONJ
ejpam-6270	284	2	w	w	PROPN
ejpam-6270	284	3	is	be	AUX
ejpam-6270	284	4	extremally	extremally	ADV
ejpam-6270	284	5	disconnected	disconnect	VERB
ejpam-6270	284	6	,	,	PUNCT
ejpam-6270	284	7	so	so	ADV
ejpam-6270	284	8	by	by	ADP
ejpam-6270	284	9	lemma	lemma	PROPN
ejpam-6270	284	10	4	4	NUM
ejpam-6270	284	11	,	,	PUNCT
ejpam-6270	284	12	w	w	ADJ
ejpam-6270	284	13	\	\	PROPN
ejpam-6270	284	14	u	u	NOUN
ejpam-6270	284	15	and	and	CCONJ
ejpam-6270	284	16	w	w	PROPN
ejpam-6270	284	17	\	\	PROPN
ejpam-6270	284	18	v	v	PROPN
ejpam-6270	284	19	are	be	AUX
ejpam-6270	284	20	dense	dense	ADJ
ejpam-6270	284	21	in	in	ADP
ejpam-6270	284	22	w.	w.	PROPN
ejpam-6270	284	23	since	since	SCONJ
ejpam-6270	284	24	w	w	PROPN
ejpam-6270	284	25	is	be	AUX
ejpam-6270	284	26	submaximal	submaximal	ADJ
ejpam-6270	284	27	,	,	PUNCT
ejpam-6270	284	28	so	so	ADV
ejpam-6270	284	29	by	by	ADP
ejpam-6270	284	30	definition	definition	NOUN
ejpam-6270	284	31	2	2	NUM
ejpam-6270	284	32	,	,	PUNCT
ejpam-6270	284	33	w	w	NOUN
ejpam-6270	284	34	\u	\u	NOUN
ejpam-6270	284	35	and	and	CCONJ
ejpam-6270	284	36	w	w	PROPN
ejpam-6270	284	37	\	\	PROPN
ejpam-6270	284	38	v	v	NOUN
ejpam-6270	284	39	are	be	AUX
ejpam-6270	284	40	open	open	ADJ
ejpam-6270	284	41	.	.	PUNCT
ejpam-6270	285	1	thus	thus	ADV
ejpam-6270	285	2	,	,	PUNCT
ejpam-6270	285	3	ζ	ζ	PROPN
ejpam-6270	285	4	∈	∈	PROPN
ejpam-6270	285	5	u	u	NOUN
ejpam-6270	285	6	∩	∩	NOUN
ejpam-6270	285	7	(	(	PUNCT
ejpam-6270	285	8	w	w	PROPN
ejpam-6270	285	9	\	\	PROPN
ejpam-6270	285	10	v	v	NOUN
ejpam-6270	285	11	)	)	PUNCT
ejpam-6270	285	12	and	and	CCONJ
ejpam-6270	285	13	η	η	PROPN
ejpam-6270	285	14	∈	∈	PROPN
ejpam-6270	285	15	v	v	ADP
ejpam-6270	285	16	∩	∩	NOUN
ejpam-6270	285	17	(	(	PUNCT
ejpam-6270	285	18	w	w	PROPN
ejpam-6270	285	19	\	\	PROPN
ejpam-6270	285	20	u	u	NOUN
ejpam-6270	285	21	)	)	PUNCT
ejpam-6270	285	22	.	.	PUNCT
ejpam-6270	286	1	obviously	obviously	ADV
ejpam-6270	286	2	,	,	PUNCT
ejpam-6270	286	3	u	u	PROPN
ejpam-6270	286	4	∩	∩	NOUN
ejpam-6270	286	5	(	(	PUNCT
ejpam-6270	286	6	w	w	PROPN
ejpam-6270	286	7	\	\	PROPN
ejpam-6270	286	8	v	v	NOUN
ejpam-6270	286	9	)	)	PUNCT
ejpam-6270	286	10	and	and	CCONJ
ejpam-6270	286	11	v	v	ADP
ejpam-6270	286	12	∩	∩	NOUN
ejpam-6270	286	13	(	(	PUNCT
ejpam-6270	286	14	w	w	PROPN
ejpam-6270	286	15	\	\	PROPN
ejpam-6270	286	16	u	u	NOUN
ejpam-6270	286	17	)	)	PUNCT
ejpam-6270	286	18	are	be	AUX
ejpam-6270	286	19	disjoint	disjoint	ADJ
ejpam-6270	286	20	b	b	X
ejpam-6270	286	21	-	-	PUNCT
ejpam-6270	286	22	open	open	ADJ
ejpam-6270	286	23	sets	set	NOUN
ejpam-6270	286	24	in	in	ADP
ejpam-6270	286	25	w.	w.	PROPN
ejpam-6270	286	26	hence	hence	PROPN
ejpam-6270	286	27	,	,	PUNCT
ejpam-6270	286	28	w	w	PROPN
ejpam-6270	286	29	is	be	AUX
ejpam-6270	286	30	b	b	NOUN
ejpam-6270	286	31	-	-	PUNCT
ejpam-6270	286	32	t2	t2	NOUN
ejpam-6270	286	33	.	.	PUNCT
ejpam-6270	287	1	proposition	proposition	NOUN
ejpam-6270	287	2	14	14	NUM
ejpam-6270	287	3	.	.	PUNCT
ejpam-6270	288	1	if	if	SCONJ
ejpam-6270	288	2	z	z	NOUN
ejpam-6270	288	3	is	be	AUX
ejpam-6270	288	4	an	an	DET
ejpam-6270	288	5	open	open	ADJ
ejpam-6270	288	6	d	d	NOUN
ejpam-6270	288	7	-	-	PUNCT
ejpam-6270	288	8	subalgebra	subalgebra	NOUN
ejpam-6270	288	9	of	of	ADP
ejpam-6270	288	10	a	a	DET
ejpam-6270	288	11	tbd	tbd	NOUN
ejpam-6270	288	12	-	-	PUNCT
ejpam-6270	288	13	algebra	algebra	NOUN
ejpam-6270	288	14	w	w	NOUN
ejpam-6270	288	15	,	,	PUNCT
ejpam-6270	288	16	then	then	ADV
ejpam-6270	288	17	z	z	PROPN
ejpam-6270	288	18	is	be	AUX
ejpam-6270	288	19	also	also	ADV
ejpam-6270	288	20	a	a	DET
ejpam-6270	288	21	tbd	tbd	NOUN
ejpam-6270	288	22	-	-	PUNCT
ejpam-6270	288	23	algebra	algebra	NOUN
ejpam-6270	288	24	.	.	PUNCT
ejpam-6270	289	1	proof	proof	NOUN
ejpam-6270	289	2	.	.	PUNCT
ejpam-6270	290	1	suppose	suppose	VERB
ejpam-6270	290	2	that	that	SCONJ
ejpam-6270	290	3	ζ	ζ	NOUN
ejpam-6270	290	4	,	,	PUNCT
ejpam-6270	290	5	η	η	PROPN
ejpam-6270	290	6	∈	∈	PROPN
ejpam-6270	290	7	z	z	PROPN
ejpam-6270	290	8	and	and	CCONJ
ejpam-6270	290	9	let	let	VERB
ejpam-6270	290	10	u	u	PRON
ejpam-6270	290	11	be	be	AUX
ejpam-6270	290	12	an	an	DET
ejpam-6270	290	13	open	open	ADJ
ejpam-6270	290	14	set	set	NOUN
ejpam-6270	290	15	in	in	ADP
ejpam-6270	290	16	the	the	DET
ejpam-6270	290	17	subspace	subspace	NOUN
ejpam-6270	290	18	z	z	NOUN
ejpam-6270	290	19	containing	contain	VERB
ejpam-6270	290	20	ζ	ζ	PROPN
ejpam-6270	290	21	⊙	⊙	PROPN
ejpam-6270	290	22	η	η	PROPN
ejpam-6270	290	23	.	.	PROPN
ejpam-6270	290	24	since	since	SCONJ
ejpam-6270	290	25	z	z	PROPN
ejpam-6270	290	26	is	be	AUX
ejpam-6270	290	27	open	open	ADJ
ejpam-6270	290	28	in	in	ADP
ejpam-6270	290	29	w	w	PROPN
ejpam-6270	290	30	,	,	PUNCT
ejpam-6270	290	31	so	so	CCONJ
ejpam-6270	290	32	u	u	NOUN
ejpam-6270	290	33	is	be	AUX
ejpam-6270	290	34	open	open	ADJ
ejpam-6270	290	35	in	in	ADP
ejpam-6270	290	36	w.	w.	PROPN
ejpam-6270	290	37	since	since	SCONJ
ejpam-6270	290	38	w	w	PROPN
ejpam-6270	290	39	is	be	AUX
ejpam-6270	290	40	a	a	DET
ejpam-6270	290	41	tbd	tbd	NOUN
ejpam-6270	290	42	-	-	PUNCT
ejpam-6270	290	43	algebra	algebra	NOUN
ejpam-6270	290	44	,	,	PUNCT
ejpam-6270	290	45	so	so	SCONJ
ejpam-6270	290	46	there	there	PRON
ejpam-6270	290	47	exist	exist	VERB
ejpam-6270	290	48	b	b	X
ejpam-6270	290	49	-	-	PUNCT
ejpam-6270	290	50	open	open	ADJ
ejpam-6270	290	51	sets	set	NOUN
ejpam-6270	290	52	h	h	NOUN
ejpam-6270	290	53	,	,	PUNCT
ejpam-6270	290	54	g	g	PROPN
ejpam-6270	290	55	in	in	ADP
ejpam-6270	290	56	w	w	NOUN
ejpam-6270	290	57	having	have	VERB
ejpam-6270	290	58	ζ	ζ	NOUN
ejpam-6270	290	59	and	and	CCONJ
ejpam-6270	290	60	η	η	NOUN
ejpam-6270	290	61	respectively	respectively	ADV
ejpam-6270	290	62	such	such	ADJ
ejpam-6270	290	63	that	that	SCONJ
ejpam-6270	290	64	h	h	NOUN
ejpam-6270	290	65	⊙g	⊙g	NOUN
ejpam-6270	290	66	⊆	⊆	NUM
ejpam-6270	290	67	u	u	NOUN
ejpam-6270	290	68	.	.	PUNCT
ejpam-6270	291	1	then	then	ADV
ejpam-6270	291	2	,	,	PUNCT
ejpam-6270	291	3	by	by	ADP
ejpam-6270	291	4	lemma	lemma	PROPN
ejpam-6270	291	5	1	1	NUM
ejpam-6270	291	6	,	,	PUNCT
ejpam-6270	291	7	we	we	PRON
ejpam-6270	291	8	have	have	VERB
ejpam-6270	291	9	o1	o1	NOUN
ejpam-6270	291	10	=	=	SYM
ejpam-6270	291	11	h	h	NOUN
ejpam-6270	291	12	∩	∩	PROPN
ejpam-6270	291	13	z	z	PROPN
ejpam-6270	291	14	and	and	CCONJ
ejpam-6270	291	15	o2	o2	PROPN
ejpam-6270	291	16	=	=	SYM
ejpam-6270	291	17	g	g	PROPN
ejpam-6270	291	18	∩	∩	NOUN
ejpam-6270	291	19	z	z	NOUN
ejpam-6270	291	20	are	be	AUX
ejpam-6270	291	21	b	b	ADJ
ejpam-6270	291	22	-	-	PUNCT
ejpam-6270	291	23	open	open	ADJ
ejpam-6270	291	24	sets	set	NOUN
ejpam-6270	291	25	in	in	ADP
ejpam-6270	291	26	z	z	NOUN
ejpam-6270	291	27	having	have	VERB
ejpam-6270	291	28	ζ	ζ	NOUN
ejpam-6270	291	29	and	and	CCONJ
ejpam-6270	291	30	η	η	NOUN
ejpam-6270	291	31	respectively	respectively	ADV
ejpam-6270	291	32	and	and	CCONJ
ejpam-6270	291	33	obviously	obviously	ADV
ejpam-6270	291	34	,	,	PUNCT
ejpam-6270	291	35	o1	o1	VERB
ejpam-6270	291	36	⊙o2	⊙o2	PROPN
ejpam-6270	291	37	⊆	⊆	NUM
ejpam-6270	291	38	h	h	NOUN
ejpam-6270	291	39	⊙g	⊙g	NOUN
ejpam-6270	291	40	⊆	⊆	NUM
ejpam-6270	291	41	u	u	NOUN
ejpam-6270	291	42	.given	.given	PUNCT
ejpam-6270	291	43	the	the	DET
ejpam-6270	291	44	proof	proof	NOUN
ejpam-6270	291	45	.	.	PUNCT
ejpam-6270	292	1	m.	m.	NOUN
ejpam-6270	292	2	w.	w.	PROPN
ejpam-6270	292	3	abdulqader	abdulqader	PROPN
ejpam-6270	292	4	,	,	PUNCT
ejpam-6270	292	5	a.	a.	PROPN
ejpam-6270	292	6	b.	b.	PROPN
ejpam-6270	292	7	khalaf	khalaf	PROPN
ejpam-6270	292	8	/	/	SYM
ejpam-6270	292	9	eur	eur	PROPN
ejpam-6270	292	10	.	.	PUNCT
ejpam-6270	293	1	j.	j.	PROPN
ejpam-6270	293	2	pure	pure	PROPN
ejpam-6270	293	3	appl	appl	PROPN
ejpam-6270	293	4	.	.	PROPN
ejpam-6270	293	5	math	math	PROPN
ejpam-6270	293	6	,	,	PUNCT
ejpam-6270	293	7	18	18	NUM
ejpam-6270	293	8	(	(	PUNCT
ejpam-6270	293	9	3	3	NUM
ejpam-6270	293	10	)	)	PUNCT
ejpam-6270	293	11	(	(	PUNCT
ejpam-6270	293	12	2025	2025	NUM
ejpam-6270	293	13	)	)	PUNCT
ejpam-6270	293	14	,	,	PUNCT
ejpam-6270	293	15	6270	6270	NUM
ejpam-6270	293	16	11	11	NUM
ejpam-6270	293	17	of	of	ADP
ejpam-6270	293	18	17	17	NUM
ejpam-6270	293	19	proposition	proposition	NOUN
ejpam-6270	293	20	15	15	NUM
ejpam-6270	293	21	.	.	PUNCT
ejpam-6270	294	1	if	if	SCONJ
ejpam-6270	294	2	i	i	PRON
ejpam-6270	294	3	is	be	AUX
ejpam-6270	294	4	an	an	DET
ejpam-6270	294	5	ideal	ideal	NOUN
ejpam-6270	294	6	in	in	ADP
ejpam-6270	294	7	a	a	DET
ejpam-6270	294	8	tbd	tbd	NOUN
ejpam-6270	294	9	-	-	NOUN
ejpam-6270	294	10	algebra	algebra	NOUN
ejpam-6270	294	11	w	w	NOUN
ejpam-6270	294	12	with	with	ADP
ejpam-6270	294	13	0	0	NUM
ejpam-6270	294	14	∈	∈	PROPN
ejpam-6270	294	15	int(i	int(i	PROPN
ejpam-6270	294	16	)	)	PUNCT
ejpam-6270	294	17	,	,	PUNCT
ejpam-6270	294	18	then	then	ADV
ejpam-6270	294	19	i	i	PRON
ejpam-6270	294	20	is	be	AUX
ejpam-6270	294	21	b	b	NOUN
ejpam-6270	294	22	-	-	ADV
ejpam-6270	294	23	open	open	ADJ
ejpam-6270	294	24	.	.	PUNCT
ejpam-6270	295	1	proof	proof	NOUN
ejpam-6270	295	2	.	.	PUNCT
ejpam-6270	296	1	suppose	suppose	VERB
ejpam-6270	296	2	that	that	SCONJ
ejpam-6270	296	3	ζ	ζ	PROPN
ejpam-6270	296	4	∈	∈	PROPN
ejpam-6270	296	5	i.	i.	NOUN
ejpam-6270	296	6	since	since	SCONJ
ejpam-6270	296	7	0	0	NUM
ejpam-6270	296	8	∈	∈	PROPN
ejpam-6270	296	9	int(i	int(i	PROPN
ejpam-6270	296	10	)	)	PUNCT
ejpam-6270	296	11	,	,	PUNCT
ejpam-6270	296	12	then	then	ADV
ejpam-6270	296	13	there	there	PRON
ejpam-6270	296	14	is	be	VERB
ejpam-6270	296	15	an	an	DET
ejpam-6270	296	16	open	open	ADJ
ejpam-6270	296	17	set	set	NOUN
ejpam-6270	296	18	u	u	PRON
ejpam-6270	296	19	such	such	ADJ
ejpam-6270	296	20	that	that	DET
ejpam-6270	296	21	0	0	NUM
ejpam-6270	296	22	∈	∈	PROPN
ejpam-6270	296	23	u	u	NOUN
ejpam-6270	296	24	⊆	⊆	NUM
ejpam-6270	296	25	i.	i.	NOUN
ejpam-6270	296	26	since	since	SCONJ
ejpam-6270	296	27	w	w	PROPN
ejpam-6270	296	28	is	be	AUX
ejpam-6270	296	29	a	a	DET
ejpam-6270	296	30	tbd	tbd	NOUN
ejpam-6270	296	31	-	-	PUNCT
ejpam-6270	296	32	algebra	algebra	NOUN
ejpam-6270	296	33	,	,	PUNCT
ejpam-6270	296	34	then	then	ADV
ejpam-6270	296	35	there	there	PRON
ejpam-6270	296	36	exists	exist	VERB
ejpam-6270	296	37	a	a	DET
ejpam-6270	296	38	b	b	NOUN
ejpam-6270	296	39	-	-	PUNCT
ejpam-6270	296	40	open	open	ADJ
ejpam-6270	296	41	set	set	NOUN
ejpam-6270	296	42	v	v	ADP
ejpam-6270	296	43	having	have	VERB
ejpam-6270	296	44	ζ	ζ	NOUN
ejpam-6270	296	45	such	such	ADJ
ejpam-6270	296	46	that	that	DET
ejpam-6270	296	47	v	v	NOUN
ejpam-6270	296	48	⊙	⊙	NOUN
ejpam-6270	296	49	ζ	ζ	PROPN
ejpam-6270	296	50	⊆	⊆	NUM
ejpam-6270	296	51	u	u	NOUN
ejpam-6270	296	52	.	.	PUNCT
ejpam-6270	297	1	if	if	SCONJ
ejpam-6270	297	2	there	there	PRON
ejpam-6270	297	3	is	be	VERB
ejpam-6270	297	4	a	a	DET
ejpam-6270	297	5	point	point	NOUN
ejpam-6270	297	6	η	η	PROPN
ejpam-6270	297	7	∈	∈	PROPN
ejpam-6270	297	8	v	v	NOUN
ejpam-6270	297	9	∩	∩	NOUN
ejpam-6270	297	10	(	(	PUNCT
ejpam-6270	297	11	w	w	PROPN
ejpam-6270	297	12	\	\	PROPN
ejpam-6270	297	13	i	i	PROPN
ejpam-6270	297	14	)	)	PUNCT
ejpam-6270	297	15	,	,	PUNCT
ejpam-6270	297	16	so	so	SCONJ
ejpam-6270	297	17	we	we	PRON
ejpam-6270	297	18	get	get	VERB
ejpam-6270	297	19	η	η	PROPN
ejpam-6270	297	20	⊙	⊙	PROPN
ejpam-6270	297	21	ζ	ζ	PROPN
ejpam-6270	297	22	∈	∈	PROPN
ejpam-6270	297	23	i.	i.	NOUN
ejpam-6270	297	24	since	since	SCONJ
ejpam-6270	297	25	ζ	ζ	NOUN
ejpam-6270	297	26	∈	∈	PROPN
ejpam-6270	298	1	i	i	PRON
ejpam-6270	298	2	and	and	CCONJ
ejpam-6270	298	3	i	i	PRON
ejpam-6270	298	4	is	be	AUX
ejpam-6270	298	5	an	an	DET
ejpam-6270	298	6	ideal	ideal	NOUN
ejpam-6270	298	7	,	,	PUNCT
ejpam-6270	298	8	so	so	ADV
ejpam-6270	298	9	η	η	PROPN
ejpam-6270	298	10	∈	∈	PROPN
ejpam-6270	298	11	i	i	PRON
ejpam-6270	298	12	that	that	PRON
ejpam-6270	298	13	is	be	AUX
ejpam-6270	298	14	a	a	DET
ejpam-6270	298	15	contradiction	contradiction	NOUN
ejpam-6270	298	16	.	.	PUNCT
ejpam-6270	299	1	therefore	therefore	ADV
ejpam-6270	299	2	ζ	ζ	PROPN
ejpam-6270	299	3	∈	∈	PROPN
ejpam-6270	299	4	v	v	ADP
ejpam-6270	299	5	⊆	⊆	NUM
ejpam-6270	299	6	i	i	PRON
ejpam-6270	299	7	means	mean	VERB
ejpam-6270	299	8	that	that	SCONJ
ejpam-6270	299	9	i	i	PRON
ejpam-6270	299	10	is	be	AUX
ejpam-6270	299	11	b	b	NOUN
ejpam-6270	299	12	-	-	ADV
ejpam-6270	299	13	open	open	ADJ
ejpam-6270	299	14	.	.	PUNCT
ejpam-6270	300	1	example	example	NOUN
ejpam-6270	300	2	5	5	NUM
ejpam-6270	300	3	.	.	X
ejpam-6270	301	1	consider	consider	VERB
ejpam-6270	301	2	the	the	DET
ejpam-6270	301	3	d	d	NOUN
ejpam-6270	301	4	-	-	PUNCT
ejpam-6270	301	5	algebra	algebra	NOUN
ejpam-6270	301	6	(	(	PUNCT
ejpam-6270	301	7	w,⊙	w,⊙	PROPN
ejpam-6270	301	8	,	,	PUNCT
ejpam-6270	301	9	0	0	NUM
ejpam-6270	301	10	)	)	PUNCT
ejpam-6270	301	11	in	in	ADP
ejpam-6270	301	12	example	example	NOUN
ejpam-6270	302	1	1	1	X
ejpam-6270	302	2	.	.	PUNCT
ejpam-6270	303	1	we	we	PRON
ejpam-6270	303	2	define	define	VERB
ejpam-6270	303	3	a	a	DET
ejpam-6270	303	4	topology	topology	NOUN
ejpam-6270	303	5	ω	ω	NOUN
ejpam-6270	303	6	on	on	ADP
ejpam-6270	303	7	w	w	NOUN
ejpam-6270	303	8	as	as	SCONJ
ejpam-6270	303	9	follows	follow	VERB
ejpam-6270	303	10	:	:	PUNCT
ejpam-6270	303	11	ω	ω	NUM
ejpam-6270	303	12	=	=	SYM
ejpam-6270	303	13	{	{	PUNCT
ejpam-6270	303	14	ϕ	ϕ	NOUN
ejpam-6270	303	15	,	,	PUNCT
ejpam-6270	303	16	{	{	PUNCT
ejpam-6270	303	17	α	α	NOUN
ejpam-6270	303	18	,	,	PUNCT
ejpam-6270	303	19	β},w	β},w	NOUN
ejpam-6270	303	20	}	}	PUNCT
ejpam-6270	303	21	.	.	PUNCT
ejpam-6270	304	1	then	then	ADV
ejpam-6270	304	2	,	,	PUNCT
ejpam-6270	304	3	i	i	PRON
ejpam-6270	304	4	=	=	PUNCT
ejpam-6270	304	5	{	{	PUNCT
ejpam-6270	304	6	0	0	NUM
ejpam-6270	304	7	,	,	PUNCT
ejpam-6270	304	8	α	α	X
ejpam-6270	304	9	,	,	PUNCT
ejpam-6270	304	10	β	β	NOUN
ejpam-6270	304	11	}	}	PUNCT
ejpam-6270	304	12	is	be	AUX
ejpam-6270	304	13	an	an	DET
ejpam-6270	304	14	ideal	ideal	NOUN
ejpam-6270	304	15	which	which	PRON
ejpam-6270	304	16	is	be	AUX
ejpam-6270	304	17	b	b	NOUN
ejpam-6270	304	18	-	-	PUNCT
ejpam-6270	304	19	open	open	ADJ
ejpam-6270	304	20	but	but	CCONJ
ejpam-6270	304	21	0	0	NUM
ejpam-6270	304	22	/∈	/∈	SYM
ejpam-6270	304	23	int(i	int(i	NUM
ejpam-6270	304	24	)	)	PUNCT
ejpam-6270	304	25	.	.	PUNCT
ejpam-6270	305	1	proposition	proposition	NOUN
ejpam-6270	305	2	16	16	NUM
ejpam-6270	305	3	.	.	PUNCT
ejpam-6270	306	1	if	if	SCONJ
ejpam-6270	306	2	i	i	PRON
ejpam-6270	306	3	is	be	AUX
ejpam-6270	306	4	an	an	DET
ejpam-6270	306	5	open	open	ADJ
ejpam-6270	306	6	proper	proper	ADJ
ejpam-6270	306	7	ideal	ideal	NOUN
ejpam-6270	306	8	in	in	ADP
ejpam-6270	306	9	a	a	DET
ejpam-6270	306	10	tbd	tbd	NOUN
ejpam-6270	306	11	-	-	PUNCT
ejpam-6270	306	12	algebra	algebra	NOUN
ejpam-6270	306	13	w	w	NOUN
ejpam-6270	306	14	,	,	PUNCT
ejpam-6270	306	15	then	then	ADV
ejpam-6270	306	16	i	i	PRON
ejpam-6270	306	17	is	be	AUX
ejpam-6270	306	18	b	b	NOUN
ejpam-6270	306	19	-	-	PUNCT
ejpam-6270	306	20	closed	closed	ADJ
ejpam-6270	306	21	and	and	CCONJ
ejpam-6270	306	22	regular	regular	ADJ
ejpam-6270	306	23	open	open	ADJ
ejpam-6270	306	24	.	.	PUNCT
ejpam-6270	307	1	proof	proof	NOUN
ejpam-6270	307	2	.	.	PUNCT
ejpam-6270	308	1	suppose	suppose	VERB
ejpam-6270	308	2	that	that	SCONJ
ejpam-6270	308	3	ζ	ζ	PROPN
ejpam-6270	308	4	∈	∈	PROPN
ejpam-6270	308	5	w	w	PROPN
ejpam-6270	308	6	\	\	PROPN
ejpam-6270	308	7	i.	i.	NOUN
ejpam-6270	308	8	since	since	SCONJ
ejpam-6270	308	9	i	i	PRON
ejpam-6270	308	10	is	be	AUX
ejpam-6270	308	11	an	an	DET
ejpam-6270	308	12	ideal	ideal	NOUN
ejpam-6270	308	13	so	so	SCONJ
ejpam-6270	308	14	ζ	ζ	NOUN
ejpam-6270	308	15	⊙	⊙	X
ejpam-6270	308	16	ζ	ζ	X
ejpam-6270	308	17	=	=	SYM
ejpam-6270	308	18	0	0	NUM
ejpam-6270	308	19	∈	∈	PROPN
ejpam-6270	308	20	i.	i.	NOUN
ejpam-6270	308	21	since	since	SCONJ
ejpam-6270	308	22	w	w	PROPN
ejpam-6270	308	23	is	be	AUX
ejpam-6270	308	24	a	a	DET
ejpam-6270	308	25	tbd	tbd	NOUN
ejpam-6270	308	26	-	-	PUNCT
ejpam-6270	308	27	algebra	algebra	NOUN
ejpam-6270	308	28	,	,	PUNCT
ejpam-6270	308	29	so	so	SCONJ
ejpam-6270	308	30	there	there	PRON
ejpam-6270	308	31	exist	exist	VERB
ejpam-6270	308	32	b	b	X
ejpam-6270	308	33	-	-	PUNCT
ejpam-6270	308	34	open	open	ADJ
ejpam-6270	308	35	sets	set	NOUN
ejpam-6270	308	36	v	v	VERB
ejpam-6270	308	37	and	and	CCONJ
ejpam-6270	308	38	u	u	NOUN
ejpam-6270	308	39	having	have	VERB
ejpam-6270	308	40	ζ	ζ	NOUN
ejpam-6270	308	41	such	such	ADJ
ejpam-6270	308	42	that	that	DET
ejpam-6270	308	43	v	v	NUM
ejpam-6270	308	44	⊙	⊙	PROPN
ejpam-6270	308	45	u	u	PROPN
ejpam-6270	308	46	⊆	⊆	NUM
ejpam-6270	308	47	i.	i.	NOUN
ejpam-6270	308	48	if	if	SCONJ
ejpam-6270	308	49	there	there	PRON
ejpam-6270	308	50	exists	exist	VERB
ejpam-6270	308	51	η	η	PROPN
ejpam-6270	308	52	∈	∈	PROPN
ejpam-6270	308	53	(	(	PUNCT
ejpam-6270	308	54	u	u	NOUN
ejpam-6270	308	55	∩	∩	PROPN
ejpam-6270	308	56	i	i	PROPN
ejpam-6270	308	57	)	)	PUNCT
ejpam-6270	308	58	,	,	PUNCT
ejpam-6270	308	59	then	then	ADV
ejpam-6270	308	60	we	we	PRON
ejpam-6270	308	61	have	have	VERB
ejpam-6270	308	62	ζ	ζ	PROPN
ejpam-6270	308	63	⊙	⊙	PROPN
ejpam-6270	308	64	η	η	PROPN
ejpam-6270	308	65	∈	∈	PROPN
ejpam-6270	308	66	i	i	PROPN
ejpam-6270	308	67	and	and	CCONJ
ejpam-6270	308	68	η	η	PROPN
ejpam-6270	308	69	∈	∈	PROPN
ejpam-6270	308	70	i.	i.	NOUN
ejpam-6270	308	71	since	since	SCONJ
ejpam-6270	308	72	i	i	PRON
ejpam-6270	308	73	is	be	AUX
ejpam-6270	308	74	an	an	DET
ejpam-6270	308	75	ideal	ideal	NOUN
ejpam-6270	308	76	,	,	PUNCT
ejpam-6270	308	77	then	then	ADV
ejpam-6270	308	78	we	we	PRON
ejpam-6270	308	79	get	get	VERB
ejpam-6270	308	80	ζ	ζ	NOUN
ejpam-6270	308	81	∈	∈	NOUN
ejpam-6270	308	82	i	i	PRON
ejpam-6270	308	83	which	which	PRON
ejpam-6270	308	84	is	be	AUX
ejpam-6270	308	85	contradiction	contradiction	NOUN
ejpam-6270	308	86	.	.	PUNCT
ejpam-6270	309	1	hence	hence	ADV
ejpam-6270	309	2	,	,	PUNCT
ejpam-6270	309	3	ζ	ζ	PROPN
ejpam-6270	309	4	∈	∈	PROPN
ejpam-6270	309	5	u	u	NOUN
ejpam-6270	309	6	⊆	⊆	NUM
ejpam-6270	309	7	w	w	NOUN
ejpam-6270	309	8	\	\	NOUN
ejpam-6270	309	9	i	i	PRON
ejpam-6270	309	10	and	and	CCONJ
ejpam-6270	309	11	so	so	ADV
ejpam-6270	309	12	ζ	ζ	NOUN
ejpam-6270	309	13	\	\	NOUN
ejpam-6270	310	1	i	i	PRON
ejpam-6270	310	2	is	be	AUX
ejpam-6270	310	3	b	b	NOUN
ejpam-6270	310	4	-	-	ADV
ejpam-6270	310	5	open	open	ADJ
ejpam-6270	310	6	.	.	PUNCT
ejpam-6270	311	1	therefore	therefore	ADV
ejpam-6270	311	2	,	,	PUNCT
ejpam-6270	311	3	i	i	PRON
ejpam-6270	311	4	is	be	AUX
ejpam-6270	311	5	b	b	NOUN
ejpam-6270	311	6	-	-	PUNCT
ejpam-6270	311	7	closed	closed	ADJ
ejpam-6270	311	8	.	.	PUNCT
ejpam-6270	312	1	since	since	SCONJ
ejpam-6270	312	2	i	i	PRON
ejpam-6270	312	3	is	be	AUX
ejpam-6270	312	4	open	open	ADJ
ejpam-6270	312	5	,	,	PUNCT
ejpam-6270	312	6	so	so	ADV
ejpam-6270	312	7	by	by	ADP
ejpam-6270	312	8	lemma	lemma	PROPN
ejpam-6270	312	9	5	5	NUM
ejpam-6270	312	10	,	,	PUNCT
ejpam-6270	312	11	we	we	PRON
ejpam-6270	312	12	find	find	VERB
ejpam-6270	312	13	i	i	PRON
ejpam-6270	312	14	is	be	AUX
ejpam-6270	312	15	semi	semi	ADJ
ejpam-6270	312	16	-	-	ADJ
ejpam-6270	312	17	closed	closed	ADJ
ejpam-6270	312	18	which	which	PRON
ejpam-6270	312	19	implies	imply	VERB
ejpam-6270	312	20	that	that	SCONJ
ejpam-6270	312	21	i	i	PRON
ejpam-6270	312	22	is	be	AUX
ejpam-6270	312	23	regular	regular	ADJ
ejpam-6270	312	24	open	open	ADJ
ejpam-6270	312	25	.	.	PUNCT
ejpam-6270	313	1	corollary	corollary	ADJ
ejpam-6270	313	2	6	6	NUM
ejpam-6270	313	3	.	.	PUNCT
ejpam-6270	314	1	in	in	ADP
ejpam-6270	314	2	a	a	DET
ejpam-6270	314	3	tbd	tbd	NOUN
ejpam-6270	314	4	-	-	PUNCT
ejpam-6270	314	5	algebra	algebra	NOUN
ejpam-6270	314	6	(	(	PUNCT
ejpam-6270	314	7	w,⊙	w,⊙	PROPN
ejpam-6270	314	8	,	,	PUNCT
ejpam-6270	314	9	0	0	NUM
ejpam-6270	314	10	)	)	PUNCT
ejpam-6270	314	11	,	,	PUNCT
ejpam-6270	314	12	if	if	SCONJ
ejpam-6270	314	13	{	{	PUNCT
ejpam-6270	314	14	0	0	NUM
ejpam-6270	314	15	}	}	PUNCT
ejpam-6270	314	16	is	be	AUX
ejpam-6270	314	17	open	open	ADJ
ejpam-6270	314	18	,	,	PUNCT
ejpam-6270	314	19	then	then	ADV
ejpam-6270	314	20	w	w	PROPN
ejpam-6270	314	21	is	be	AUX
ejpam-6270	314	22	semi	semi	ADJ
ejpam-6270	314	23	-	-	ADJ
ejpam-6270	314	24	disconnected	disconnected	ADJ
ejpam-6270	314	25	.	.	PUNCT
ejpam-6270	315	1	proof	proof	NOUN
ejpam-6270	315	2	.	.	PUNCT
ejpam-6270	316	1	since	since	SCONJ
ejpam-6270	316	2	{	{	PUNCT
ejpam-6270	316	3	0	0	NUM
ejpam-6270	316	4	}	}	PUNCT
ejpam-6270	316	5	is	be	AUX
ejpam-6270	316	6	an	an	DET
ejpam-6270	316	7	ideal	ideal	ADJ
ejpam-6270	316	8	inw	inw	PROPN
ejpam-6270	316	9	,	,	PUNCT
ejpam-6270	316	10	by	by	ADP
ejpam-6270	316	11	using	use	VERB
ejpam-6270	316	12	proposition	proposition	NOUN
ejpam-6270	316	13	16	16	NUM
ejpam-6270	316	14	,	,	PUNCT
ejpam-6270	316	15	{	{	PUNCT
ejpam-6270	316	16	0	0	NUM
ejpam-6270	316	17	}	}	PUNCT
ejpam-6270	316	18	is	be	AUX
ejpam-6270	316	19	regular	regular	ADJ
ejpam-6270	316	20	open	open	ADJ
ejpam-6270	316	21	.	.	PUNCT
ejpam-6270	317	1	thus	thus	ADV
ejpam-6270	317	2	,	,	PUNCT
ejpam-6270	317	3	w	w	PROPN
ejpam-6270	317	4	is	be	AUX
ejpam-6270	317	5	semi	semi	ADJ
ejpam-6270	317	6	-	-	ADJ
ejpam-6270	317	7	disconnected	disconnected	ADJ
ejpam-6270	317	8	so	so	SCONJ
ejpam-6270	317	9	it	it	PRON
ejpam-6270	317	10	is	be	AUX
ejpam-6270	317	11	having	have	VERB
ejpam-6270	317	12	a	a	DET
ejpam-6270	317	13	proper	proper	ADJ
ejpam-6270	317	14	non	non	ADJ
ejpam-6270	317	15	-	-	ADJ
ejpam-6270	317	16	empty	empty	ADJ
ejpam-6270	317	17	set	set	NOUN
ejpam-6270	317	18	which	which	PRON
ejpam-6270	317	19	is	be	AUX
ejpam-6270	317	20	open	open	ADJ
ejpam-6270	317	21	and	and	CCONJ
ejpam-6270	317	22	semi	semi	ADJ
ejpam-6270	317	23	-	-	ADJ
ejpam-6270	317	24	closed	closed	ADJ
ejpam-6270	317	25	.	.	PUNCT
ejpam-6270	318	1	proposition	proposition	NOUN
ejpam-6270	318	2	17	17	NUM
ejpam-6270	318	3	.	.	PUNCT
ejpam-6270	319	1	in	in	ADP
ejpam-6270	319	2	a	a	DET
ejpam-6270	319	3	tbd	tbd	NOUN
ejpam-6270	319	4	-	-	PUNCT
ejpam-6270	319	5	algebra	algebra	NOUN
ejpam-6270	319	6	(	(	PUNCT
ejpam-6270	319	7	w,⊙	w,⊙	PROPN
ejpam-6270	319	8	,	,	PUNCT
ejpam-6270	319	9	0	0	NUM
ejpam-6270	319	10	)	)	PUNCT
ejpam-6270	319	11	.	.	PUNCT
ejpam-6270	320	1	if	if	SCONJ
ejpam-6270	320	2	i	i	PRON
ejpam-6270	320	3	is	be	AUX
ejpam-6270	320	4	an	an	DET
ejpam-6270	320	5	ideal	ideal	NOUN
ejpam-6270	320	6	such	such	ADJ
ejpam-6270	320	7	that	that	SCONJ
ejpam-6270	320	8	every	every	DET
ejpam-6270	320	9	sequence	sequence	NOUN
ejpam-6270	320	10	in	in	ADP
ejpam-6270	320	11	i	i	PRON
ejpam-6270	320	12	converging	converge	VERB
ejpam-6270	320	13	to	to	ADP
ejpam-6270	320	14	0	0	NUM
ejpam-6270	320	15	contains	contain	VERB
ejpam-6270	320	16	0	0	NUM
ejpam-6270	320	17	,	,	PUNCT
ejpam-6270	320	18	then	then	ADV
ejpam-6270	320	19	i	i	PRON
ejpam-6270	320	20	is	be	AUX
ejpam-6270	320	21	b	b	NOUN
ejpam-6270	320	22	-	-	PUNCT
ejpam-6270	320	23	closed	closed	ADJ
ejpam-6270	320	24	.	.	PUNCT
ejpam-6270	321	1	proof	proof	NOUN
ejpam-6270	321	2	.	.	PUNCT
ejpam-6270	322	1	let	let	VERB
ejpam-6270	322	2	ζ	ζ	NOUN
ejpam-6270	322	3	∈	∈	PROPN
ejpam-6270	322	4	clb(i	clb(i	PROPN
ejpam-6270	322	5	)	)	PUNCT
ejpam-6270	322	6	,	,	PUNCT
ejpam-6270	322	7	so	so	CCONJ
ejpam-6270	322	8	there	there	PRON
ejpam-6270	322	9	exists	exist	VERB
ejpam-6270	322	10	a	a	DET
ejpam-6270	322	11	sequence	sequence	NOUN
ejpam-6270	322	12	≪	≪	VERB
ejpam-6270	322	13	ζn	ζn	ADP
ejpam-6270	322	14	≫	≫	PROPN
ejpam-6270	322	15	in	in	ADP
ejpam-6270	322	16	i	i	PRON
ejpam-6270	322	17	which	which	PRON
ejpam-6270	322	18	is	be	AUX
ejpam-6270	322	19	b	b	NOUN
ejpam-6270	322	20	-	-	PUNCT
ejpam-6270	322	21	convergent	convergent	NOUN
ejpam-6270	322	22	to	to	ADP
ejpam-6270	322	23	ζ	ζ	PRON
ejpam-6270	322	24	.	.	PUNCT
ejpam-6270	323	1	now	now	ADV
ejpam-6270	323	2	,	,	PUNCT
ejpam-6270	323	3	we	we	PRON
ejpam-6270	323	4	claim	claim	VERB
ejpam-6270	323	5	that	that	SCONJ
ejpam-6270	323	6	the	the	DET
ejpam-6270	323	7	sequence	sequence	NOUN
ejpam-6270	323	8	≪	≪	PUNCT
ejpam-6270	323	9	ζ	ζ	NOUN
ejpam-6270	323	10	⊙	⊙	NOUN
ejpam-6270	323	11	ζn	ζn	ADP
ejpam-6270	323	12	≫	≫	PROPN
ejpam-6270	323	13	converges	converge	VERB
ejpam-6270	323	14	to	to	ADP
ejpam-6270	323	15	0	0	NUM
ejpam-6270	323	16	.	.	PUNCT
ejpam-6270	324	1	for	for	ADP
ejpam-6270	324	2	this	this	PRON
ejpam-6270	324	3	,	,	PUNCT
ejpam-6270	324	4	assume	assume	VERB
ejpam-6270	324	5	that	that	SCONJ
ejpam-6270	324	6	u	u	NOUN
ejpam-6270	324	7	is	be	AUX
ejpam-6270	324	8	any	any	DET
ejpam-6270	324	9	open	open	ADJ
ejpam-6270	324	10	set	set	NOUN
ejpam-6270	324	11	that	that	PRON
ejpam-6270	324	12	contains	contain	VERB
ejpam-6270	324	13	0	0	PUNCT
ejpam-6270	325	1	and	and	CCONJ
ejpam-6270	325	2	we	we	PRON
ejpam-6270	325	3	have	have	VERB
ejpam-6270	325	4	ζ	ζ	NOUN
ejpam-6270	325	5	⊙	⊙	X
ejpam-6270	325	6	ζ	ζ	X
ejpam-6270	325	7	=	=	NOUN
ejpam-6270	325	8	0	0	NUM
ejpam-6270	325	9	.	.	PUNCT
ejpam-6270	326	1	since	since	ADV
ejpam-6270	326	2	,	,	PUNCT
ejpam-6270	326	3	w	w	PROPN
ejpam-6270	326	4	is	be	AUX
ejpam-6270	326	5	a	a	DET
ejpam-6270	326	6	tbdalgebra	tbdalgebra	NOUN
ejpam-6270	326	7	,	,	PUNCT
ejpam-6270	326	8	so	so	SCONJ
ejpam-6270	326	9	there	there	PRON
ejpam-6270	326	10	exists	exist	VERB
ejpam-6270	326	11	a	a	DET
ejpam-6270	326	12	b	b	NOUN
ejpam-6270	326	13	-	-	PUNCT
ejpam-6270	326	14	open	open	ADJ
ejpam-6270	326	15	set	set	NOUN
ejpam-6270	326	16	v	v	NOUN
ejpam-6270	326	17	containing	contain	VERB
ejpam-6270	326	18	ζ	ζ	NOUN
ejpam-6270	326	19	such	such	DET
ejpam-6270	326	20	that	that	SCONJ
ejpam-6270	326	21	ζ	ζ	NOUN
ejpam-6270	326	22	⊙	⊙	NOUN
ejpam-6270	326	23	v	v	ADP
ejpam-6270	326	24	⊆	⊆	NUM
ejpam-6270	326	25	u	u	NOUN
ejpam-6270	326	26	.	.	PUNCT
ejpam-6270	327	1	again	again	ADV
ejpam-6270	327	2	,	,	PUNCT
ejpam-6270	327	3	we	we	PRON
ejpam-6270	327	4	have	have	AUX
ejpam-6270	327	5	≪	≪	VERB
ejpam-6270	327	6	ζn	ζn	PRON
ejpam-6270	327	7	≫	≫	PROPN
ejpam-6270	327	8	b	b	NOUN
ejpam-6270	327	9	-	-	PUNCT
ejpam-6270	327	10	converges	converge	NOUN
ejpam-6270	327	11	to	to	ADP
ejpam-6270	327	12	ζ	ζ	NOUN
ejpam-6270	327	13	,	,	PUNCT
ejpam-6270	327	14	so	so	SCONJ
ejpam-6270	327	15	there	there	PRON
ejpam-6270	327	16	is	be	VERB
ejpam-6270	327	17	k	k	PROPN
ejpam-6270	327	18	∈	∈	PROPN
ejpam-6270	327	19	n	n	PRON
ejpam-6270	327	20	such	such	ADJ
ejpam-6270	327	21	that	that	SCONJ
ejpam-6270	327	22	ζn	ζn	DET
ejpam-6270	327	23	∈	∈	PROPN
ejpam-6270	327	24	v	v	NOUN
ejpam-6270	327	25	for	for	ADP
ejpam-6270	327	26	all	all	DET
ejpam-6270	327	27	n	n	PRON
ejpam-6270	327	28	≫	≫	PROPN
ejpam-6270	327	29	k.	k.	PROPN
ejpam-6270	328	1	therefore	therefore	ADV
ejpam-6270	328	2	,	,	PUNCT
ejpam-6270	328	3	ζ	ζ	PROPN
ejpam-6270	328	4	⊙	⊙	NOUN
ejpam-6270	328	5	ζn	ζn	ADP
ejpam-6270	328	6	∈	∈	PROPN
ejpam-6270	328	7	w	w	PROPN
ejpam-6270	328	8	⊙	⊙	PROPN
ejpam-6270	328	9	v	v	ADP
ejpam-6270	328	10	⊆	⊆	NUM
ejpam-6270	328	11	u	u	NOUN
ejpam-6270	328	12	for	for	ADP
ejpam-6270	328	13	all	all	DET
ejpam-6270	328	14	n	n	PRON
ejpam-6270	328	15	≫	≫	PROPN
ejpam-6270	328	16	k.	k.	PROPN
ejpam-6270	328	17	hence	hence	ADV
ejpam-6270	328	18	,	,	PUNCT
ejpam-6270	328	19	≪	≪	PUNCT
ejpam-6270	328	20	ζ	ζ	NOUN
ejpam-6270	328	21	⊙	⊙	NOUN
ejpam-6270	328	22	ζn	ζn	ADP
ejpam-6270	328	23	≫	≫	PROPN
ejpam-6270	328	24	converges	converge	VERB
ejpam-6270	328	25	to	to	ADP
ejpam-6270	328	26	0	0	NUM
ejpam-6270	328	27	and	and	CCONJ
ejpam-6270	328	28	by	by	ADP
ejpam-6270	328	29	hypothesis	hypothesis	NOUN
ejpam-6270	328	30	the	the	DET
ejpam-6270	328	31	sequence	sequence	NOUN
ejpam-6270	328	32	≪	≪	PUNCT
ejpam-6270	328	33	ζ	ζ	NOUN
ejpam-6270	328	34	⊙	⊙	NOUN
ejpam-6270	328	35	ζn	ζn	ADP
ejpam-6270	328	36	≫	≫	PROPN
ejpam-6270	328	37	contains	contain	VERB
ejpam-6270	328	38	0	0	NUM
ejpam-6270	328	39	.	.	PUNCT
ejpam-6270	329	1	thus	thus	ADV
ejpam-6270	329	2	,	,	PUNCT
ejpam-6270	329	3	there	there	PRON
ejpam-6270	329	4	exists	exist	VERB
ejpam-6270	329	5	n	n	PRON
ejpam-6270	329	6	∈	∈	PROPN
ejpam-6270	329	7	n	n	PRON
ejpam-6270	329	8	such	such	ADJ
ejpam-6270	329	9	that	that	SCONJ
ejpam-6270	329	10	ζ	ζ	NOUN
ejpam-6270	329	11	⊙	⊙	NOUN
ejpam-6270	329	12	ζn	ζn	ADP
ejpam-6270	329	13	=	=	NOUN
ejpam-6270	329	14	0	0	PROPN
ejpam-6270	329	15	.	.	PUNCT
ejpam-6270	330	1	since	since	SCONJ
ejpam-6270	330	2	ζn	ζn	PRON
ejpam-6270	330	3	∈	∈	PROPN
ejpam-6270	331	1	i	i	PRON
ejpam-6270	331	2	and	and	CCONJ
ejpam-6270	331	3	i	i	PRON
ejpam-6270	331	4	is	be	AUX
ejpam-6270	331	5	an	an	DET
ejpam-6270	331	6	ideal	ideal	NOUN
ejpam-6270	331	7	,	,	PUNCT
ejpam-6270	331	8	so	so	ADV
ejpam-6270	331	9	ζ	ζ	PROPN
ejpam-6270	331	10	∈	∈	PROPN
ejpam-6270	331	11	i.	i.	NOUN
ejpam-6270	331	12	hence	hence	ADV
ejpam-6270	331	13	,	,	PUNCT
ejpam-6270	331	14	i	i	PRON
ejpam-6270	331	15	is	be	AUX
ejpam-6270	331	16	b	b	NOUN
ejpam-6270	331	17	-	-	PUNCT
ejpam-6270	331	18	closed	closed	ADJ
ejpam-6270	331	19	.	.	PUNCT
ejpam-6270	332	1	proposition	proposition	NOUN
ejpam-6270	332	2	18	18	NUM
ejpam-6270	332	3	.	.	PUNCT
ejpam-6270	333	1	in	in	ADP
ejpam-6270	333	2	an	an	DET
ejpam-6270	333	3	edge	edge	NOUN
ejpam-6270	333	4	tbd	tbd	NOUN
ejpam-6270	333	5	-	-	PUNCT
ejpam-6270	333	6	algebra	algebra	NOUN
ejpam-6270	333	7	(	(	PUNCT
ejpam-6270	333	8	w,⊙	w,⊙	PROPN
ejpam-6270	333	9	,	,	PUNCT
ejpam-6270	333	10	0	0	NUM
ejpam-6270	333	11	)	)	PUNCT
ejpam-6270	333	12	.	.	PUNCT
ejpam-6270	334	1	if	if	SCONJ
ejpam-6270	334	2	all	all	DET
ejpam-6270	334	3	elements	element	NOUN
ejpam-6270	334	4	of	of	ADP
ejpam-6270	334	5	w	w	PROPN
ejpam-6270	334	6	are	be	AUX
ejpam-6270	334	7	atoms	atom	NOUN
ejpam-6270	334	8	and	and	CCONJ
ejpam-6270	335	1	ϕ	ϕ	PROPN
ejpam-6270	335	2	̸=	̸=	PROPN
ejpam-6270	335	3	s	s	PROPN
ejpam-6270	335	4	⊆	⊆	NUM
ejpam-6270	335	5	w	w	NOUN
ejpam-6270	335	6	not	not	PART
ejpam-6270	335	7	containing	contain	VERB
ejpam-6270	335	8	0	0	NUM
ejpam-6270	335	9	,	,	PUNCT
ejpam-6270	335	10	then	then	ADV
ejpam-6270	335	11	0	0	NUM
ejpam-6270	335	12	∈	∈	PROPN
ejpam-6270	335	13	cl(s	cl(s	NOUN
ejpam-6270	335	14	)	)	PUNCT
ejpam-6270	335	15	.	.	PUNCT
ejpam-6270	336	1	proof	proof	NOUN
ejpam-6270	336	2	.	.	PUNCT
ejpam-6270	337	1	suppose	suppose	VERB
ejpam-6270	337	2	that	that	SCONJ
ejpam-6270	337	3	0	0	NUM
ejpam-6270	337	4	̸=	̸=	PROPN
ejpam-6270	337	5	ζ	ζ	NOUN
ejpam-6270	337	6	∈	∈	PROPN
ejpam-6270	337	7	clb(s	clb(s	PROPN
ejpam-6270	337	8	)	)	PUNCT
ejpam-6270	337	9	,	,	PUNCT
ejpam-6270	337	10	then	then	ADV
ejpam-6270	337	11	there	there	PRON
ejpam-6270	337	12	exists	exist	VERB
ejpam-6270	337	13	a	a	DET
ejpam-6270	337	14	sequence	sequence	NOUN
ejpam-6270	337	15	≪	≪	VERB
ejpam-6270	337	16	sn	sn	PROPN
ejpam-6270	337	17	≫	≫	PROPN
ejpam-6270	337	18	in	in	ADP
ejpam-6270	337	19	s	s	PROPN
ejpam-6270	337	20	which	which	DET
ejpam-6270	337	21	b	b	X
ejpam-6270	337	22	-	-	PUNCT
ejpam-6270	337	23	converges	converge	NOUN
ejpam-6270	337	24	to	to	ADP
ejpam-6270	337	25	ζ	ζ	NOUN
ejpam-6270	337	26	.	.	PUNCT
ejpam-6270	338	1	hence	hence	ADV
ejpam-6270	338	2	,	,	PUNCT
ejpam-6270	338	3	as	as	ADP
ejpam-6270	338	4	in	in	ADP
ejpam-6270	338	5	proposition	proposition	NOUN
ejpam-6270	338	6	17	17	NUM
ejpam-6270	338	7	,	,	PUNCT
ejpam-6270	338	8	we	we	PRON
ejpam-6270	338	9	obtain	obtain	VERB
ejpam-6270	338	10	that	that	DET
ejpam-6270	338	11	≪	≪	VERB
ejpam-6270	338	12	sn	sn	PROPN
ejpam-6270	338	13	⊙	⊙	PROPN
ejpam-6270	338	14	ζ	ζ	PROPN
ejpam-6270	338	15	≫	≫	PROPN
ejpam-6270	338	16	converges	converge	VERB
ejpam-6270	338	17	to	to	ADP
ejpam-6270	338	18	0	0	NUM
ejpam-6270	338	19	.	.	PUNCT
ejpam-6270	339	1	since	since	SCONJ
ejpam-6270	339	2	all	all	DET
ejpam-6270	339	3	elements	element	NOUN
ejpam-6270	339	4	of	of	ADP
ejpam-6270	339	5	w	w	PROPN
ejpam-6270	339	6	are	be	AUX
ejpam-6270	339	7	atoms	atom	NOUN
ejpam-6270	339	8	and	and	CCONJ
ejpam-6270	339	9	0	0	NUM
ejpam-6270	339	10	̸=	̸=	PROPN
ejpam-6270	339	11	ζ	ζ	PROPN
ejpam-6270	339	12	̸=	̸=	PROPN
ejpam-6270	339	13	sn	sn	PROPN
ejpam-6270	339	14	,	,	PUNCT
ejpam-6270	339	15	so	so	ADV
ejpam-6270	339	16	sn	sn	PROPN
ejpam-6270	339	17	⊙	⊙	PROPN
ejpam-6270	339	18	ζ	ζ	PROPN
ejpam-6270	339	19	̸=	̸=	PROPN
ejpam-6270	339	20	0	0	NUM
ejpam-6270	339	21	implies	imply	VERB
ejpam-6270	339	22	that	that	SCONJ
ejpam-6270	339	23	sn	sn	PROPN
ejpam-6270	339	24	⊙	⊙	X
ejpam-6270	339	25	ζ	ζ	PROPN
ejpam-6270	339	26	=	=	SYM
ejpam-6270	339	27	sn	sn	PROPN
ejpam-6270	339	28	.	.	PUNCT
ejpam-6270	340	1	therefore	therefore	ADV
ejpam-6270	340	2	,	,	PUNCT
ejpam-6270	340	3	the	the	DET
ejpam-6270	340	4	sequence	sequence	NOUN
ejpam-6270	340	5	,	,	PUNCT
ejpam-6270	340	6	≪	≪	VERB
ejpam-6270	340	7	sn	sn	PROPN
ejpam-6270	340	8	≫	≫	PROPN
ejpam-6270	340	9	in	in	ADP
ejpam-6270	340	10	s	s	PART
ejpam-6270	340	11	converges	converge	NOUN
ejpam-6270	340	12	to	to	ADP
ejpam-6270	340	13	0	0	NUM
ejpam-6270	340	14	implies	imply	VERB
ejpam-6270	340	15	that	that	SCONJ
ejpam-6270	340	16	0	0	NUM
ejpam-6270	340	17	∈	∈	PROPN
ejpam-6270	340	18	cl(s	cl(s	NOUN
ejpam-6270	340	19	)	)	PUNCT
ejpam-6270	340	20	.	.	PUNCT
ejpam-6270	341	1	m.	m.	NOUN
ejpam-6270	341	2	w.	w.	PROPN
ejpam-6270	341	3	abdulqader	abdulqader	PROPN
ejpam-6270	341	4	,	,	PUNCT
ejpam-6270	341	5	a.	a.	PROPN
ejpam-6270	341	6	b.	b.	PROPN
ejpam-6270	341	7	khalaf	khalaf	PROPN
ejpam-6270	341	8	/	/	SYM
ejpam-6270	341	9	eur	eur	PROPN
ejpam-6270	341	10	.	.	PUNCT
ejpam-6270	342	1	j.	j.	PROPN
ejpam-6270	342	2	pure	pure	PROPN
ejpam-6270	342	3	appl	appl	PROPN
ejpam-6270	342	4	.	.	PROPN
ejpam-6270	342	5	math	math	PROPN
ejpam-6270	342	6	,	,	PUNCT
ejpam-6270	342	7	18	18	NUM
ejpam-6270	342	8	(	(	PUNCT
ejpam-6270	342	9	3	3	NUM
ejpam-6270	342	10	)	)	PUNCT
ejpam-6270	342	11	(	(	PUNCT
ejpam-6270	342	12	2025	2025	NUM
ejpam-6270	342	13	)	)	PUNCT
ejpam-6270	342	14	,	,	PUNCT
ejpam-6270	342	15	6270	6270	NUM
ejpam-6270	342	16	12	12	NUM
ejpam-6270	342	17	of	of	ADP
ejpam-6270	342	18	17	17	NUM
ejpam-6270	342	19	proposition	proposition	NOUN
ejpam-6270	342	20	19	19	NUM
ejpam-6270	342	21	.	.	PUNCT
ejpam-6270	343	1	in	in	ADP
ejpam-6270	343	2	an	an	DET
ejpam-6270	343	3	edge	edge	NOUN
ejpam-6270	343	4	tbd	tbd	NOUN
ejpam-6270	343	5	-	-	PUNCT
ejpam-6270	343	6	algebra	algebra	NOUN
ejpam-6270	343	7	(	(	PUNCT
ejpam-6270	343	8	w,⊙	w,⊙	PROPN
ejpam-6270	343	9	,	,	PUNCT
ejpam-6270	343	10	0	0	NUM
ejpam-6270	343	11	)	)	PUNCT
ejpam-6270	343	12	.	.	PUNCT
ejpam-6270	344	1	if	if	SCONJ
ejpam-6270	344	2	s	s	VERB
ejpam-6270	344	3	⊆	⊆	NUM
ejpam-6270	344	4	w	w	NOUN
ejpam-6270	344	5	and	and	CCONJ
ejpam-6270	344	6	there	there	PRON
ejpam-6270	344	7	is	be	VERB
ejpam-6270	344	8	a	a	DET
ejpam-6270	344	9	sequence	sequence	NOUN
ejpam-6270	344	10	of	of	ADP
ejpam-6270	344	11	atom	atom	NOUN
ejpam-6270	344	12	elements	element	NOUN
ejpam-6270	344	13	in	in	ADP
ejpam-6270	344	14	s	s	NOUN
ejpam-6270	344	15	b	b	NOUN
ejpam-6270	344	16	-	-	PUNCT
ejpam-6270	344	17	converges	converge	NOUN
ejpam-6270	344	18	to	to	ADP
ejpam-6270	344	19	an	an	DET
ejpam-6270	344	20	element	element	NOUN
ejpam-6270	344	21	ζ	ζ	NOUN
ejpam-6270	344	22	/∈	/∈	PUNCT
ejpam-6270	345	1	s	s	X
ejpam-6270	345	2	,	,	PUNCT
ejpam-6270	345	3	then	then	ADV
ejpam-6270	345	4	the	the	DET
ejpam-6270	345	5	sequence	sequence	NOUN
ejpam-6270	345	6	converges	converge	VERB
ejpam-6270	345	7	to	to	ADP
ejpam-6270	345	8	0	0	NUM
ejpam-6270	345	9	and	and	CCONJ
ejpam-6270	345	10	0	0	NUM
ejpam-6270	345	11	∈	∈	PROPN
ejpam-6270	345	12	cl(s	cl(s	NOUN
ejpam-6270	345	13	)	)	PUNCT
ejpam-6270	345	14	.	.	PUNCT
ejpam-6270	346	1	proof	proof	NOUN
ejpam-6270	346	2	.	.	PUNCT
ejpam-6270	347	1	let	let	VERB
ejpam-6270	347	2	≪	≪	VERB
ejpam-6270	347	3	ζn	ζn	PRON
ejpam-6270	347	4	≫	≫	PROPN
ejpam-6270	347	5	be	be	AUX
ejpam-6270	347	6	a	a	DET
ejpam-6270	347	7	sequence	sequence	NOUN
ejpam-6270	347	8	of	of	ADP
ejpam-6270	347	9	atom	atom	NOUN
ejpam-6270	347	10	elements	element	NOUN
ejpam-6270	347	11	in	in	ADP
ejpam-6270	347	12	s	s	PRON
ejpam-6270	347	13	which	which	PRON
ejpam-6270	347	14	is	be	AUX
ejpam-6270	347	15	b	b	NOUN
ejpam-6270	347	16	-	-	PUNCT
ejpam-6270	347	17	convergent	convergent	NOUN
ejpam-6270	347	18	to	to	ADP
ejpam-6270	347	19	ζ	ζ	NOUN
ejpam-6270	347	20	/∈	/∈	PUNCT
ejpam-6270	348	1	s	s	X
ejpam-6270	348	2	,	,	PUNCT
ejpam-6270	348	3	so	so	SCONJ
ejpam-6270	348	4	as	as	SCONJ
ejpam-6270	348	5	in	in	ADP
ejpam-6270	348	6	proposition	proposition	NOUN
ejpam-6270	348	7	16	16	NUM
ejpam-6270	348	8	,	,	PUNCT
ejpam-6270	348	9	we	we	PRON
ejpam-6270	348	10	obtain	obtain	VERB
ejpam-6270	348	11	the	the	DET
ejpam-6270	348	12	sequence	sequence	NOUN
ejpam-6270	348	13	≪	≪	VERB
ejpam-6270	348	14	ζn	ζn	DET
ejpam-6270	348	15	⊙	⊙	PROPN
ejpam-6270	348	16	ζ	ζ	PROPN
ejpam-6270	348	17	≫	≫	PROPN
ejpam-6270	348	18	which	which	PRON
ejpam-6270	348	19	converges	converge	VERB
ejpam-6270	348	20	to	to	ADP
ejpam-6270	348	21	0	0	NUM
ejpam-6270	348	22	.	.	PUNCT
ejpam-6270	349	1	since	since	SCONJ
ejpam-6270	349	2	w	w	PROPN
ejpam-6270	349	3	is	be	AUX
ejpam-6270	349	4	an	an	DET
ejpam-6270	349	5	edge	edge	NOUN
ejpam-6270	349	6	d	d	NOUN
ejpam-6270	349	7	-	-	PUNCT
ejpam-6270	349	8	algebra	algebra	NOUN
ejpam-6270	349	9	,	,	PUNCT
ejpam-6270	349	10	so	so	ADV
ejpam-6270	349	11	ζn	ζn	DET
ejpam-6270	349	12	⊙	⊙	PROPN
ejpam-6270	349	13	ζ	ζ	PROPN
ejpam-6270	349	14	=	=	PUNCT
ejpam-6270	349	15	{	{	PUNCT
ejpam-6270	349	16	0	0	NUM
ejpam-6270	349	17	,	,	PUNCT
ejpam-6270	349	18	ζn	ζn	NOUN
ejpam-6270	349	19	}	}	PUNCT
ejpam-6270	349	20	but	but	CCONJ
ejpam-6270	349	21	ζn	ζn	PRON
ejpam-6270	349	22	are	be	AUX
ejpam-6270	349	23	atoms	atom	NOUN
ejpam-6270	349	24	and	and	CCONJ
ejpam-6270	349	25	ζ	ζ	NOUN
ejpam-6270	349	26	/∈	/∈	PUNCT
ejpam-6270	349	27	s	s	X
ejpam-6270	349	28	,	,	PUNCT
ejpam-6270	349	29	so	so	ADV
ejpam-6270	349	30	ζn	ζn	DET
ejpam-6270	349	31	⊙	⊙	PROPN
ejpam-6270	349	32	ζ	ζ	PROPN
ejpam-6270	349	33	=	=	SYM
ejpam-6270	349	34	ζn	ζn	PROPN
ejpam-6270	349	35	.	.	PUNCT
ejpam-6270	349	36	therefore	therefore	ADV
ejpam-6270	349	37	,	,	PUNCT
ejpam-6270	349	38	≪	≪	VERB
ejpam-6270	349	39	ζn	ζn	SCONJ
ejpam-6270	349	40	≫	≫	PROPN
ejpam-6270	349	41	converges	converge	VERB
ejpam-6270	349	42	to	to	ADP
ejpam-6270	349	43	0	0	NUM
ejpam-6270	349	44	and	and	CCONJ
ejpam-6270	349	45	hence	hence	ADV
ejpam-6270	349	46	0	0	NUM
ejpam-6270	349	47	∈	∈	PROPN
ejpam-6270	349	48	cl(s	cl(s	NOUN
ejpam-6270	349	49	)	)	PUNCT
ejpam-6270	349	50	.	.	PUNCT
ejpam-6270	350	1	definition	definition	NOUN
ejpam-6270	350	2	17	17	NUM
ejpam-6270	350	3	.	.	PUNCT
ejpam-6270	351	1	let	let	VERB
ejpam-6270	351	2	w	w	NOUN
ejpam-6270	351	3	be	be	AUX
ejpam-6270	351	4	a	a	DET
ejpam-6270	351	5	d	d	NOUN
ejpam-6270	351	6	-	-	NOUN
ejpam-6270	351	7	algebra	algebra	NOUN
ejpam-6270	351	8	.	.	PUNCT
ejpam-6270	352	1	we	we	PRON
ejpam-6270	352	2	can	can	AUX
ejpam-6270	352	3	define	define	VERB
ejpam-6270	352	4	the	the	DET
ejpam-6270	352	5	binary	binary	ADJ
ejpam-6270	352	6	operation	operation	NOUN
ejpam-6270	352	7	◦	◦	NOUN
ejpam-6270	352	8	on	on	ADP
ejpam-6270	352	9	l(w	l(w	NOUN
ejpam-6270	352	10	)	)	PUNCT
ejpam-6270	352	11	by	by	ADP
ejpam-6270	352	12	(	(	PUNCT
ejpam-6270	352	13	lα	lα	ADP
ejpam-6270	352	14	◦	◦	NOUN
ejpam-6270	352	15	lβ)(ζ	lβ)(ζ	PROPN
ejpam-6270	352	16	)	)	PUNCT
ejpam-6270	352	17	=	=	SYM
ejpam-6270	352	18	lα(ζ)⊙	lα(ζ)⊙	NOUN
ejpam-6270	352	19	lβ(ζ	lβ(ζ	X
ejpam-6270	352	20	)	)	PUNCT
ejpam-6270	352	21	for	for	ADP
ejpam-6270	352	22	each	each	DET
ejpam-6270	352	23	ζ	ζ	PROPN
ejpam-6270	352	24	∈	∈	PROPN
ejpam-6270	352	25	w.	w.	NOUN
ejpam-6270	352	26	theorem	theorem	VERB
ejpam-6270	352	27	1	1	X
ejpam-6270	352	28	.	.	PUNCT
ejpam-6270	353	1	let	let	VERB
ejpam-6270	353	2	w	w	NOUN
ejpam-6270	353	3	be	be	AUX
ejpam-6270	353	4	a	a	DET
ejpam-6270	353	5	positive	positive	ADJ
ejpam-6270	353	6	implicative	implicative	ADJ
ejpam-6270	353	7	d	d	NOUN
ejpam-6270	353	8	-	-	PUNCT
ejpam-6270	353	9	algebra	algebra	NOUN
ejpam-6270	353	10	,	,	PUNCT
ejpam-6270	353	11	then	then	ADV
ejpam-6270	353	12	(	(	PUNCT
ejpam-6270	353	13	l(w	l(w	PROPN
ejpam-6270	353	14	)	)	PUNCT
ejpam-6270	353	15	,	,	PUNCT
ejpam-6270	353	16	◦	◦	NOUN
ejpam-6270	353	17	,	,	PUNCT
ejpam-6270	353	18	l0	l0	PROPN
ejpam-6270	353	19	)	)	PUNCT
ejpam-6270	353	20	is	be	AUX
ejpam-6270	353	21	a	a	DET
ejpam-6270	353	22	d	d	NOUN
ejpam-6270	353	23	-	-	NOUN
ejpam-6270	353	24	algebra	algebra	NOUN
ejpam-6270	353	25	.	.	PUNCT
ejpam-6270	354	1	proof	proof	NOUN
ejpam-6270	354	2	.	.	PUNCT
ejpam-6270	355	1	assume	assume	VERB
ejpam-6270	355	2	thatlα	thatlα	NOUN
ejpam-6270	355	3	,	,	PUNCT
ejpam-6270	355	4	lβ	lβ	ADP
ejpam-6270	355	5	∈	∈	PROPN
ejpam-6270	355	6	l(w	l(w	PROPN
ejpam-6270	355	7	)	)	PUNCT
ejpam-6270	355	8	.	.	PUNCT
ejpam-6270	356	1	then	then	ADV
ejpam-6270	356	2	,	,	PUNCT
ejpam-6270	356	3	by	by	ADP
ejpam-6270	356	4	using	use	VERB
ejpam-6270	356	5	the	the	DET
ejpam-6270	356	6	definition	definition	NOUN
ejpam-6270	356	7	of	of	ADP
ejpam-6270	356	8	the	the	DET
ejpam-6270	356	9	binary	binary	ADJ
ejpam-6270	356	10	operation	operation	NOUN
ejpam-6270	356	11	◦	◦	NOUN
ejpam-6270	356	12	on	on	ADP
ejpam-6270	356	13	l(w	l(w	PROPN
ejpam-6270	356	14	)	)	PUNCT
ejpam-6270	356	15	we	we	PRON
ejpam-6270	356	16	get	get	VERB
ejpam-6270	356	17	(	(	PUNCT
ejpam-6270	356	18	lα	lα	ADP
ejpam-6270	356	19	◦	◦	NOUN
ejpam-6270	356	20	lβ)(ζ	lβ)(ζ	PROPN
ejpam-6270	356	21	)	)	PUNCT
ejpam-6270	356	22	=	=	SYM
ejpam-6270	356	23	lα(ζ	lα(ζ	NOUN
ejpam-6270	356	24	)	)	PUNCT
ejpam-6270	356	25	⊙	⊙	NOUN
ejpam-6270	356	26	lβ(ζ	lβ(ζ	PUNCT
ejpam-6270	356	27	)	)	PUNCT
ejpam-6270	357	1	=	=	SYM
ejpam-6270	357	2	(	(	PUNCT
ejpam-6270	357	3	α	α	PROPN
ejpam-6270	357	4	⊙	⊙	PROPN
ejpam-6270	357	5	ζ	ζ	PROPN
ejpam-6270	357	6	)	)	PUNCT
ejpam-6270	357	7	⊙	⊙	NOUN
ejpam-6270	357	8	(	(	PUNCT
ejpam-6270	357	9	β	β	PROPN
ejpam-6270	357	10	⊙	⊙	X
ejpam-6270	357	11	ζ	ζ	PROPN
ejpam-6270	357	12	)	)	PUNCT
ejpam-6270	357	13	.	.	PUNCT
ejpam-6270	358	1	since	since	SCONJ
ejpam-6270	358	2	w	w	PROPN
ejpam-6270	358	3	is	be	AUX
ejpam-6270	358	4	a	a	DET
ejpam-6270	358	5	positive	positive	ADJ
ejpam-6270	358	6	implication	implication	NOUN
ejpam-6270	358	7	d	d	NOUN
ejpam-6270	358	8	-	-	PUNCT
ejpam-6270	358	9	algebra	algebra	NOUN
ejpam-6270	358	10	,	,	PUNCT
ejpam-6270	358	11	then	then	ADV
ejpam-6270	358	12	(	(	PUNCT
ejpam-6270	358	13	α	α	PROPN
ejpam-6270	358	14	⊙	⊙	PROPN
ejpam-6270	358	15	ζ	ζ	PROPN
ejpam-6270	358	16	)	)	PUNCT
ejpam-6270	358	17	⊙	⊙	NOUN
ejpam-6270	358	18	(	(	PUNCT
ejpam-6270	358	19	β	β	X
ejpam-6270	358	20	⊙	⊙	X
ejpam-6270	358	21	ζ	ζ	PROPN
ejpam-6270	358	22	)	)	PUNCT
ejpam-6270	359	1	=	=	SYM
ejpam-6270	359	2	(	(	PUNCT
ejpam-6270	359	3	α	α	PROPN
ejpam-6270	359	4	⊙	⊙	PROPN
ejpam-6270	359	5	β	β	X
ejpam-6270	359	6	)	)	PUNCT
ejpam-6270	359	7	⊙	⊙	PROPN
ejpam-6270	359	8	ζ	ζ	PROPN
ejpam-6270	359	9	.	.	PUNCT
ejpam-6270	360	1	therefore	therefore	ADV
ejpam-6270	360	2	,	,	PUNCT
ejpam-6270	360	3	(	(	PUNCT
ejpam-6270	360	4	lα	lα	ADP
ejpam-6270	360	5	◦	◦	NOUN
ejpam-6270	360	6	lβ)(ζ	lβ)(ζ	PROPN
ejpam-6270	360	7	)	)	PUNCT
ejpam-6270	360	8	=	=	SYM
ejpam-6270	360	9	lα⊙β(ζ	lα⊙β(ζ	PROPN
ejpam-6270	360	10	)	)	PUNCT
ejpam-6270	360	11	which	which	PRON
ejpam-6270	360	12	implies	imply	VERB
ejpam-6270	360	13	that	that	SCONJ
ejpam-6270	360	14	lα	lα	ADP
ejpam-6270	360	15	◦	◦	NOUN
ejpam-6270	360	16	lβ	lβ	ADP
ejpam-6270	360	17	=	=	X
ejpam-6270	360	18	lα⊙β	lα⊙β	X
ejpam-6270	360	19	∀	∀	X
ejpam-6270	360	20	α	α	X
ejpam-6270	360	21	,	,	PUNCT
ejpam-6270	360	22	β	β	PROPN
ejpam-6270	360	23	∈	∈	PROPN
ejpam-6270	360	24	w.	w.	PROPN
ejpam-6270	360	25	furthermore	furthermore	ADV
ejpam-6270	360	26	,	,	PUNCT
ejpam-6270	360	27	the	the	DET
ejpam-6270	360	28	following	follow	VERB
ejpam-6270	360	29	statements	statement	NOUN
ejpam-6270	360	30	are	be	AUX
ejpam-6270	360	31	correct	correct	ADJ
ejpam-6270	360	32	.	.	PUNCT
ejpam-6270	361	1	(	(	PUNCT
ejpam-6270	361	2	i	i	NOUN
ejpam-6270	361	3	)	)	PUNCT
ejpam-6270	361	4	lζ	lζ	ADP
ejpam-6270	361	5	◦	◦	NOUN
ejpam-6270	361	6	lζ	lζ	ADJ
ejpam-6270	361	7	=	=	NOUN
ejpam-6270	361	8	lζ⊙ζ	lζ⊙ζ	X
ejpam-6270	361	9	=	=	SYM
ejpam-6270	361	10	l0	l0	PROPN
ejpam-6270	361	11	,	,	PUNCT
ejpam-6270	361	12	(	(	PUNCT
ejpam-6270	361	13	ii	ii	NOUN
ejpam-6270	361	14	)	)	PUNCT
ejpam-6270	361	15	lζ	lζ	ADP
ejpam-6270	361	16	◦	◦	NOUN
ejpam-6270	361	17	lη	lη	NOUN
ejpam-6270	361	18	=	=	PROPN
ejpam-6270	361	19	l0	l0	PROPN
ejpam-6270	361	20	and	and	CCONJ
ejpam-6270	361	21	lη	lη	NOUN
ejpam-6270	361	22	◦	◦	VERB
ejpam-6270	361	23	lζ	lζ	PROPN
ejpam-6270	361	24	=	=	SYM
ejpam-6270	361	25	l0	l0	PROPN
ejpam-6270	361	26	,	,	PUNCT
ejpam-6270	361	27	then	then	ADV
ejpam-6270	361	28	lζ⊙η	lζ⊙η	AUX
ejpam-6270	361	29	=	=	SYM
ejpam-6270	361	30	l0	l0	PROPN
ejpam-6270	361	31	and	and	CCONJ
ejpam-6270	361	32	lη⊙ζ	lη⊙ζ	X
ejpam-6270	361	33	=	=	PUNCT
ejpam-6270	361	34	l0	l0	NOUN
ejpam-6270	361	35	which	which	PRON
ejpam-6270	361	36	implies	imply	VERB
ejpam-6270	361	37	that	that	SCONJ
ejpam-6270	361	38	ζ	ζ	PROPN
ejpam-6270	361	39	⊙	⊙	PROPN
ejpam-6270	361	40	η	η	PROPN
ejpam-6270	361	41	=	=	PROPN
ejpam-6270	361	42	0	0	NUM
ejpam-6270	361	43	and	and	CCONJ
ejpam-6270	361	44	η	η	PROPN
ejpam-6270	361	45	⊙	⊙	PROPN
ejpam-6270	361	46	ζ	ζ	PROPN
ejpam-6270	361	47	=	=	SYM
ejpam-6270	361	48	0	0	NUM
ejpam-6270	361	49	⇒	⇒	NOUN
ejpam-6270	361	50	ζ	ζ	X
ejpam-6270	361	51	=	=	SYM
ejpam-6270	361	52	η	η	PROPN
ejpam-6270	361	53	and	and	CCONJ
ejpam-6270	361	54	hence	hence	ADV
ejpam-6270	361	55	,	,	PUNCT
ejpam-6270	361	56	lζ	lζ	PROPN
ejpam-6270	361	57	=	=	PROPN
ejpam-6270	361	58	lη	lη	PROPN
ejpam-6270	361	59	,	,	PUNCT
ejpam-6270	361	60	(	(	PUNCT
ejpam-6270	361	61	iii	iii	NOUN
ejpam-6270	361	62	)	)	PUNCT
ejpam-6270	361	63	l0	l0	NOUN
ejpam-6270	361	64	◦	◦	NOUN
ejpam-6270	361	65	lζ	lζ	PROPN
ejpam-6270	361	66	=	=	PUNCT
ejpam-6270	361	67	l0⊙ζ	l0⊙ζ	PROPN
ejpam-6270	361	68	=	=	SYM
ejpam-6270	361	69	l0	l0	PROPN
ejpam-6270	361	70	.	.	PUNCT
ejpam-6270	362	1	therefore	therefore	ADV
ejpam-6270	362	2	,	,	PUNCT
ejpam-6270	362	3	l(w	l(w	PROPN
ejpam-6270	362	4	)	)	PUNCT
ejpam-6270	362	5	is	be	AUX
ejpam-6270	362	6	a	a	DET
ejpam-6270	362	7	d	d	NOUN
ejpam-6270	362	8	-	-	NOUN
ejpam-6270	362	9	algebra	algebra	NOUN
ejpam-6270	362	10	.	.	PUNCT
ejpam-6270	363	1	proposition	proposition	NOUN
ejpam-6270	363	2	20	20	NUM
ejpam-6270	363	3	.	.	PUNCT
ejpam-6270	364	1	let	let	VERB
ejpam-6270	364	2	w	w	NOUN
ejpam-6270	364	3	be	be	AUX
ejpam-6270	364	4	a	a	DET
ejpam-6270	364	5	tbd	tbd	NOUN
ejpam-6270	364	6	-	-	PUNCT
ejpam-6270	364	7	algebra	algebra	NOUN
ejpam-6270	364	8	,	,	PUNCT
ejpam-6270	364	9	then	then	ADV
ejpam-6270	364	10	every	every	DET
ejpam-6270	364	11	left	left	ADJ
ejpam-6270	364	12	map	map	NOUN
ejpam-6270	364	13	on	on	ADP
ejpam-6270	364	14	w	w	PROPN
ejpam-6270	364	15	is	be	AUX
ejpam-6270	364	16	b	b	NOUN
ejpam-6270	364	17	-	-	PUNCT
ejpam-6270	364	18	continuous	continuous	ADJ
ejpam-6270	364	19	.	.	PUNCT
ejpam-6270	365	1	proof	proof	NOUN
ejpam-6270	365	2	.	.	PUNCT
ejpam-6270	366	1	let	let	VERB
ejpam-6270	366	2	ζ	ζ	NOUN
ejpam-6270	366	3	∈	∈	PROPN
ejpam-6270	366	4	w	w	NOUN
ejpam-6270	366	5	and	and	CCONJ
ejpam-6270	366	6	w	w	PROPN
ejpam-6270	366	7	be	be	AUX
ejpam-6270	366	8	any	any	DET
ejpam-6270	366	9	open	open	ADJ
ejpam-6270	366	10	set	set	NOUN
ejpam-6270	366	11	having	have	VERB
ejpam-6270	366	12	lα(ζ	lα(ζ	NOUN
ejpam-6270	366	13	)	)	PUNCT
ejpam-6270	366	14	=	=	PUNCT
ejpam-6270	367	1	α	α	PROPN
ejpam-6270	367	2	⊙	⊙	PROPN
ejpam-6270	367	3	ζ	ζ	PROPN
ejpam-6270	367	4	.	.	PUNCT
ejpam-6270	368	1	since	since	SCONJ
ejpam-6270	368	2	w	w	PROPN
ejpam-6270	368	3	is	be	AUX
ejpam-6270	368	4	a	a	DET
ejpam-6270	368	5	tbdalgebra	tbdalgebra	NOUN
ejpam-6270	368	6	,	,	PUNCT
ejpam-6270	368	7	so	so	SCONJ
ejpam-6270	368	8	there	there	PRON
ejpam-6270	368	9	exists	exist	VERB
ejpam-6270	368	10	a	a	DET
ejpam-6270	368	11	b	b	NOUN
ejpam-6270	368	12	-	-	PUNCT
ejpam-6270	368	13	open	open	ADJ
ejpam-6270	368	14	set	set	NOUN
ejpam-6270	368	15	v	v	ADP
ejpam-6270	368	16	having	have	VERB
ejpam-6270	368	17	ζ	ζ	NOUN
ejpam-6270	368	18	such	such	ADJ
ejpam-6270	368	19	that	that	DET
ejpam-6270	368	20	a⊙v	a⊙v	NOUN
ejpam-6270	368	21	⊆	⊆	NUM
ejpam-6270	368	22	w	w	NOUN
ejpam-6270	368	23	.	.	PUNCT
ejpam-6270	369	1	hence	hence	ADV
ejpam-6270	369	2	,	,	PUNCT
ejpam-6270	369	3	lα(v	lα(v	PUNCT
ejpam-6270	369	4	)	)	PUNCT
ejpam-6270	369	5	⊆	⊆	NUM
ejpam-6270	369	6	w	w	NOUN
ejpam-6270	369	7	.	.	PUNCT
ejpam-6270	370	1	thus	thus	ADV
ejpam-6270	370	2	,	,	PUNCT
ejpam-6270	370	3	we	we	PRON
ejpam-6270	370	4	get	get	VERB
ejpam-6270	370	5	lα	lα	ADP
ejpam-6270	370	6	is	be	AUX
ejpam-6270	370	7	b	b	NOUN
ejpam-6270	370	8	-	-	PUNCT
ejpam-6270	370	9	continuous	continuous	ADJ
ejpam-6270	370	10	.	.	PUNCT
ejpam-6270	371	1	proposition	proposition	NOUN
ejpam-6270	371	2	21	21	NUM
ejpam-6270	371	3	.	.	PUNCT
ejpam-6270	372	1	let	let	VERB
ejpam-6270	372	2	w	w	NOUN
ejpam-6270	372	3	be	be	AUX
ejpam-6270	372	4	an	an	DET
ejpam-6270	372	5	edge	edge	NOUN
ejpam-6270	372	6	tbd	tbd	NOUN
ejpam-6270	372	7	-	-	PUNCT
ejpam-6270	372	8	algebra	algebra	NOUN
ejpam-6270	372	9	.	.	PUNCT
ejpam-6270	373	1	if	if	SCONJ
ejpam-6270	373	2	α	α	PROPN
ejpam-6270	373	3	∈	∈	PROPN
ejpam-6270	373	4	w	w	ADP
ejpam-6270	373	5	such	such	ADJ
ejpam-6270	373	6	that	that	SCONJ
ejpam-6270	373	7	α	α	PROPN
ejpam-6270	373	8	⊙	⊙	PROPN
ejpam-6270	373	9	(	(	PUNCT
ejpam-6270	373	10	α	α	PROPN
ejpam-6270	373	11	⊙	⊙	PROPN
ejpam-6270	373	12	ζ	ζ	NOUN
ejpam-6270	373	13	)	)	PUNCT
ejpam-6270	373	14	is	be	AUX
ejpam-6270	373	15	an	an	DET
ejpam-6270	373	16	atom	atom	NOUN
ejpam-6270	373	17	for	for	ADP
ejpam-6270	373	18	every	every	DET
ejpam-6270	373	19	ζ	ζ	PROPN
ejpam-6270	373	20	∈	∈	PROPN
ejpam-6270	373	21	w	w	NOUN
ejpam-6270	373	22	,	,	PUNCT
ejpam-6270	373	23	then	then	ADV
ejpam-6270	373	24	the	the	DET
ejpam-6270	373	25	left	left	ADJ
ejpam-6270	373	26	map	map	NOUN
ejpam-6270	373	27	lα	lα	NOUN
ejpam-6270	373	28	on	on	ADP
ejpam-6270	373	29	w	w	PROPN
ejpam-6270	373	30	is	be	AUX
ejpam-6270	373	31	b	b	NOUN
ejpam-6270	373	32	-	-	ADV
ejpam-6270	373	33	open	open	ADJ
ejpam-6270	373	34	.	.	PUNCT
ejpam-6270	374	1	proof	proof	NOUN
ejpam-6270	374	2	.	.	PUNCT
ejpam-6270	375	1	let	let	VERB
ejpam-6270	375	2	w	w	NOUN
ejpam-6270	375	3	be	be	AUX
ejpam-6270	375	4	any	any	DET
ejpam-6270	375	5	open	open	ADJ
ejpam-6270	375	6	set	set	NOUN
ejpam-6270	375	7	in	in	ADP
ejpam-6270	375	8	w	w	PROPN
ejpam-6270	375	9	and	and	CCONJ
ejpam-6270	375	10	α	α	PROPN
ejpam-6270	375	11	∈	∈	PROPN
ejpam-6270	375	12	w.	w.	NOUN
ejpam-6270	375	13	we	we	PRON
ejpam-6270	375	14	have	have	VERB
ejpam-6270	375	15	to	to	PART
ejpam-6270	375	16	prove	prove	VERB
ejpam-6270	375	17	that	that	PRON
ejpam-6270	375	18	lα(w	lα(w	PRON
ejpam-6270	375	19	)	)	PUNCT
ejpam-6270	375	20	is	be	AUX
ejpam-6270	375	21	b	b	NOUN
ejpam-6270	375	22	-	-	ADV
ejpam-6270	375	23	open	open	ADJ
ejpam-6270	375	24	.	.	PUNCT
ejpam-6270	376	1	let	let	VERB
ejpam-6270	376	2	ζ	ζ	NOUN
ejpam-6270	376	3	∈	∈	PROPN
ejpam-6270	376	4	lα(w	lα(w	PRON
ejpam-6270	376	5	)	)	PUNCT
ejpam-6270	376	6	,	,	PUNCT
ejpam-6270	376	7	so	so	CCONJ
ejpam-6270	376	8	there	there	PRON
ejpam-6270	376	9	exists	exist	VERB
ejpam-6270	376	10	η	η	PROPN
ejpam-6270	376	11	∈	∈	PROPN
ejpam-6270	376	12	w	w	ADP
ejpam-6270	376	13	such	such	ADJ
ejpam-6270	376	14	that	that	SCONJ
ejpam-6270	376	15	ζ	ζ	NOUN
ejpam-6270	376	16	=	=	PUNCT
ejpam-6270	376	17	lα(η	lα(η	X
ejpam-6270	376	18	)	)	PUNCT
ejpam-6270	376	19	=	=	PUNCT
ejpam-6270	377	1	α	α	PROPN
ejpam-6270	377	2	⊙	⊙	PROPN
ejpam-6270	377	3	η	η	PROPN
ejpam-6270	377	4	.	.	PROPN
ejpam-6270	377	5	since	since	SCONJ
ejpam-6270	377	6	w	w	PROPN
ejpam-6270	377	7	,	,	PUNCT
ejpam-6270	377	8	is	be	AUX
ejpam-6270	377	9	an	an	DET
ejpam-6270	377	10	edge	edge	NOUN
ejpam-6270	377	11	d	d	NOUN
ejpam-6270	377	12	-	-	PUNCT
ejpam-6270	377	13	algebra	algebra	NOUN
ejpam-6270	377	14	,	,	PUNCT
ejpam-6270	377	15	so	so	SCONJ
ejpam-6270	377	16	it	it	PRON
ejpam-6270	377	17	satisfies	satisfy	VERB
ejpam-6270	377	18	condition	condition	NOUN
ejpam-6270	377	19	(	(	PUNCT
ejpam-6270	377	20	b2	b2	NOUN
ejpam-6270	377	21	)	)	PUNCT
ejpam-6270	377	22	,	,	PUNCT
ejpam-6270	377	23	that	that	ADV
ejpam-6270	377	24	is	is	ADV
ejpam-6270	377	25	(	(	PUNCT
ejpam-6270	377	26	α	α	PROPN
ejpam-6270	377	27	⊙	⊙	PROPN
ejpam-6270	377	28	(	(	PUNCT
ejpam-6270	377	29	α	α	PROPN
ejpam-6270	377	30	⊙	⊙	PROPN
ejpam-6270	377	31	η	η	PROPN
ejpam-6270	377	32	)	)	PUNCT
ejpam-6270	377	33	)	)	PUNCT
ejpam-6270	378	1	⊙	⊙	PROPN
ejpam-6270	378	2	η	η	PROPN
ejpam-6270	378	3	=	=	PROPN
ejpam-6270	378	4	0	0	PROPN
ejpam-6270	378	5	for	for	ADP
ejpam-6270	378	6	each	each	DET
ejpam-6270	378	7	η	η	PROPN
ejpam-6270	378	8	∈	∈	PROPN
ejpam-6270	378	9	w.	w.	PROPN
ejpam-6270	378	10	also	also	ADV
ejpam-6270	378	11	,	,	PUNCT
ejpam-6270	378	12	by	by	ADP
ejpam-6270	378	13	hypothesis	hypothesis	NOUN
ejpam-6270	378	14	,	,	PUNCT
ejpam-6270	378	15	we	we	PRON
ejpam-6270	378	16	have	have	VERB
ejpam-6270	378	17	α	α	PRON
ejpam-6270	378	18	⊙	⊙	PROPN
ejpam-6270	378	19	(	(	PUNCT
ejpam-6270	378	20	α	α	PROPN
ejpam-6270	378	21	⊙	⊙	PROPN
ejpam-6270	378	22	η	η	PROPN
ejpam-6270	378	23	)	)	PUNCT
ejpam-6270	378	24	is	be	AUX
ejpam-6270	378	25	an	an	DET
ejpam-6270	378	26	atom	atom	NOUN
ejpam-6270	378	27	.	.	PUNCT
ejpam-6270	379	1	hence	hence	ADV
ejpam-6270	379	2	,	,	PUNCT
ejpam-6270	379	3	we	we	PRON
ejpam-6270	379	4	get	get	VERB
ejpam-6270	379	5	α⊙	α⊙	NOUN
ejpam-6270	379	6	ζ	ζ	NOUN
ejpam-6270	379	7	=	=	SYM
ejpam-6270	379	8	α⊙	α⊙	NOUN
ejpam-6270	379	9	(	(	PUNCT
ejpam-6270	379	10	α⊙	α⊙	NOUN
ejpam-6270	379	11	η	η	NOUN
ejpam-6270	379	12	)	)	PUNCT
ejpam-6270	379	13	=	=	SYM
ejpam-6270	379	14	η	η	PROPN
ejpam-6270	379	15	.	.	PROPN
ejpam-6270	379	16	therefore	therefore	ADV
ejpam-6270	379	17	,	,	PUNCT
ejpam-6270	379	18	α⊙	α⊙	NOUN
ejpam-6270	379	19	ζ	ζ	NOUN
ejpam-6270	379	20	∈	∈	PROPN
ejpam-6270	379	21	w	w	NOUN
ejpam-6270	379	22	.	.	PUNCT
ejpam-6270	380	1	since	since	SCONJ
ejpam-6270	380	2	w	w	PROPN
ejpam-6270	380	3	is	be	AUX
ejpam-6270	380	4	a	a	DET
ejpam-6270	380	5	tbd	tbd	NOUN
ejpam-6270	380	6	-	-	PUNCT
ejpam-6270	380	7	algebra	algebra	NOUN
ejpam-6270	380	8	,	,	PUNCT
ejpam-6270	380	9	so	so	SCONJ
ejpam-6270	380	10	there	there	PRON
ejpam-6270	380	11	exists	exist	VERB
ejpam-6270	380	12	a	a	DET
ejpam-6270	380	13	b	b	NOUN
ejpam-6270	380	14	-	-	PUNCT
ejpam-6270	380	15	open	open	ADJ
ejpam-6270	380	16	set	set	NOUN
ejpam-6270	380	17	v	v	NOUN
ejpam-6270	380	18	containing	contain	VERB
ejpam-6270	380	19	ζ	ζ	NOUN
ejpam-6270	380	20	such	such	DET
ejpam-6270	380	21	that	that	SCONJ
ejpam-6270	380	22	a	a	DET
ejpam-6270	380	23	⊙	⊙	NOUN
ejpam-6270	380	24	v	v	ADP
ejpam-6270	380	25	⊆	⊆	NUM
ejpam-6270	380	26	w	w	NOUN
ejpam-6270	380	27	.	.	PUNCT
ejpam-6270	381	1	since	since	SCONJ
ejpam-6270	381	2	w	w	PROPN
ejpam-6270	381	3	,	,	PUNCT
ejpam-6270	381	4	satisfies	satisfie	NOUN
ejpam-6270	381	5	(	(	PUNCT
ejpam-6270	381	6	b2	b2	NOUN
ejpam-6270	381	7	)	)	PUNCT
ejpam-6270	381	8	,	,	PUNCT
ejpam-6270	381	9	so	so	SCONJ
ejpam-6270	381	10	we	we	PRON
ejpam-6270	381	11	get	get	VERB
ejpam-6270	381	12	v	v	NOUN
ejpam-6270	381	13	=	=	NOUN
ejpam-6270	381	14	α⊙	α⊙	NOUN
ejpam-6270	381	15	(	(	PUNCT
ejpam-6270	381	16	α⊙	α⊙	NOUN
ejpam-6270	381	17	v	v	NOUN
ejpam-6270	381	18	)	)	PUNCT
ejpam-6270	381	19	⊆	⊆	NUM
ejpam-6270	381	20	α⊙w	α⊙w	NUM
ejpam-6270	381	21	=	=	SYM
ejpam-6270	381	22	lα(w	lα(w	PRON
ejpam-6270	381	23	)	)	PUNCT
ejpam-6270	381	24	.	.	PUNCT
ejpam-6270	382	1	this	this	PRON
ejpam-6270	382	2	implies	imply	VERB
ejpam-6270	382	3	that	that	PRON
ejpam-6270	382	4	lα(w	lα(w	X
ejpam-6270	382	5	)	)	PUNCT
ejpam-6270	382	6	is	be	AUX
ejpam-6270	382	7	b	b	NOUN
ejpam-6270	382	8	-	-	ADV
ejpam-6270	382	9	open	open	ADJ
ejpam-6270	382	10	.	.	PUNCT
ejpam-6270	383	1	m.	m.	NOUN
ejpam-6270	383	2	w.	w.	PROPN
ejpam-6270	383	3	abdulqader	abdulqader	PROPN
ejpam-6270	383	4	,	,	PUNCT
ejpam-6270	383	5	a.	a.	PROPN
ejpam-6270	383	6	b.	b.	PROPN
ejpam-6270	383	7	khalaf	khalaf	PROPN
ejpam-6270	383	8	/	/	SYM
ejpam-6270	383	9	eur	eur	PROPN
ejpam-6270	383	10	.	.	PUNCT
ejpam-6270	384	1	j.	j.	PROPN
ejpam-6270	384	2	pure	pure	PROPN
ejpam-6270	384	3	appl	appl	PROPN
ejpam-6270	384	4	.	.	PROPN
ejpam-6270	384	5	math	math	PROPN
ejpam-6270	384	6	,	,	PUNCT
ejpam-6270	384	7	18	18	NUM
ejpam-6270	384	8	(	(	PUNCT
ejpam-6270	384	9	3	3	NUM
ejpam-6270	384	10	)	)	PUNCT
ejpam-6270	384	11	(	(	PUNCT
ejpam-6270	384	12	2025	2025	NUM
ejpam-6270	384	13	)	)	PUNCT
ejpam-6270	384	14	,	,	PUNCT
ejpam-6270	384	15	6270	6270	NUM
ejpam-6270	384	16	13	13	NUM
ejpam-6270	384	17	of	of	ADP
ejpam-6270	384	18	17	17	NUM
ejpam-6270	384	19	proposition	proposition	NOUN
ejpam-6270	384	20	22	22	NUM
ejpam-6270	384	21	.	.	PUNCT
ejpam-6270	385	1	let	let	VERB
ejpam-6270	385	2	w	w	NOUN
ejpam-6270	385	3	be	be	AUX
ejpam-6270	385	4	a	a	DET
ejpam-6270	385	5	tbd	tbd	NOUN
ejpam-6270	385	6	-	-	PUNCT
ejpam-6270	385	7	algebra	algebra	NOUN
ejpam-6270	385	8	,	,	PUNCT
ejpam-6270	385	9	then	then	ADV
ejpam-6270	385	10	every	every	DET
ejpam-6270	385	11	right	right	ADJ
ejpam-6270	385	12	map	map	NOUN
ejpam-6270	385	13	on	on	ADP
ejpam-6270	385	14	w	w	PROPN
ejpam-6270	385	15	is	be	AUX
ejpam-6270	385	16	b	b	NOUN
ejpam-6270	385	17	-	-	PUNCT
ejpam-6270	385	18	continuous	continuous	ADJ
ejpam-6270	385	19	.	.	PUNCT
ejpam-6270	386	1	proof	proof	NOUN
ejpam-6270	386	2	.	.	PUNCT
ejpam-6270	387	1	the	the	DET
ejpam-6270	387	2	proof	proof	NOUN
ejpam-6270	387	3	is	be	AUX
ejpam-6270	387	4	similar	similar	ADJ
ejpam-6270	387	5	to	to	ADP
ejpam-6270	387	6	the	the	DET
ejpam-6270	387	7	proof	proof	NOUN
ejpam-6270	387	8	of	of	ADP
ejpam-6270	387	9	proposition	proposition	NOUN
ejpam-6270	387	10	20	20	NUM
ejpam-6270	387	11	.	.	PUNCT
ejpam-6270	388	1	proposition	proposition	NOUN
ejpam-6270	388	2	23	23	NUM
ejpam-6270	388	3	.	.	PUNCT
ejpam-6270	389	1	if	if	SCONJ
ejpam-6270	389	2	w	w	NOUN
ejpam-6270	389	3	is	be	AUX
ejpam-6270	389	4	an	an	DET
ejpam-6270	389	5	edge	edge	NOUN
ejpam-6270	389	6	d	d	NOUN
ejpam-6270	389	7	-	-	NOUN
ejpam-6270	389	8	algebra	algebra	NOUN
ejpam-6270	389	9	in	in	ADP
ejpam-6270	389	10	which	which	DET
ejpam-6270	389	11	condition	condition	NOUN
ejpam-6270	389	12	(	(	PUNCT
ejpam-6270	389	13	b1	b1	NOUN
ejpam-6270	389	14	)	)	PUNCT
ejpam-6270	389	15	does	do	AUX
ejpam-6270	389	16	not	not	PART
ejpam-6270	389	17	hold	hold	VERB
ejpam-6270	389	18	for	for	ADP
ejpam-6270	389	19	all	all	DET
ejpam-6270	389	20	ζ	ζ	NOUN
ejpam-6270	389	21	,	,	PUNCT
ejpam-6270	389	22	η	η	PROPN
ejpam-6270	389	23	∈	∈	PROPN
ejpam-6270	389	24	w	w	PROPN
ejpam-6270	389	25	,	,	PUNCT
ejpam-6270	389	26	then	then	ADV
ejpam-6270	389	27	(	(	PUNCT
ejpam-6270	389	28	ζ	ζ	PROPN
ejpam-6270	389	29	⊙	⊙	X
ejpam-6270	389	30	η)⊙	η)⊙	VERB
ejpam-6270	389	31	y	y	PROPN
ejpam-6270	389	32	=	=	PUNCT
ejpam-6270	389	33	ζ	ζ	PROPN
ejpam-6270	389	34	for	for	ADP
ejpam-6270	389	35	all	all	DET
ejpam-6270	389	36	ζ	ζ	NOUN
ejpam-6270	389	37	,	,	PUNCT
ejpam-6270	389	38	η	η	PROPN
ejpam-6270	389	39	∈	∈	PROPN
ejpam-6270	389	40	w.	w.	NOUN
ejpam-6270	389	41	proof	proof	NOUN
ejpam-6270	389	42	.	.	PUNCT
ejpam-6270	390	1	since	since	SCONJ
ejpam-6270	390	2	w	w	PROPN
ejpam-6270	390	3	is	be	AUX
ejpam-6270	390	4	an	an	DET
ejpam-6270	390	5	edge	edge	NOUN
ejpam-6270	390	6	d	d	NOUN
ejpam-6270	390	7	-	-	PUNCT
ejpam-6270	390	8	algebra	algebra	NOUN
ejpam-6270	390	9	,	,	PUNCT
ejpam-6270	390	10	so	so	ADV
ejpam-6270	390	11	ζ	ζ	NOUN
ejpam-6270	390	12	⊙	⊙	NOUN
ejpam-6270	391	1	y	y	PROPN
ejpam-6270	391	2	=	=	PUNCT
ejpam-6270	391	3	{	{	PUNCT
ejpam-6270	391	4	ζ	ζ	NOUN
ejpam-6270	391	5	,	,	PUNCT
ejpam-6270	391	6	0	0	NUM
ejpam-6270	391	7	}	}	PUNCT
ejpam-6270	391	8	.	.	PUNCT
ejpam-6270	392	1	now	now	ADV
ejpam-6270	392	2	if	if	SCONJ
ejpam-6270	392	3	ζ	ζ	PROPN
ejpam-6270	392	4	⊙	⊙	X
ejpam-6270	392	5	y	y	PROPN
ejpam-6270	392	6	=	=	SYM
ejpam-6270	392	7	0	0	NUM
ejpam-6270	392	8	,	,	PUNCT
ejpam-6270	392	9	and	and	CCONJ
ejpam-6270	392	10	by	by	ADP
ejpam-6270	392	11	hypothesis	hypothesis	NOUN
ejpam-6270	392	12	,	,	PUNCT
ejpam-6270	392	13	we	we	PRON
ejpam-6270	392	14	have	have	VERB
ejpam-6270	392	15	(	(	PUNCT
ejpam-6270	392	16	ζ	ζ	PROPN
ejpam-6270	392	17	⊙	⊙	PROPN
ejpam-6270	392	18	η	η	PROPN
ejpam-6270	392	19	)	)	PUNCT
ejpam-6270	392	20	⊙	⊙	NOUN
ejpam-6270	392	21	(	(	PUNCT
ejpam-6270	392	22	ζ	ζ	PROPN
ejpam-6270	392	23	⊙	⊙	X
ejpam-6270	392	24	θ	θ	PROPN
ejpam-6270	392	25	)	)	PUNCT
ejpam-6270	392	26	)	)	PUNCT
ejpam-6270	392	27	⊙	⊙	NOUN
ejpam-6270	392	28	(	(	PUNCT
ejpam-6270	392	29	θ	θ	PROPN
ejpam-6270	392	30	⊙	⊙	PROPN
ejpam-6270	392	31	η	η	PROPN
ejpam-6270	392	32	)	)	PUNCT
ejpam-6270	392	33	̸=	̸=	PROPN
ejpam-6270	392	34	0	0	NUM
ejpam-6270	392	35	for	for	ADP
ejpam-6270	392	36	all	all	DET
ejpam-6270	392	37	ζ	ζ	NOUN
ejpam-6270	392	38	,	,	PUNCT
ejpam-6270	392	39	η	η	PROPN
ejpam-6270	392	40	,	,	PUNCT
ejpam-6270	392	41	θ	θ	PROPN
ejpam-6270	392	42	∈	∈	PROPN
ejpam-6270	392	43	w.	w.	PROPN
ejpam-6270	392	44	hence	hence	ADV
ejpam-6270	392	45	,	,	PUNCT
ejpam-6270	392	46	we	we	PRON
ejpam-6270	392	47	get	get	VERB
ejpam-6270	392	48	0	0	NUM
ejpam-6270	392	49	̸=	̸=	PROPN
ejpam-6270	392	50	(	(	PUNCT
ejpam-6270	392	51	ζ	ζ	PROPN
ejpam-6270	392	52	⊙	⊙	PROPN
ejpam-6270	392	53	η	η	PROPN
ejpam-6270	392	54	)	)	PUNCT
ejpam-6270	392	55	⊙	⊙	NOUN
ejpam-6270	392	56	(	(	PUNCT
ejpam-6270	392	57	ζ	ζ	PROPN
ejpam-6270	392	58	⊙	⊙	X
ejpam-6270	392	59	θ	θ	PROPN
ejpam-6270	392	60	)	)	PUNCT
ejpam-6270	392	61	)	)	PUNCT
ejpam-6270	392	62	⊙	⊙	NOUN
ejpam-6270	392	63	(	(	PUNCT
ejpam-6270	392	64	θ	θ	PROPN
ejpam-6270	392	65	⊙	⊙	PROPN
ejpam-6270	392	66	η	η	PROPN
ejpam-6270	392	67	)	)	PUNCT
ejpam-6270	393	1	=	=	SYM
ejpam-6270	393	2	0	0	NUM
ejpam-6270	393	3	⊙	⊙	NOUN
ejpam-6270	393	4	(	(	PUNCT
ejpam-6270	393	5	θ	θ	PROPN
ejpam-6270	393	6	⊙	⊙	PROPN
ejpam-6270	393	7	η	η	PROPN
ejpam-6270	393	8	)	)	PUNCT
ejpam-6270	393	9	=	=	SYM
ejpam-6270	393	10	0	0	NUM
ejpam-6270	393	11	which	which	PRON
ejpam-6270	393	12	is	be	AUX
ejpam-6270	393	13	contradiction	contradiction	NOUN
ejpam-6270	393	14	.	.	PUNCT
ejpam-6270	394	1	therefore	therefore	ADV
ejpam-6270	394	2	,	,	PUNCT
ejpam-6270	394	3	ζ	ζ	PROPN
ejpam-6270	394	4	⊙	⊙	PROPN
ejpam-6270	394	5	η	η	PROPN
ejpam-6270	394	6	=	=	PROPN
ejpam-6270	394	7	ζ	ζ	PROPN
ejpam-6270	394	8	and	and	CCONJ
ejpam-6270	394	9	thus	thus	ADV
ejpam-6270	394	10	(	(	PUNCT
ejpam-6270	394	11	ζ	ζ	PROPN
ejpam-6270	394	12	⊙	⊙	PROPN
ejpam-6270	394	13	η)⊙	η)⊙	PROPN
ejpam-6270	395	1	η	η	PROPN
ejpam-6270	395	2	=	=	SYM
ejpam-6270	395	3	ζ	ζ	PROPN
ejpam-6270	395	4	.	.	PUNCT
ejpam-6270	395	5	corollary	corollary	ADJ
ejpam-6270	395	6	7	7	NUM
ejpam-6270	395	7	.	.	PUNCT
ejpam-6270	396	1	if	if	SCONJ
ejpam-6270	396	2	w	w	NOUN
ejpam-6270	396	3	is	be	AUX
ejpam-6270	396	4	an	an	DET
ejpam-6270	396	5	edge	edge	NOUN
ejpam-6270	396	6	d	d	NOUN
ejpam-6270	396	7	-	-	NOUN
ejpam-6270	396	8	algebra	algebra	NOUN
ejpam-6270	396	9	in	in	ADP
ejpam-6270	396	10	which	which	PRON
ejpam-6270	396	11	all	all	DET
ejpam-6270	396	12	elements	element	NOUN
ejpam-6270	396	13	of	of	ADP
ejpam-6270	396	14	w	w	PROPN
ejpam-6270	396	15	are	be	AUX
ejpam-6270	396	16	atoms	atom	NOUN
ejpam-6270	396	17	,	,	PUNCT
ejpam-6270	396	18	then	then	ADV
ejpam-6270	396	19	(	(	PUNCT
ejpam-6270	396	20	ζ	ζ	PROPN
ejpam-6270	396	21	⊙	⊙	PROPN
ejpam-6270	396	22	η)⊙	η)⊙	PROPN
ejpam-6270	396	23	η	η	PROPN
ejpam-6270	396	24	=	=	PROPN
ejpam-6270	396	25	ζ	ζ	PROPN
ejpam-6270	396	26	for	for	ADP
ejpam-6270	396	27	all	all	DET
ejpam-6270	396	28	ζ	ζ	NOUN
ejpam-6270	396	29	,	,	PUNCT
ejpam-6270	396	30	η	η	PROPN
ejpam-6270	396	31	∈	∈	PROPN
ejpam-6270	396	32	w.	w.	NOUN
ejpam-6270	396	33	proof	proof	NOUN
ejpam-6270	396	34	.	.	PUNCT
ejpam-6270	397	1	since	since	SCONJ
ejpam-6270	397	2	each	each	DET
ejpam-6270	397	3	element	element	NOUN
ejpam-6270	397	4	of	of	ADP
ejpam-6270	397	5	w	w	PROPN
ejpam-6270	397	6	is	be	AUX
ejpam-6270	397	7	an	an	DET
ejpam-6270	397	8	atom	atom	NOUN
ejpam-6270	397	9	,	,	PUNCT
ejpam-6270	397	10	so	so	SCONJ
ejpam-6270	397	11	if	if	SCONJ
ejpam-6270	397	12	ζ	ζ	X
ejpam-6270	397	13	,	,	PUNCT
ejpam-6270	397	14	y	y	PROPN
ejpam-6270	397	15	∈	∈	PROPN
ejpam-6270	397	16	w	w	PROPN
ejpam-6270	397	17	,	,	PUNCT
ejpam-6270	397	18	then	then	ADV
ejpam-6270	397	19	ζ	ζ	NOUN
ejpam-6270	397	20	⊙	⊙	NOUN
ejpam-6270	397	21	y	y	PROPN
ejpam-6270	397	22	̸=	̸=	PROPN
ejpam-6270	397	23	0	0	NUM
ejpam-6270	397	24	.	.	PUNCT
ejpam-6270	398	1	since	since	SCONJ
ejpam-6270	398	2	w	w	PROPN
ejpam-6270	398	3	is	be	AUX
ejpam-6270	398	4	an	an	DET
ejpam-6270	398	5	edge	edge	NOUN
ejpam-6270	398	6	d	d	NOUN
ejpam-6270	398	7	-	-	PUNCT
ejpam-6270	398	8	algebra	algebra	NOUN
ejpam-6270	398	9	,	,	PUNCT
ejpam-6270	398	10	so	so	ADV
ejpam-6270	398	11	ζ	ζ	PROPN
ejpam-6270	398	12	⊙	⊙	PROPN
ejpam-6270	398	13	η	η	PROPN
ejpam-6270	398	14	=	=	PROPN
ejpam-6270	398	15	ζ	ζ	PROPN
ejpam-6270	398	16	.	.	PUNCT
ejpam-6270	399	1	hence	hence	ADV
ejpam-6270	399	2	,	,	PUNCT
ejpam-6270	399	3	(	(	PUNCT
ejpam-6270	399	4	ζ	ζ	PROPN
ejpam-6270	399	5	⊙	⊙	PROPN
ejpam-6270	399	6	η)⊙	η)⊙	PROPN
ejpam-6270	399	7	η	η	PROPN
ejpam-6270	399	8	=	=	PROPN
ejpam-6270	399	9	ζ	ζ	PROPN
ejpam-6270	399	10	for	for	ADP
ejpam-6270	399	11	all	all	DET
ejpam-6270	399	12	ζ	ζ	NOUN
ejpam-6270	399	13	,	,	PUNCT
ejpam-6270	399	14	η	η	PROPN
ejpam-6270	399	15	∈	∈	PROPN
ejpam-6270	399	16	w.	w.	NOUN
ejpam-6270	399	17	proposition	proposition	NOUN
ejpam-6270	399	18	24	24	NUM
ejpam-6270	399	19	.	.	PUNCT
ejpam-6270	400	1	let	let	VERB
ejpam-6270	400	2	w	w	NOUN
ejpam-6270	400	3	be	be	AUX
ejpam-6270	400	4	an	an	DET
ejpam-6270	400	5	edge	edge	NOUN
ejpam-6270	400	6	tbd	tbd	NOUN
ejpam-6270	400	7	-	-	PUNCT
ejpam-6270	400	8	algebra	algebra	NOUN
ejpam-6270	400	9	not	not	PART
ejpam-6270	400	10	satisfying	satisfy	VERB
ejpam-6270	400	11	condition	condition	NOUN
ejpam-6270	400	12	(	(	PUNCT
ejpam-6270	400	13	b1	b1	NOUN
ejpam-6270	400	14	)	)	PUNCT
ejpam-6270	400	15	for	for	ADP
ejpam-6270	400	16	all	all	DET
ejpam-6270	400	17	ζ	ζ	PROPN
ejpam-6270	400	18	,	,	PUNCT
ejpam-6270	400	19	η	η	PROPN
ejpam-6270	400	20	,	,	PUNCT
ejpam-6270	400	21	θ	θ	PROPN
ejpam-6270	400	22	∈	∈	PROPN
ejpam-6270	400	23	w	w	PROPN
ejpam-6270	400	24	,	,	PUNCT
ejpam-6270	400	25	then	then	ADV
ejpam-6270	400	26	every	every	DET
ejpam-6270	400	27	right	right	ADJ
ejpam-6270	400	28	map	map	NOUN
ejpam-6270	400	29	on	on	ADP
ejpam-6270	400	30	w	w	PROPN
ejpam-6270	400	31	is	be	AUX
ejpam-6270	400	32	b	b	NOUN
ejpam-6270	400	33	-	-	ADV
ejpam-6270	400	34	open	open	ADJ
ejpam-6270	400	35	.	.	PUNCT
ejpam-6270	401	1	proof	proof	NOUN
ejpam-6270	401	2	.	.	PUNCT
ejpam-6270	402	1	let	let	VERB
ejpam-6270	402	2	w	w	NOUN
ejpam-6270	402	3	be	be	AUX
ejpam-6270	402	4	any	any	DET
ejpam-6270	402	5	open	open	ADJ
ejpam-6270	402	6	set	set	NOUN
ejpam-6270	402	7	in	in	ADP
ejpam-6270	402	8	w	w	PROPN
ejpam-6270	402	9	and	and	CCONJ
ejpam-6270	402	10	α	α	PROPN
ejpam-6270	402	11	∈	∈	PROPN
ejpam-6270	402	12	w.	w.	NOUN
ejpam-6270	402	13	we	we	PRON
ejpam-6270	402	14	have	have	VERB
ejpam-6270	402	15	to	to	PART
ejpam-6270	402	16	prove	prove	VERB
ejpam-6270	402	17	that	that	PRON
ejpam-6270	402	18	rα(w	rα(w	PUNCT
ejpam-6270	402	19	)	)	PUNCT
ejpam-6270	402	20	is	be	AUX
ejpam-6270	402	21	b	b	NOUN
ejpam-6270	402	22	-	-	ADV
ejpam-6270	402	23	open	open	ADJ
ejpam-6270	402	24	.	.	PUNCT
ejpam-6270	403	1	let	let	VERB
ejpam-6270	403	2	ζ	ζ	NOUN
ejpam-6270	403	3	∈	∈	PROPN
ejpam-6270	403	4	rα(w	rα(w	PUNCT
ejpam-6270	403	5	)	)	PUNCT
ejpam-6270	403	6	,	,	PUNCT
ejpam-6270	403	7	then	then	ADV
ejpam-6270	403	8	∃	∃	PROPN
ejpam-6270	403	9	η	η	PROPN
ejpam-6270	403	10	∈	∈	PROPN
ejpam-6270	403	11	w	w	ADP
ejpam-6270	403	12	such	such	ADJ
ejpam-6270	403	13	that	that	SCONJ
ejpam-6270	403	14	ζ	ζ	NOUN
ejpam-6270	403	15	=	=	SYM
ejpam-6270	403	16	rα(η	rα(η	NOUN
ejpam-6270	403	17	)	)	PUNCT
ejpam-6270	403	18	=	=	SYM
ejpam-6270	403	19	η	η	PROPN
ejpam-6270	403	20	⊙	⊙	PROPN
ejpam-6270	403	21	α	α	PROPN
ejpam-6270	403	22	.	.	PUNCT
ejpam-6270	404	1	hence	hence	ADV
ejpam-6270	404	2	,	,	PUNCT
ejpam-6270	404	3	we	we	PRON
ejpam-6270	404	4	have	have	VERB
ejpam-6270	404	5	ζ	ζ	NOUN
ejpam-6270	404	6	⊙	⊙	NOUN
ejpam-6270	404	7	α	α	PROPN
ejpam-6270	405	1	=	=	SYM
ejpam-6270	406	1	(	(	PUNCT
ejpam-6270	406	2	η	η	PROPN
ejpam-6270	406	3	⊙	⊙	PROPN
ejpam-6270	406	4	α	α	PROPN
ejpam-6270	406	5	)	)	PUNCT
ejpam-6270	406	6	⊙	⊙	PROPN
ejpam-6270	406	7	α	α	PROPN
ejpam-6270	406	8	and	and	CCONJ
ejpam-6270	406	9	by	by	ADP
ejpam-6270	406	10	proposition	proposition	NOUN
ejpam-6270	406	11	23	23	NUM
ejpam-6270	406	12	,	,	PUNCT
ejpam-6270	406	13	we	we	PRON
ejpam-6270	406	14	get	get	VERB
ejpam-6270	406	15	ζ	ζ	NOUN
ejpam-6270	406	16	⊙	⊙	NOUN
ejpam-6270	406	17	α	α	PROPN
ejpam-6270	407	1	=	=	SYM
ejpam-6270	408	1	(	(	PUNCT
ejpam-6270	408	2	η	η	PROPN
ejpam-6270	408	3	⊙	⊙	PROPN
ejpam-6270	408	4	α	α	X
ejpam-6270	408	5	)	)	PUNCT
ejpam-6270	408	6	⊙	⊙	PROPN
ejpam-6270	408	7	α	α	PROPN
ejpam-6270	409	1	=	=	SYM
ejpam-6270	409	2	η	η	PROPN
ejpam-6270	409	3	.	.	PROPN
ejpam-6270	409	4	hence	hence	ADV
ejpam-6270	409	5	,	,	PUNCT
ejpam-6270	410	1	ζ	ζ	NOUN
ejpam-6270	410	2	⊙α	⊙α	PROPN
ejpam-6270	410	3	∈	∈	PROPN
ejpam-6270	410	4	w	w	PROPN
ejpam-6270	410	5	.	.	PUNCT
ejpam-6270	411	1	since	since	SCONJ
ejpam-6270	411	2	w	w	PROPN
ejpam-6270	411	3	is	be	AUX
ejpam-6270	411	4	a	a	DET
ejpam-6270	411	5	tbd	tbd	NOUN
ejpam-6270	411	6	-	-	PUNCT
ejpam-6270	411	7	algebra	algebra	NOUN
ejpam-6270	411	8	,	,	PUNCT
ejpam-6270	411	9	so	so	ADV
ejpam-6270	411	10	∃	∃	PROPN
ejpam-6270	411	11	a	a	DET
ejpam-6270	411	12	b	b	NOUN
ejpam-6270	411	13	-	-	PUNCT
ejpam-6270	411	14	open	open	ADJ
ejpam-6270	411	15	set	set	NOUN
ejpam-6270	411	16	v	v	ADP
ejpam-6270	411	17	having	have	VERB
ejpam-6270	411	18	ζ	ζ	NOUN
ejpam-6270	411	19	such	such	ADJ
ejpam-6270	411	20	that	that	DET
ejpam-6270	411	21	v	v	NOUN
ejpam-6270	411	22	⊙α	⊙α	PROPN
ejpam-6270	411	23	⊆	⊆	NUM
ejpam-6270	411	24	w	w	NOUN
ejpam-6270	411	25	.	.	PUNCT
ejpam-6270	411	26	again	again	ADV
ejpam-6270	411	27	by	by	ADP
ejpam-6270	411	28	proposition	proposition	NOUN
ejpam-6270	411	29	23	23	NUM
ejpam-6270	411	30	,	,	PUNCT
ejpam-6270	411	31	we	we	PRON
ejpam-6270	411	32	get	get	VERB
ejpam-6270	411	33	v	v	NOUN
ejpam-6270	411	34	=	=	PUNCT
ejpam-6270	411	35	(	(	PUNCT
ejpam-6270	411	36	v	v	NUM
ejpam-6270	411	37	⊙	⊙	PROPN
ejpam-6270	411	38	α)⊙	α)⊙	PROPN
ejpam-6270	411	39	α	α	PROPN
ejpam-6270	411	40	⊆	⊆	PROPN
ejpam-6270	411	41	w	w	PROPN
ejpam-6270	411	42	⊙	⊙	PROPN
ejpam-6270	411	43	α	α	PROPN
ejpam-6270	411	44	=	=	X
ejpam-6270	411	45	rα(w	rα(w	X
ejpam-6270	411	46	)	)	PUNCT
ejpam-6270	411	47	.	.	PUNCT
ejpam-6270	412	1	thus	thus	ADV
ejpam-6270	412	2	,	,	PUNCT
ejpam-6270	412	3	rα(w	rα(w	X
ejpam-6270	412	4	)	)	PUNCT
ejpam-6270	412	5	is	be	AUX
ejpam-6270	412	6	b	b	NOUN
ejpam-6270	412	7	-	-	PUNCT
ejpam-6270	412	8	open	open	ADJ
ejpam-6270	412	9	.	.	PUNCT
ejpam-6270	413	1	corollary	corollary	ADJ
ejpam-6270	413	2	8	8	NUM
ejpam-6270	413	3	.	.	PUNCT
ejpam-6270	414	1	let	let	VERB
ejpam-6270	414	2	w	w	NOUN
ejpam-6270	414	3	be	be	AUX
ejpam-6270	414	4	an	an	DET
ejpam-6270	414	5	edge	edge	NOUN
ejpam-6270	414	6	tbd	tbd	NOUN
ejpam-6270	414	7	-	-	NOUN
ejpam-6270	414	8	algebra	algebra	NOUN
ejpam-6270	414	9	such	such	ADJ
ejpam-6270	414	10	that	that	SCONJ
ejpam-6270	414	11	every	every	DET
ejpam-6270	414	12	element	element	NOUN
ejpam-6270	414	13	of	of	ADP
ejpam-6270	414	14	w	w	PROPN
ejpam-6270	414	15	is	be	AUX
ejpam-6270	414	16	an	an	DET
ejpam-6270	414	17	atom	atom	NOUN
ejpam-6270	414	18	,	,	PUNCT
ejpam-6270	414	19	then	then	ADV
ejpam-6270	414	20	every	every	DET
ejpam-6270	414	21	right	right	ADJ
ejpam-6270	414	22	map	map	NOUN
ejpam-6270	414	23	on	on	ADP
ejpam-6270	414	24	w	w	PROPN
ejpam-6270	414	25	is	be	AUX
ejpam-6270	414	26	b	b	NOUN
ejpam-6270	414	27	-	-	ADV
ejpam-6270	414	28	open	open	ADJ
ejpam-6270	414	29	.	.	PUNCT
ejpam-6270	415	1	proof	proof	NOUN
ejpam-6270	415	2	.	.	PUNCT
ejpam-6270	416	1	follows	follow	VERB
ejpam-6270	416	2	from	from	ADP
ejpam-6270	416	3	proposition	proposition	NOUN
ejpam-6270	416	4	24	24	NUM
ejpam-6270	416	5	and	and	CCONJ
ejpam-6270	416	6	corollary	corollary	ADJ
ejpam-6270	416	7	7	7	NUM
ejpam-6270	416	8	.	.	PUNCT
ejpam-6270	416	9	definition	definition	NOUN
ejpam-6270	416	10	18	18	NUM
ejpam-6270	416	11	.	.	PUNCT
ejpam-6270	417	1	let	let	VERB
ejpam-6270	417	2	w	w	NOUN
ejpam-6270	417	3	be	be	AUX
ejpam-6270	417	4	a	a	DET
ejpam-6270	417	5	d	d	NOUN
ejpam-6270	417	6	-	-	NOUN
ejpam-6270	417	7	algebra	algebra	NOUN
ejpam-6270	417	8	,	,	PUNCT
ejpam-6270	417	9	we	we	PRON
ejpam-6270	417	10	define	define	VERB
ejpam-6270	417	11	a	a	DET
ejpam-6270	417	12	map	map	NOUN
ejpam-6270	418	1	f	f	NOUN
ejpam-6270	418	2	:	:	PUNCT
ejpam-6270	418	3	ζ	ζ	NOUN
ejpam-6270	418	4	→	→	SYM
ejpam-6270	418	5	l(w	l(w	PROPN
ejpam-6270	418	6	)	)	PUNCT
ejpam-6270	418	7	by	by	ADP
ejpam-6270	418	8	f(w	f(w	PROPN
ejpam-6270	418	9	)	)	PUNCT
ejpam-6270	418	10	=	=	PRON
ejpam-6270	418	11	lζ	lζ	ADJ
ejpam-6270	418	12	for	for	ADP
ejpam-6270	418	13	all	all	DET
ejpam-6270	418	14	ζ	ζ	PROPN
ejpam-6270	418	15	∈	∈	PROPN
ejpam-6270	418	16	w.	w.	NOUN
ejpam-6270	418	17	if	if	SCONJ
ejpam-6270	418	18	m	m	PROPN
ejpam-6270	418	19	⊆	⊆	NUM
ejpam-6270	418	20	w	w	NOUN
ejpam-6270	418	21	,	,	PUNCT
ejpam-6270	418	22	then	then	ADV
ejpam-6270	418	23	f(m	f(m	PROPN
ejpam-6270	418	24	)	)	PUNCT
ejpam-6270	418	25	=	=	PRON
ejpam-6270	418	26	{	{	PUNCT
ejpam-6270	418	27	lζ	lζ	ADJ
ejpam-6270	418	28	:	:	PUNCT
ejpam-6270	418	29	ζ	ζ	PROPN
ejpam-6270	418	30	∈	∈	PROPN
ejpam-6270	418	31	m	m	PRON
ejpam-6270	418	32	}	}	PUNCT
ejpam-6270	418	33	.	.	PUNCT
ejpam-6270	419	1	proposition	proposition	NOUN
ejpam-6270	419	2	25	25	NUM
ejpam-6270	419	3	.	.	PUNCT
ejpam-6270	420	1	if	if	SCONJ
ejpam-6270	420	2	w	w	NOUN
ejpam-6270	420	3	is	be	AUX
ejpam-6270	420	4	a	a	DET
ejpam-6270	420	5	d	d	NOUN
ejpam-6270	420	6	-	-	NOUN
ejpam-6270	420	7	algebra	algebra	NOUN
ejpam-6270	420	8	,	,	PUNCT
ejpam-6270	420	9	then	then	ADV
ejpam-6270	420	10	the	the	DET
ejpam-6270	420	11	following	following	ADJ
ejpam-6270	420	12	statements	statement	NOUN
ejpam-6270	420	13	are	be	AUX
ejpam-6270	420	14	true	true	ADJ
ejpam-6270	420	15	:	:	PUNCT
ejpam-6270	420	16	(	(	PUNCT
ejpam-6270	420	17	i	i	NOUN
ejpam-6270	420	18	)	)	PUNCT
ejpam-6270	420	19	if	if	SCONJ
ejpam-6270	420	20	m	m	PROPN
ejpam-6270	420	21	⊆	⊆	NUM
ejpam-6270	420	22	n	n	NOUN
ejpam-6270	420	23	,	,	PUNCT
ejpam-6270	420	24	then	then	ADV
ejpam-6270	420	25	f(m	f(m	PROPN
ejpam-6270	420	26	)	)	PUNCT
ejpam-6270	420	27	⊆	⊆	NUM
ejpam-6270	420	28	f(n	f(n	PROPN
ejpam-6270	420	29	)	)	PUNCT
ejpam-6270	420	30	.	.	PUNCT
ejpam-6270	421	1	(	(	PUNCT
ejpam-6270	421	2	ii	ii	X
ejpam-6270	421	3	)	)	PUNCT
ejpam-6270	421	4	f(m	f(m	PROPN
ejpam-6270	421	5	c	c	NOUN
ejpam-6270	421	6	)	)	PUNCT
ejpam-6270	421	7	=	=	SYM
ejpam-6270	421	8	(	(	PUNCT
ejpam-6270	421	9	f(m))c	f(m))c	PROPN
ejpam-6270	421	10	.	.	PUNCT
ejpam-6270	422	1	(	(	PUNCT
ejpam-6270	422	2	iii	iii	X
ejpam-6270	422	3	)	)	PUNCT
ejpam-6270	422	4	if	if	SCONJ
ejpam-6270	422	5	{	{	PUNCT
ejpam-6270	422	6	mλ	mλ	INTJ
ejpam-6270	422	7	:	:	PUNCT
ejpam-6270	422	8	λ	λ	X
ejpam-6270	422	9	∈	∈	PROPN
ejpam-6270	422	10	λ	λ	PROPN
ejpam-6270	422	11	}	}	PUNCT
ejpam-6270	422	12	is	be	AUX
ejpam-6270	422	13	any	any	DET
ejpam-6270	422	14	family	family	NOUN
ejpam-6270	422	15	of	of	ADP
ejpam-6270	422	16	subsets	subset	NOUN
ejpam-6270	422	17	of	of	ADP
ejpam-6270	422	18	w	w	NOUN
ejpam-6270	422	19	,	,	PUNCT
ejpam-6270	422	20	then	then	ADV
ejpam-6270	422	21	f	f	X
ejpam-6270	422	22	(	(	PUNCT
ejpam-6270	422	23	⋃	⋃	PROPN
ejpam-6270	422	24	λ∈λmλ	λ∈λmλ	NOUN
ejpam-6270	422	25	)	)	PUNCT
ejpam-6270	422	26	=	=	PUNCT
ejpam-6270	422	27	⋃	⋃	NOUN
ejpam-6270	422	28	λ∈λf(mλ	λ∈λf(mλ	NOUN
ejpam-6270	422	29	)	)	PUNCT
ejpam-6270	422	30	and	and	CCONJ
ejpam-6270	422	31	f	f	X
ejpam-6270	422	32	(	(	PUNCT
ejpam-6270	422	33	⋂	⋂	PROPN
ejpam-6270	422	34	λ∈λmλ	λ∈λmλ	PROPN
ejpam-6270	422	35	)	)	PUNCT
ejpam-6270	423	1	=	=	SYM
ejpam-6270	423	2	⋂	⋂	PROPN
ejpam-6270	423	3	λ∈λf(mλ	λ∈λf(mλ	PROPN
ejpam-6270	423	4	)	)	PUNCT
ejpam-6270	423	5	.	.	PUNCT
ejpam-6270	424	1	proof	proof	NOUN
ejpam-6270	424	2	.	.	PUNCT
ejpam-6270	425	1	m.	m.	NOUN
ejpam-6270	425	2	w.	w.	PROPN
ejpam-6270	425	3	abdulqader	abdulqader	PROPN
ejpam-6270	425	4	,	,	PUNCT
ejpam-6270	425	5	a.	a.	PROPN
ejpam-6270	425	6	b.	b.	PROPN
ejpam-6270	425	7	khalaf	khalaf	PROPN
ejpam-6270	425	8	/	/	SYM
ejpam-6270	425	9	eur	eur	PROPN
ejpam-6270	425	10	.	.	PUNCT
ejpam-6270	426	1	j.	j.	PROPN
ejpam-6270	426	2	pure	pure	PROPN
ejpam-6270	426	3	appl	appl	PROPN
ejpam-6270	426	4	.	.	PROPN
ejpam-6270	426	5	math	math	PROPN
ejpam-6270	426	6	,	,	PUNCT
ejpam-6270	426	7	18	18	NUM
ejpam-6270	426	8	(	(	PUNCT
ejpam-6270	426	9	3	3	NUM
ejpam-6270	426	10	)	)	PUNCT
ejpam-6270	426	11	(	(	PUNCT
ejpam-6270	426	12	2025	2025	NUM
ejpam-6270	426	13	)	)	PUNCT
ejpam-6270	426	14	,	,	PUNCT
ejpam-6270	426	15	6270	6270	NUM
ejpam-6270	426	16	14	14	NUM
ejpam-6270	426	17	of	of	ADP
ejpam-6270	426	18	17	17	NUM
ejpam-6270	426	19	(	(	PUNCT
ejpam-6270	426	20	i	i	NOUN
ejpam-6270	426	21	)	)	PUNCT
ejpam-6270	426	22	let	let	VERB
ejpam-6270	426	23	m	m	PROPN
ejpam-6270	426	24	⊆	⊆	NUM
ejpam-6270	426	25	n	n	NOUN
ejpam-6270	426	26	and	and	CCONJ
ejpam-6270	426	27	let	let	VERB
ejpam-6270	426	28	lζ	lζ	PROPN
ejpam-6270	426	29	∈	∈	PROPN
ejpam-6270	426	30	f(m	f(m	PROPN
ejpam-6270	426	31	)	)	PUNCT
ejpam-6270	426	32	.	.	PUNCT
ejpam-6270	427	1	hence	hence	ADV
ejpam-6270	427	2	,	,	PUNCT
ejpam-6270	427	3	ζ	ζ	PROPN
ejpam-6270	427	4	∈	∈	PROPN
ejpam-6270	427	5	m	m	VERB
ejpam-6270	427	6	⊆	⊆	NUM
ejpam-6270	427	7	n	n	PRON
ejpam-6270	427	8	implies	imply	VERB
ejpam-6270	427	9	lζ	lζ	PROPN
ejpam-6270	427	10	∈	∈	PROPN
ejpam-6270	427	11	f(n	f(n	PROPN
ejpam-6270	427	12	)	)	PUNCT
ejpam-6270	427	13	.	.	PUNCT
ejpam-6270	428	1	thus	thus	ADV
ejpam-6270	428	2	,	,	PUNCT
ejpam-6270	428	3	f(m	f(m	PROPN
ejpam-6270	428	4	)	)	PUNCT
ejpam-6270	428	5	⊆	⊆	NUM
ejpam-6270	428	6	f(n	f(n	PROPN
ejpam-6270	428	7	)	)	PUNCT
ejpam-6270	428	8	.	.	PUNCT
ejpam-6270	429	1	(	(	PUNCT
ejpam-6270	429	2	ii	ii	NOUN
ejpam-6270	429	3	)	)	PUNCT
ejpam-6270	429	4	lζ	lζ	PROPN
ejpam-6270	429	5	∈	∈	PROPN
ejpam-6270	429	6	f(m	f(m	PROPN
ejpam-6270	429	7	c	c	PROPN
ejpam-6270	429	8	)	)	PUNCT
ejpam-6270	429	9	if	if	SCONJ
ejpam-6270	429	10	,	,	PUNCT
ejpam-6270	429	11	and	and	CCONJ
ejpam-6270	429	12	only	only	ADV
ejpam-6270	429	13	if	if	SCONJ
ejpam-6270	429	14	ζ	ζ	PROPN
ejpam-6270	429	15	∈	∈	PROPN
ejpam-6270	429	16	m	m	VERB
ejpam-6270	429	17	c	c	NOUN
ejpam-6270	429	18	implies	imply	VERB
ejpam-6270	429	19	ζ	ζ	NOUN
ejpam-6270	429	20	/∈	/∈	PUNCT
ejpam-6270	430	1	m	m	VERB
ejpam-6270	430	2	if	if	SCONJ
ejpam-6270	430	3	,	,	PUNCT
ejpam-6270	430	4	and	and	CCONJ
ejpam-6270	430	5	only	only	ADV
ejpam-6270	430	6	if	if	SCONJ
ejpam-6270	430	7	lζ	lζ	ADJ
ejpam-6270	430	8	/∈	/∈	PUNCT
ejpam-6270	430	9	f(m	f(m	PROPN
ejpam-6270	430	10	)	)	PUNCT
ejpam-6270	431	1	if	if	SCONJ
ejpam-6270	431	2	,	,	PUNCT
ejpam-6270	431	3	and	and	CCONJ
ejpam-6270	431	4	only	only	ADV
ejpam-6270	431	5	if	if	SCONJ
ejpam-6270	431	6	lζ	lζ	PROPN
ejpam-6270	431	7	∈	∈	PROPN
ejpam-6270	431	8	(	(	PUNCT
ejpam-6270	431	9	f(m))c	f(m))c	PROPN
ejpam-6270	431	10	.	.	PUNCT
ejpam-6270	431	11	(	(	PUNCT
ejpam-6270	431	12	iii	iii	X
ejpam-6270	431	13	)	)	PUNCT
ejpam-6270	431	14	we	we	PRON
ejpam-6270	431	15	shall	shall	AUX
ejpam-6270	431	16	prove	prove	VERB
ejpam-6270	431	17	for	for	ADP
ejpam-6270	431	18	the	the	DET
ejpam-6270	431	19	union	union	NOUN
ejpam-6270	431	20	,	,	PUNCT
ejpam-6270	431	21	the	the	DET
ejpam-6270	431	22	other	other	ADJ
ejpam-6270	431	23	proof	proof	NOUN
ejpam-6270	431	24	is	be	AUX
ejpam-6270	431	25	similar	similar	ADJ
ejpam-6270	431	26	.	.	PUNCT
ejpam-6270	432	1	let	let	VERB
ejpam-6270	432	2	lζ	lζ	PROPN
ejpam-6270	432	3	∈	∈	PROPN
ejpam-6270	432	4	f	f	X
ejpam-6270	432	5	(	(	PUNCT
ejpam-6270	432	6	⋃	⋃	PROPN
ejpam-6270	432	7	λ∈λmλ	λ∈λmλ	PROPN
ejpam-6270	432	8	)	)	PUNCT
ejpam-6270	432	9	,	,	PUNCT
ejpam-6270	432	10	then	then	ADV
ejpam-6270	432	11	ζ	ζ	NOUN
ejpam-6270	432	12	∈	∈	NOUN
ejpam-6270	432	13	⋃	⋃	PROPN
ejpam-6270	432	14	λ∈λmλ	λ∈λmλ	PROPN
ejpam-6270	432	15	that	that	PRON
ejpam-6270	432	16	is	be	AUX
ejpam-6270	432	17	there	there	PRON
ejpam-6270	432	18	is	be	VERB
ejpam-6270	432	19	λ	λ	PROPN
ejpam-6270	432	20	∈	∈	NOUN
ejpam-6270	432	21	λ	λ	NOUN
ejpam-6270	432	22	such	such	ADJ
ejpam-6270	432	23	that	that	SCONJ
ejpam-6270	432	24	ζ	ζ	PROPN
ejpam-6270	432	25	∈	∈	PROPN
ejpam-6270	432	26	mλ	mλ	NOUN
ejpam-6270	432	27	,	,	PUNCT
ejpam-6270	432	28	so	so	ADV
ejpam-6270	432	29	lζ	lζ	PROPN
ejpam-6270	432	30	∈	∈	PROPN
ejpam-6270	432	31	f(mλ	f(mλ	NOUN
ejpam-6270	432	32	)	)	PUNCT
ejpam-6270	432	33	for	for	ADP
ejpam-6270	432	34	some	some	DET
ejpam-6270	432	35	λ	λ	PROPN
ejpam-6270	432	36	∈	∈	PROPN
ejpam-6270	432	37	λ	λ	PROPN
ejpam-6270	432	38	.	.	PUNCT
ejpam-6270	433	1	hence	hence	ADV
ejpam-6270	433	2	,	,	PUNCT
ejpam-6270	433	3	lζ	lζ	PROPN
ejpam-6270	433	4	∈	∈	PROPN
ejpam-6270	433	5	⋃	⋃	PROPN
ejpam-6270	433	6	λ∈λf(mλ	λ∈λf(mλ	NOUN
ejpam-6270	433	7	)	)	PUNCT
ejpam-6270	433	8	.	.	PUNCT
ejpam-6270	434	1	proposition	proposition	NOUN
ejpam-6270	434	2	26	26	NUM
ejpam-6270	434	3	.	.	PUNCT
ejpam-6270	435	1	let	let	VERB
ejpam-6270	435	2	w	w	NOUN
ejpam-6270	435	3	be	be	AUX
ejpam-6270	435	4	a	a	DET
ejpam-6270	435	5	positive	positive	ADJ
ejpam-6270	435	6	implicative	implicative	ADJ
ejpam-6270	435	7	d	d	NOUN
ejpam-6270	435	8	-	-	PUNCT
ejpam-6270	435	9	algebra	algebra	NOUN
ejpam-6270	435	10	,	,	PUNCT
ejpam-6270	435	11	then	then	ADV
ejpam-6270	435	12	the	the	DET
ejpam-6270	435	13	map	map	NOUN
ejpam-6270	435	14	f	f	X
ejpam-6270	435	15	:	:	PUNCT
ejpam-6270	435	16	ζ	ζ	NOUN
ejpam-6270	435	17	→	→	SYM
ejpam-6270	435	18	l(w	l(w	PROPN
ejpam-6270	435	19	)	)	PUNCT
ejpam-6270	435	20	is	be	AUX
ejpam-6270	435	21	a	a	DET
ejpam-6270	435	22	d	d	NOUN
ejpam-6270	435	23	-	-	NOUN
ejpam-6270	435	24	isomorphism	isomorphism	NOUN
ejpam-6270	435	25	.	.	PUNCT
ejpam-6270	436	1	proof	proof	NOUN
ejpam-6270	436	2	.	.	PUNCT
ejpam-6270	437	1	it	it	PRON
ejpam-6270	437	2	is	be	AUX
ejpam-6270	437	3	obvious	obvious	ADJ
ejpam-6270	437	4	that	that	SCONJ
ejpam-6270	437	5	f	f	PROPN
ejpam-6270	437	6	is	be	AUX
ejpam-6270	437	7	a	a	DET
ejpam-6270	437	8	bijection	bijection	NOUN
ejpam-6270	437	9	.	.	PUNCT
ejpam-6270	438	1	we	we	PRON
ejpam-6270	438	2	have	have	VERB
ejpam-6270	438	3	f(ζ	f(ζ	PROPN
ejpam-6270	438	4	⊙	⊙	PROPN
ejpam-6270	438	5	η	η	PROPN
ejpam-6270	438	6	)	)	PUNCT
ejpam-6270	438	7	=	=	NOUN
ejpam-6270	438	8	lζ⊙η	lζ⊙η	X
ejpam-6270	438	9	and	and	CCONJ
ejpam-6270	438	10	lζ⊙η(θ	lζ⊙η(θ	PROPN
ejpam-6270	438	11	)	)	PUNCT
ejpam-6270	438	12	=	=	SYM
ejpam-6270	438	13	(	(	PUNCT
ejpam-6270	438	14	ζ	ζ	PROPN
ejpam-6270	438	15	⊙	⊙	PROPN
ejpam-6270	438	16	η	η	PROPN
ejpam-6270	438	17	)	)	PUNCT
ejpam-6270	439	1	⊙	⊙	PROPN
ejpam-6270	439	2	θ	θ	PROPN
ejpam-6270	439	3	.	.	PUNCT
ejpam-6270	440	1	since	since	SCONJ
ejpam-6270	440	2	w	w	PROPN
ejpam-6270	440	3	is	be	AUX
ejpam-6270	440	4	positive	positive	ADJ
ejpam-6270	440	5	implicative	implicative	ADJ
ejpam-6270	440	6	,	,	PUNCT
ejpam-6270	440	7	we	we	PRON
ejpam-6270	440	8	have	have	VERB
ejpam-6270	440	9	(	(	PUNCT
ejpam-6270	440	10	ζ	ζ	PROPN
ejpam-6270	440	11	⊙	⊙	PROPN
ejpam-6270	440	12	η	η	PROPN
ejpam-6270	440	13	)	)	PUNCT
ejpam-6270	440	14	⊙	⊙	NOUN
ejpam-6270	440	15	θ	θ	PROPN
ejpam-6270	441	1	=	=	PUNCT
ejpam-6270	441	2	(	(	PUNCT
ejpam-6270	441	3	ζ	ζ	PROPN
ejpam-6270	441	4	⊙	⊙	PROPN
ejpam-6270	441	5	θ	θ	PROPN
ejpam-6270	441	6	)	)	PUNCT
ejpam-6270	441	7	⊙	⊙	NOUN
ejpam-6270	441	8	(	(	PUNCT
ejpam-6270	441	9	η	η	PROPN
ejpam-6270	441	10	⊙	⊙	PROPN
ejpam-6270	441	11	θ	θ	PROPN
ejpam-6270	441	12	)	)	PUNCT
ejpam-6270	441	13	.	.	PUNCT
ejpam-6270	442	1	therefore	therefore	ADV
ejpam-6270	442	2	,	,	PUNCT
ejpam-6270	442	3	lζ⊙η(θ	lζ⊙η(θ	PROPN
ejpam-6270	442	4	)	)	PUNCT
ejpam-6270	442	5	=	=	SYM
ejpam-6270	442	6	lζ(θ	lζ(θ	NOUN
ejpam-6270	442	7	)	)	PUNCT
ejpam-6270	442	8	◦	◦	NOUN
ejpam-6270	442	9	lη(θ	lη(θ	PUNCT
ejpam-6270	442	10	)	)	PUNCT
ejpam-6270	443	1	=	=	SYM
ejpam-6270	443	2	(	(	PUNCT
ejpam-6270	443	3	lζ	lζ	PROPN
ejpam-6270	443	4	◦	◦	PROPN
ejpam-6270	443	5	lη)(θ	lη)(θ	PROPN
ejpam-6270	443	6	)	)	PUNCT
ejpam-6270	443	7	.	.	PUNCT
ejpam-6270	444	1	hence	hence	ADV
ejpam-6270	444	2	,	,	PUNCT
ejpam-6270	444	3	f(ζ	f(ζ	PROPN
ejpam-6270	444	4	⊙	⊙	PROPN
ejpam-6270	444	5	η	η	PROPN
ejpam-6270	444	6	)	)	PUNCT
ejpam-6270	444	7	=	=	SYM
ejpam-6270	444	8	f(ζ	f(ζ	NOUN
ejpam-6270	444	9	)	)	PUNCT
ejpam-6270	444	10	◦	◦	NOUN
ejpam-6270	444	11	f(η	f(η	PROPN
ejpam-6270	444	12	)	)	PUNCT
ejpam-6270	444	13	for	for	ADP
ejpam-6270	444	14	all	all	DET
ejpam-6270	444	15	ζ	ζ	NOUN
ejpam-6270	444	16	,	,	PUNCT
ejpam-6270	444	17	η	η	PROPN
ejpam-6270	444	18	∈	∈	PROPN
ejpam-6270	444	19	w	w	PROPN
ejpam-6270	444	20	,	,	PUNCT
ejpam-6270	444	21	so	so	CCONJ
ejpam-6270	444	22	f	f	PROPN
ejpam-6270	444	23	is	be	AUX
ejpam-6270	444	24	a	a	DET
ejpam-6270	444	25	d	d	NOUN
ejpam-6270	444	26	-	-	NOUN
ejpam-6270	444	27	isomorphism	isomorphism	NOUN
ejpam-6270	444	28	.	.	PUNCT
ejpam-6270	445	1	proposition	proposition	NOUN
ejpam-6270	445	2	27	27	NUM
ejpam-6270	445	3	.	.	PUNCT
ejpam-6270	446	1	let	let	VERB
ejpam-6270	446	2	w	w	NOUN
ejpam-6270	446	3	be	be	AUX
ejpam-6270	446	4	a	a	DET
ejpam-6270	446	5	positive	positive	ADJ
ejpam-6270	446	6	implicative	implicative	ADJ
ejpam-6270	446	7	d	d	NOUN
ejpam-6270	446	8	-	-	PUNCT
ejpam-6270	446	9	algebra	algebra	NOUN
ejpam-6270	446	10	and	and	CCONJ
ejpam-6270	446	11	ω	ω	NUM
ejpam-6270	446	12	be	be	AUX
ejpam-6270	446	13	a	a	DET
ejpam-6270	446	14	topology	topology	NOUN
ejpam-6270	446	15	on	on	ADP
ejpam-6270	446	16	w	w	NOUN
ejpam-6270	446	17	,	,	PUNCT
ejpam-6270	446	18	consequently	consequently	ADV
ejpam-6270	446	19	,	,	PUNCT
ejpam-6270	446	20	the	the	DET
ejpam-6270	446	21	following	follow	VERB
ejpam-6270	446	22	statements	statement	NOUN
ejpam-6270	446	23	are	be	AUX
ejpam-6270	446	24	correct	correct	ADJ
ejpam-6270	446	25	:	:	PUNCT
ejpam-6270	446	26	(	(	PUNCT
ejpam-6270	446	27	i	i	NOUN
ejpam-6270	446	28	)	)	PUNCT
ejpam-6270	446	29	the	the	DET
ejpam-6270	446	30	family	family	NOUN
ejpam-6270	446	31	σ	σ	PROPN
ejpam-6270	446	32	=	=	PUNCT
ejpam-6270	446	33	{	{	PUNCT
ejpam-6270	446	34	f(g	f(g	NOUN
ejpam-6270	446	35	)	)	PUNCT
ejpam-6270	446	36	⊆	⊆	NUM
ejpam-6270	446	37	l(w	l(w	NOUN
ejpam-6270	446	38	)	)	PUNCT
ejpam-6270	446	39	:	:	PUNCT
ejpam-6270	446	40	g	g	PROPN
ejpam-6270	446	41	∈	∈	PROPN
ejpam-6270	446	42	ω	ω	PROPN
ejpam-6270	446	43	}	}	PUNCT
ejpam-6270	446	44	is	be	AUX
ejpam-6270	446	45	a	a	DET
ejpam-6270	446	46	topology	topology	NOUN
ejpam-6270	446	47	on	on	ADP
ejpam-6270	446	48	l(w	l(w	NOUN
ejpam-6270	446	49	)	)	PUNCT
ejpam-6270	446	50	.	.	PUNCT
ejpam-6270	447	1	(	(	PUNCT
ejpam-6270	447	2	ii	ii	NOUN
ejpam-6270	447	3	)	)	PUNCT
ejpam-6270	447	4	for	for	ADP
ejpam-6270	447	5	every	every	DET
ejpam-6270	447	6	subset	subset	NOUN
ejpam-6270	447	7	m	m	NOUN
ejpam-6270	447	8	of	of	ADP
ejpam-6270	447	9	w	w	PROPN
ejpam-6270	447	10	,	,	PUNCT
ejpam-6270	447	11	lcl(m	lcl(m	PROPN
ejpam-6270	447	12	)	)	PUNCT
ejpam-6270	447	13	=	=	NOUN
ejpam-6270	447	14	σcl(lm	σcl(lm	NOUN
ejpam-6270	447	15	)	)	PUNCT
ejpam-6270	447	16	.	.	PUNCT
ejpam-6270	448	1	(	(	PUNCT
ejpam-6270	448	2	iii	iii	X
ejpam-6270	448	3	)	)	PUNCT
ejpam-6270	448	4	for	for	ADP
ejpam-6270	448	5	any	any	DET
ejpam-6270	448	6	subset	subset	NOUN
ejpam-6270	448	7	m	m	NOUN
ejpam-6270	448	8	of	of	ADP
ejpam-6270	448	9	w	w	PROPN
ejpam-6270	448	10	,	,	PUNCT
ejpam-6270	448	11	f(int(m	f(int(m	PROPN
ejpam-6270	448	12	)	)	PUNCT
ejpam-6270	448	13	)	)	PUNCT
ejpam-6270	449	1	=	=	SYM
ejpam-6270	449	2	σint(f(m	σint(f(m	NOUN
ejpam-6270	449	3	)	)	PUNCT
ejpam-6270	449	4	)	)	PUNCT
ejpam-6270	449	5	.	.	PUNCT
ejpam-6270	450	1	(	(	PUNCT
ejpam-6270	450	2	iv	iv	X
ejpam-6270	450	3	)	)	PUNCT
ejpam-6270	450	4	if	if	SCONJ
ejpam-6270	450	5	m	m	NOUN
ejpam-6270	450	6	is	be	AUX
ejpam-6270	450	7	any	any	DET
ejpam-6270	450	8	pre	pre	ADJ
ejpam-6270	450	9	-	-	ADJ
ejpam-6270	450	10	open	open	ADJ
ejpam-6270	450	11	set	set	NOUN
ejpam-6270	450	12	in	in	ADP
ejpam-6270	450	13	(	(	PUNCT
ejpam-6270	450	14	w	w	PROPN
ejpam-6270	450	15	,	,	PUNCT
ejpam-6270	450	16	ω	ω	NOUN
ejpam-6270	450	17	)	)	PUNCT
ejpam-6270	450	18	,	,	PUNCT
ejpam-6270	450	19	then	then	ADV
ejpam-6270	450	20	f(m	f(m	PROPN
ejpam-6270	450	21	)	)	PUNCT
ejpam-6270	450	22	is	be	AUX
ejpam-6270	450	23	a	a	DET
ejpam-6270	450	24	pre	pre	ADJ
ejpam-6270	450	25	-	-	ADJ
ejpam-6270	450	26	open	open	ADJ
ejpam-6270	450	27	set	set	NOUN
ejpam-6270	450	28	in	in	ADP
ejpam-6270	450	29	(	(	PUNCT
ejpam-6270	450	30	l(w	l(w	PROPN
ejpam-6270	450	31	)	)	PUNCT
ejpam-6270	450	32	,	,	PUNCT
ejpam-6270	450	33	σ	σ	PROPN
ejpam-6270	450	34	)	)	PUNCT
ejpam-6270	450	35	.	.	PUNCT
ejpam-6270	451	1	(	(	PUNCT
ejpam-6270	451	2	v	v	NOUN
ejpam-6270	451	3	)	)	PUNCT
ejpam-6270	451	4	if	if	SCONJ
ejpam-6270	451	5	m	m	NOUN
ejpam-6270	451	6	is	be	AUX
ejpam-6270	451	7	any	any	DET
ejpam-6270	451	8	semi	semi	ADJ
ejpam-6270	451	9	-	-	ADJ
ejpam-6270	451	10	open	open	ADJ
ejpam-6270	451	11	set	set	NOUN
ejpam-6270	451	12	in	in	ADP
ejpam-6270	451	13	(	(	PUNCT
ejpam-6270	451	14	w	w	PROPN
ejpam-6270	451	15	,	,	PUNCT
ejpam-6270	451	16	ω	ω	NOUN
ejpam-6270	451	17	)	)	PUNCT
ejpam-6270	451	18	,	,	PUNCT
ejpam-6270	451	19	then	then	ADV
ejpam-6270	451	20	f(m	f(m	PROPN
ejpam-6270	451	21	)	)	PUNCT
ejpam-6270	451	22	is	be	AUX
ejpam-6270	451	23	a	a	DET
ejpam-6270	451	24	semi	semi	ADJ
ejpam-6270	451	25	-	-	ADJ
ejpam-6270	451	26	open	open	ADJ
ejpam-6270	451	27	set	set	NOUN
ejpam-6270	451	28	in	in	ADP
ejpam-6270	451	29	(	(	PUNCT
ejpam-6270	451	30	l(w	l(w	PROPN
ejpam-6270	451	31	)	)	PUNCT
ejpam-6270	451	32	,	,	PUNCT
ejpam-6270	451	33	σ	σ	PROPN
ejpam-6270	451	34	)	)	PUNCT
ejpam-6270	451	35	.	.	PUNCT
ejpam-6270	452	1	proof	proof	NOUN
ejpam-6270	452	2	.	.	PUNCT
ejpam-6270	453	1	(	(	PUNCT
ejpam-6270	453	2	i	i	NOUN
ejpam-6270	453	3	)	)	PUNCT
ejpam-6270	453	4	the	the	DET
ejpam-6270	453	5	proof	proof	NOUN
ejpam-6270	453	6	of	of	ADP
ejpam-6270	453	7	σ	σ	PROPN
ejpam-6270	453	8	being	be	AUX
ejpam-6270	453	9	a	a	DET
ejpam-6270	453	10	topology	topology	NOUN
ejpam-6270	453	11	is	be	AUX
ejpam-6270	453	12	clear	clear	ADJ
ejpam-6270	453	13	.	.	PUNCT
ejpam-6270	454	1	(	(	PUNCT
ejpam-6270	454	2	ii	ii	NOUN
ejpam-6270	454	3	)	)	PUNCT
ejpam-6270	454	4	for	for	ADP
ejpam-6270	454	5	every	every	DET
ejpam-6270	454	6	subset	subset	NOUN
ejpam-6270	454	7	m	m	NOUN
ejpam-6270	454	8	of	of	ADP
ejpam-6270	454	9	w	w	PROPN
ejpam-6270	454	10	,	,	PUNCT
ejpam-6270	454	11	we	we	PRON
ejpam-6270	454	12	have	have	VERB
ejpam-6270	454	13	m	m	PROPN
ejpam-6270	454	14	⊆	⊆	NUM
ejpam-6270	454	15	cl(m	cl(m	NUM
ejpam-6270	454	16	)	)	PUNCT
ejpam-6270	454	17	.	.	PUNCT
ejpam-6270	455	1	hence	hence	ADV
ejpam-6270	455	2	,	,	PUNCT
ejpam-6270	455	3	lm	lm	PROPN
ejpam-6270	455	4	⊆	⊆	NUM
ejpam-6270	455	5	lcl(m	lcl(m	PROPN
ejpam-6270	455	6	)	)	PUNCT
ejpam-6270	455	7	and	and	CCONJ
ejpam-6270	455	8	cl(m	cl(m	NUM
ejpam-6270	455	9	)	)	PUNCT
ejpam-6270	455	10	is	be	AUX
ejpam-6270	455	11	closed	close	VERB
ejpam-6270	455	12	in	in	ADP
ejpam-6270	455	13	w	w	PROPN
ejpam-6270	455	14	,	,	PUNCT
ejpam-6270	455	15	so	so	ADV
ejpam-6270	455	16	by	by	ADP
ejpam-6270	455	17	definition	definition	NOUN
ejpam-6270	455	18	of	of	ADP
ejpam-6270	455	19	σ	σ	PROPN
ejpam-6270	455	20	,	,	PUNCT
ejpam-6270	455	21	we	we	PRON
ejpam-6270	455	22	have	have	VERB
ejpam-6270	455	23	lcl(m	lcl(m	PROPN
ejpam-6270	455	24	)	)	PUNCT
ejpam-6270	455	25	is	be	AUX
ejpam-6270	455	26	σ	σ	NOUN
ejpam-6270	455	27	-	-	PUNCT
ejpam-6270	455	28	closed	closed	ADJ
ejpam-6270	455	29	in	in	ADP
ejpam-6270	455	30	l(w	l(w	NOUN
ejpam-6270	455	31	)	)	PUNCT
ejpam-6270	455	32	.	.	PUNCT
ejpam-6270	456	1	therefore	therefore	ADV
ejpam-6270	456	2	,	,	PUNCT
ejpam-6270	456	3	we	we	PRON
ejpam-6270	456	4	obtain	obtain	VERB
ejpam-6270	456	5	σcl(lm	σcl(lm	NOUN
ejpam-6270	456	6	)	)	PUNCT
ejpam-6270	456	7	⊆	⊆	NUM
ejpam-6270	456	8	σcl(lcl(m	σcl(lcl(m	PROPN
ejpam-6270	456	9	)	)	PUNCT
ejpam-6270	456	10	)	)	PUNCT
ejpam-6270	457	1	=	=	SYM
ejpam-6270	457	2	lcl(m	lcl(m	PROPN
ejpam-6270	457	3	)	)	PUNCT
ejpam-6270	457	4	.	.	PUNCT
ejpam-6270	458	1	to	to	PART
ejpam-6270	458	2	prove	prove	VERB
ejpam-6270	458	3	lcl(m	lcl(m	PROPN
ejpam-6270	458	4	)	)	PUNCT
ejpam-6270	458	5	⊆	⊆	NUM
ejpam-6270	458	6	σcl(lm	σcl(lm	NOUN
ejpam-6270	458	7	)	)	PUNCT
ejpam-6270	458	8	,	,	PUNCT
ejpam-6270	458	9	let	let	VERB
ejpam-6270	458	10	lζ	lζ	PROPN
ejpam-6270	458	11	∈	∈	PROPN
ejpam-6270	458	12	lcl(m	lcl(m	PROPN
ejpam-6270	458	13	)	)	PUNCT
ejpam-6270	458	14	,	,	PUNCT
ejpam-6270	458	15	then	then	ADV
ejpam-6270	458	16	ζ	ζ	PROPN
ejpam-6270	458	17	∈	∈	PROPN
ejpam-6270	458	18	cl(m	cl(m	NOUN
ejpam-6270	458	19	)	)	PUNCT
ejpam-6270	458	20	and	and	CCONJ
ejpam-6270	458	21	let	let	VERB
ejpam-6270	458	22	f(g	f(g	NOUN
ejpam-6270	458	23	)	)	PUNCT
ejpam-6270	458	24	be	be	AUX
ejpam-6270	458	25	any	any	DET
ejpam-6270	458	26	σ	σ	NOUN
ejpam-6270	458	27	-	-	PUNCT
ejpam-6270	458	28	open	open	ADJ
ejpam-6270	458	29	set	set	NOUN
ejpam-6270	458	30	containing	contain	VERB
ejpam-6270	458	31	lζ	lζ	ADV
ejpam-6270	458	32	.	.	PUNCT
ejpam-6270	459	1	hence	hence	ADV
ejpam-6270	459	2	g	g	PROPN
ejpam-6270	459	3	is	be	AUX
ejpam-6270	459	4	an	an	DET
ejpam-6270	459	5	open	open	ADJ
ejpam-6270	459	6	set	set	NOUN
ejpam-6270	459	7	that	that	PRON
ejpam-6270	459	8	contains	contain	VERB
ejpam-6270	459	9	ζ	ζ	NOUN
ejpam-6270	459	10	,	,	PUNCT
ejpam-6270	459	11	so	so	ADV
ejpam-6270	459	12	m	m	ADP
ejpam-6270	459	13	∩	∩	NOUN
ejpam-6270	459	14	g	g	PROPN
ejpam-6270	459	15	̸=	̸=	PROPN
ejpam-6270	459	16	ϕ	ϕ	PROPN
ejpam-6270	459	17	and	and	CCONJ
ejpam-6270	459	18	by	by	ADP
ejpam-6270	459	19	proposition	proposition	NOUN
ejpam-6270	459	20	25	25	NUM
ejpam-6270	459	21	,	,	PUNCT
ejpam-6270	459	22	f(m	f(m	PROPN
ejpam-6270	459	23	∩	∩	NOUN
ejpam-6270	459	24	g	g	NOUN
ejpam-6270	459	25	)	)	PUNCT
ejpam-6270	459	26	=	=	SYM
ejpam-6270	459	27	f(m	f(m	PROPN
ejpam-6270	459	28	)	)	PUNCT
ejpam-6270	459	29	∩	∩	NOUN
ejpam-6270	459	30	f(g	f(g	NOUN
ejpam-6270	459	31	)	)	PUNCT
ejpam-6270	459	32	.	.	PUNCT
ejpam-6270	460	1	therefore	therefore	ADV
ejpam-6270	460	2	,	,	PUNCT
ejpam-6270	460	3	f(m	f(m	PROPN
ejpam-6270	460	4	)	)	PUNCT
ejpam-6270	460	5	∩	∩	ADJ
ejpam-6270	460	6	f(g	f(g	NOUN
ejpam-6270	460	7	)	)	PUNCT
ejpam-6270	460	8	̸=	̸=	PROPN
ejpam-6270	460	9	ϕ.	ϕ.	NOUN
ejpam-6270	460	10	implies	imply	VERB
ejpam-6270	460	11	that	that	SCONJ
ejpam-6270	460	12	lζ	lζ	PROPN
ejpam-6270	460	13	∈	∈	PROPN
ejpam-6270	460	14	σcl(lm	σcl(lm	NOUN
ejpam-6270	460	15	)	)	PUNCT
ejpam-6270	460	16	,	,	PUNCT
ejpam-6270	460	17	so	so	ADV
ejpam-6270	460	18	lcl(m	lcl(m	PROPN
ejpam-6270	460	19	)	)	PUNCT
ejpam-6270	460	20	⊆	⊆	NUM
ejpam-6270	460	21	σcl(lm	σcl(lm	NOUN
ejpam-6270	460	22	)	)	PUNCT
ejpam-6270	460	23	and	and	CCONJ
ejpam-6270	460	24	hence	hence	ADV
ejpam-6270	460	25	lcl(m	lcl(m	PROPN
ejpam-6270	460	26	)	)	PUNCT
ejpam-6270	460	27	=	=	SYM
ejpam-6270	460	28	σcl(lm	σcl(lm	NOUN
ejpam-6270	460	29	)	)	PUNCT
ejpam-6270	460	30	.	.	PUNCT
ejpam-6270	461	1	m.	m.	NOUN
ejpam-6270	461	2	w.	w.	PROPN
ejpam-6270	461	3	abdulqader	abdulqader	PROPN
ejpam-6270	461	4	,	,	PUNCT
ejpam-6270	461	5	a.	a.	PROPN
ejpam-6270	461	6	b.	b.	PROPN
ejpam-6270	461	7	khalaf	khalaf	PROPN
ejpam-6270	461	8	/	/	SYM
ejpam-6270	461	9	eur	eur	PROPN
ejpam-6270	461	10	.	.	PUNCT
ejpam-6270	462	1	j.	j.	PROPN
ejpam-6270	462	2	pure	pure	PROPN
ejpam-6270	462	3	appl	appl	PROPN
ejpam-6270	462	4	.	.	PROPN
ejpam-6270	462	5	math	math	PROPN
ejpam-6270	462	6	,	,	PUNCT
ejpam-6270	462	7	18	18	NUM
ejpam-6270	462	8	(	(	PUNCT
ejpam-6270	462	9	3	3	NUM
ejpam-6270	462	10	)	)	PUNCT
ejpam-6270	462	11	(	(	PUNCT
ejpam-6270	462	12	2025	2025	NUM
ejpam-6270	462	13	)	)	PUNCT
ejpam-6270	462	14	,	,	PUNCT
ejpam-6270	462	15	6270	6270	NUM
ejpam-6270	462	16	15	15	NUM
ejpam-6270	462	17	of	of	ADP
ejpam-6270	462	18	17	17	NUM
ejpam-6270	462	19	(	(	PUNCT
ejpam-6270	462	20	iii	iii	NOUN
ejpam-6270	462	21	)	)	PUNCT
ejpam-6270	462	22	we	we	PRON
ejpam-6270	462	23	have	have	VERB
ejpam-6270	462	24	int(m	int(m	NOUN
ejpam-6270	462	25	)	)	PUNCT
ejpam-6270	462	26	⊆	⊆	NUM
ejpam-6270	462	27	m	m	NOUN
ejpam-6270	462	28	,	,	PUNCT
ejpam-6270	462	29	so	so	ADV
ejpam-6270	462	30	f(int(m	f(int(m	ADJ
ejpam-6270	462	31	)	)	PUNCT
ejpam-6270	462	32	)	)	PUNCT
ejpam-6270	463	1	∈	∈	PROPN
ejpam-6270	463	2	σ	σ	PROPN
ejpam-6270	463	3	and	and	CCONJ
ejpam-6270	463	4	f(int(m	f(int(m	NUM
ejpam-6270	463	5	)	)	PUNCT
ejpam-6270	463	6	)	)	PUNCT
ejpam-6270	464	1	⊆	⊆	NUM
ejpam-6270	464	2	f(m	f(m	PROPN
ejpam-6270	464	3	)	)	PUNCT
ejpam-6270	464	4	.	.	PUNCT
ejpam-6270	465	1	hence	hence	ADV
ejpam-6270	465	2	f(int(m	f(int(m	ADV
ejpam-6270	465	3	)	)	PUNCT
ejpam-6270	465	4	)	)	PUNCT
ejpam-6270	466	1	⊆	⊆	NUM
ejpam-6270	466	2	σint(f(m	σint(f(m	NOUN
ejpam-6270	466	3	)	)	PUNCT
ejpam-6270	466	4	)	)	PUNCT
ejpam-6270	466	5	.	.	PUNCT
ejpam-6270	467	1	now	now	ADV
ejpam-6270	467	2	if	if	SCONJ
ejpam-6270	467	3	lζ	lζ	PROPN
ejpam-6270	467	4	∈	∈	PROPN
ejpam-6270	467	5	σint(f(m	σint(f(m	PRON
ejpam-6270	467	6	)	)	PUNCT
ejpam-6270	467	7	)	)	PUNCT
ejpam-6270	467	8	,	,	PUNCT
ejpam-6270	467	9	so	so	CCONJ
ejpam-6270	467	10	there	there	PRON
ejpam-6270	467	11	exists	exist	VERB
ejpam-6270	467	12	f(g	f(g	NOUN
ejpam-6270	467	13	)	)	PUNCT
ejpam-6270	467	14	∈	∈	PROPN
ejpam-6270	467	15	σ	σ	NOUN
ejpam-6270	467	16	such	such	ADJ
ejpam-6270	467	17	that	that	SCONJ
ejpam-6270	467	18	lζ	lζ	PROPN
ejpam-6270	467	19	∈	∈	PROPN
ejpam-6270	467	20	f(g	f(g	NOUN
ejpam-6270	467	21	)	)	PUNCT
ejpam-6270	467	22	⊂	⊂	PROPN
ejpam-6270	467	23	f(m	f(m	PROPN
ejpam-6270	467	24	)	)	PUNCT
ejpam-6270	467	25	.	.	PUNCT
ejpam-6270	468	1	hence	hence	ADV
ejpam-6270	468	2	,	,	PUNCT
ejpam-6270	468	3	ζ	ζ	PROPN
ejpam-6270	468	4	∈	∈	PROPN
ejpam-6270	468	5	g	g	ADP
ejpam-6270	468	6	⊆	⊆	NUM
ejpam-6270	468	7	m	m	NOUN
ejpam-6270	468	8	implies	imply	VERB
ejpam-6270	468	9	that	that	SCONJ
ejpam-6270	468	10	ζ	ζ	SYM
ejpam-6270	468	11	∈	∈	NOUN
ejpam-6270	468	12	int(m	int(m	PROPN
ejpam-6270	468	13	)	)	PUNCT
ejpam-6270	468	14	.	.	PUNCT
ejpam-6270	469	1	therefore	therefore	ADV
ejpam-6270	469	2	,	,	PUNCT
ejpam-6270	469	3	lζ	lζ	PROPN
ejpam-6270	469	4	∈	∈	PROPN
ejpam-6270	469	5	f(int(m	f(int(m	PROPN
ejpam-6270	469	6	)	)	PUNCT
ejpam-6270	469	7	)	)	PUNCT
ejpam-6270	469	8	.	.	PUNCT
ejpam-6270	470	1	thus	thus	ADV
ejpam-6270	470	2	,	,	PUNCT
ejpam-6270	470	3	f(int(m	f(int(m	NUM
ejpam-6270	470	4	)	)	PUNCT
ejpam-6270	470	5	)	)	PUNCT
ejpam-6270	471	1	=	=	SYM
ejpam-6270	471	2	σint(f(m	σint(f(m	NOUN
ejpam-6270	471	3	)	)	PUNCT
ejpam-6270	471	4	)	)	PUNCT
ejpam-6270	471	5	.	.	PUNCT
ejpam-6270	472	1	(	(	PUNCT
ejpam-6270	472	2	iv	iv	X
ejpam-6270	472	3	)	)	PUNCT
ejpam-6270	472	4	let	let	VERB
ejpam-6270	472	5	m	m	PRON
ejpam-6270	472	6	be	be	AUX
ejpam-6270	472	7	any	any	DET
ejpam-6270	472	8	pre	pre	ADJ
ejpam-6270	472	9	-	-	ADJ
ejpam-6270	472	10	open	open	ADJ
ejpam-6270	472	11	set	set	NOUN
ejpam-6270	472	12	in	in	ADP
ejpam-6270	472	13	w	w	NOUN
ejpam-6270	472	14	,	,	PUNCT
ejpam-6270	472	15	so	so	SCONJ
ejpam-6270	472	16	there	there	PRON
ejpam-6270	472	17	exists	exist	VERB
ejpam-6270	472	18	an	an	DET
ejpam-6270	472	19	open	open	ADJ
ejpam-6270	472	20	set	set	NOUN
ejpam-6270	472	21	v	v	NOUN
ejpam-6270	472	22	in	in	ADP
ejpam-6270	472	23	w	w	ADP
ejpam-6270	472	24	such	such	ADJ
ejpam-6270	472	25	that	that	SCONJ
ejpam-6270	472	26	m	m	PROPN
ejpam-6270	472	27	⊆	⊆	NUM
ejpam-6270	472	28	v	v	ADP
ejpam-6270	472	29	⊆	⊆	NUM
ejpam-6270	472	30	cl(m	cl(m	NUM
ejpam-6270	472	31	)	)	PUNCT
ejpam-6270	472	32	.	.	PUNCT
ejpam-6270	473	1	hence	hence	ADV
ejpam-6270	473	2	f(m	f(m	PROPN
ejpam-6270	473	3	)	)	PUNCT
ejpam-6270	473	4	⊆	⊆	NUM
ejpam-6270	473	5	f(v	f(v	NOUN
ejpam-6270	473	6	)	)	PUNCT
ejpam-6270	473	7	⊆	⊆	NUM
ejpam-6270	473	8	f(cl(m	f(cl(m	PROPN
ejpam-6270	473	9	)	)	PUNCT
ejpam-6270	473	10	)	)	PUNCT
ejpam-6270	473	11	and	and	CCONJ
ejpam-6270	473	12	by	by	ADP
ejpam-6270	473	13	(	(	PUNCT
ejpam-6270	473	14	2	2	NUM
ejpam-6270	473	15	,	,	PUNCT
ejpam-6270	473	16	3	3	NUM
ejpam-6270	473	17	)	)	PUNCT
ejpam-6270	473	18	,	,	PUNCT
ejpam-6270	473	19	we	we	PRON
ejpam-6270	473	20	have	have	VERB
ejpam-6270	473	21	f(m	f(m	PROPN
ejpam-6270	473	22	)	)	PUNCT
ejpam-6270	474	1	⊆	⊆	NUM
ejpam-6270	474	2	f(v	f(v	NOUN
ejpam-6270	474	3	)	)	PUNCT
ejpam-6270	474	4	⊆	⊆	NUM
ejpam-6270	474	5	σcl(f(m	σcl(f(m	NOUN
ejpam-6270	474	6	)	)	PUNCT
ejpam-6270	474	7	)	)	PUNCT
ejpam-6270	474	8	and	and	CCONJ
ejpam-6270	474	9	f(v	f(v	PROPN
ejpam-6270	474	10	)	)	PUNCT
ejpam-6270	474	11	is	be	AUX
ejpam-6270	474	12	σ	σ	NOUN
ejpam-6270	474	13	-	-	NOUN
ejpam-6270	474	14	open	open	ADJ
ejpam-6270	474	15	.	.	PUNCT
ejpam-6270	475	1	hence	hence	ADV
ejpam-6270	475	2	,	,	PUNCT
ejpam-6270	475	3	f(m	f(m	PROPN
ejpam-6270	475	4	)	)	PUNCT
ejpam-6270	475	5	is	be	AUX
ejpam-6270	475	6	pre	pre	ADJ
ejpam-6270	475	7	-	-	ADJ
ejpam-6270	475	8	open	open	ADJ
ejpam-6270	475	9	in	in	ADP
ejpam-6270	475	10	(	(	PUNCT
ejpam-6270	475	11	l(w	l(w	PROPN
ejpam-6270	475	12	)	)	PUNCT
ejpam-6270	475	13	,	,	PUNCT
ejpam-6270	475	14	σ	σ	PROPN
ejpam-6270	475	15	)	)	PUNCT
ejpam-6270	475	16	.	.	PUNCT
ejpam-6270	476	1	(	(	PUNCT
ejpam-6270	476	2	v	v	X
ejpam-6270	476	3	)	)	PUNCT
ejpam-6270	476	4	the	the	DET
ejpam-6270	476	5	proof	proof	NOUN
ejpam-6270	476	6	is	be	AUX
ejpam-6270	476	7	similar	similar	ADJ
ejpam-6270	476	8	to	to	ADP
ejpam-6270	476	9	the	the	DET
ejpam-6270	476	10	proof	proof	NOUN
ejpam-6270	476	11	of	of	ADP
ejpam-6270	476	12	(	(	PUNCT
ejpam-6270	476	13	iv	iv	X
ejpam-6270	476	14	)	)	PUNCT
ejpam-6270	476	15	.	.	PUNCT
ejpam-6270	477	1	corollary	corollary	ADJ
ejpam-6270	477	2	9	9	NUM
ejpam-6270	477	3	.	.	PUNCT
ejpam-6270	478	1	if	if	SCONJ
ejpam-6270	478	2	m	m	NOUN
ejpam-6270	478	3	is	be	AUX
ejpam-6270	478	4	any	any	DET
ejpam-6270	478	5	subset	subset	NOUN
ejpam-6270	478	6	of	of	ADP
ejpam-6270	478	7	(	(	PUNCT
ejpam-6270	478	8	w	w	PROPN
ejpam-6270	478	9	,	,	PUNCT
ejpam-6270	478	10	ω	ω	NOUN
ejpam-6270	478	11	)	)	PUNCT
ejpam-6270	478	12	,	,	PUNCT
ejpam-6270	478	13	then	then	ADV
ejpam-6270	478	14	f(int(cl(m	f(int(cl(m	PROPN
ejpam-6270	478	15	)	)	PUNCT
ejpam-6270	478	16	)	)	PUNCT
ejpam-6270	478	17	)	)	PUNCT
ejpam-6270	479	1	=	=	SYM
ejpam-6270	479	2	σint(σcl(f(m	σint(σcl(f(m	X
ejpam-6270	479	3	)	)	PUNCT
ejpam-6270	479	4	)	)	PUNCT
ejpam-6270	479	5	)	)	PUNCT
ejpam-6270	480	1	and	and	CCONJ
ejpam-6270	480	2	f(cl(int(m	f(cl(int(m	NUM
ejpam-6270	480	3	)	)	PUNCT
ejpam-6270	480	4	)	)	PUNCT
ejpam-6270	480	5	)	)	PUNCT
ejpam-6270	481	1	=	=	SYM
ejpam-6270	481	2	σcl(σint(f(m	σcl(σint(f(m	NOUN
ejpam-6270	481	3	)	)	PUNCT
ejpam-6270	481	4	)	)	PUNCT
ejpam-6270	481	5	)	)	PUNCT
ejpam-6270	482	1	where	where	SCONJ
ejpam-6270	482	2	(	(	PUNCT
ejpam-6270	482	3	l(w	l(w	NOUN
ejpam-6270	482	4	)	)	PUNCT
ejpam-6270	482	5	,	,	PUNCT
ejpam-6270	482	6	σ	σ	PROPN
ejpam-6270	482	7	)	)	PUNCT
ejpam-6270	482	8	is	be	AUX
ejpam-6270	482	9	defined	define	VERB
ejpam-6270	482	10	as	as	ADP
ejpam-6270	482	11	in	in	ADP
ejpam-6270	482	12	proposition	proposition	NOUN
ejpam-6270	482	13	27	27	NUM
ejpam-6270	482	14	.	.	PUNCT
ejpam-6270	483	1	proof	proof	NOUN
ejpam-6270	483	2	.	.	PUNCT
ejpam-6270	484	1	the	the	DET
ejpam-6270	484	2	proof	proof	NOUN
ejpam-6270	484	3	follows	follow	VERB
ejpam-6270	484	4	from	from	ADP
ejpam-6270	484	5	(	(	PUNCT
ejpam-6270	484	6	ii	ii	PROPN
ejpam-6270	484	7	,	,	PUNCT
ejpam-6270	484	8	iii	iii	NOUN
ejpam-6270	484	9	)	)	PUNCT
ejpam-6270	484	10	of	of	ADP
ejpam-6270	484	11	proposition	proposition	NOUN
ejpam-6270	484	12	27	27	NUM
ejpam-6270	484	13	.	.	PUNCT
ejpam-6270	485	1	proposition	proposition	NOUN
ejpam-6270	485	2	28	28	NUM
ejpam-6270	485	3	.	.	PUNCT
ejpam-6270	486	1	a	a	DET
ejpam-6270	486	2	subset	subset	NOUN
ejpam-6270	486	3	m	m	VERB
ejpam-6270	486	4	is	be	AUX
ejpam-6270	486	5	b	b	NOUN
ejpam-6270	486	6	-	-	PUNCT
ejpam-6270	486	7	open	open	ADJ
ejpam-6270	486	8	in	in	ADP
ejpam-6270	486	9	(	(	PUNCT
ejpam-6270	486	10	w	w	PROPN
ejpam-6270	486	11	,	,	PUNCT
ejpam-6270	486	12	ω	ω	NOUN
ejpam-6270	486	13	)	)	PUNCT
ejpam-6270	487	1	if	if	SCONJ
ejpam-6270	487	2	and	and	CCONJ
ejpam-6270	487	3	only	only	ADV
ejpam-6270	487	4	if	if	SCONJ
ejpam-6270	487	5	f(m	f(m	PROPN
ejpam-6270	487	6	)	)	PUNCT
ejpam-6270	487	7	is	be	AUX
ejpam-6270	487	8	a	a	DET
ejpam-6270	487	9	b	b	NOUN
ejpam-6270	487	10	-	-	PUNCT
ejpam-6270	487	11	open	open	ADJ
ejpam-6270	487	12	set	set	NOUN
ejpam-6270	487	13	in	in	ADP
ejpam-6270	487	14	(	(	PUNCT
ejpam-6270	487	15	l(w	l(w	PROPN
ejpam-6270	487	16	)	)	PUNCT
ejpam-6270	487	17	,	,	PUNCT
ejpam-6270	487	18	σ	σ	PROPN
ejpam-6270	487	19	)	)	PUNCT
ejpam-6270	487	20	.	.	PUNCT
ejpam-6270	488	1	proof	proof	NOUN
ejpam-6270	488	2	.	.	PUNCT
ejpam-6270	489	1	suppose	suppose	VERB
ejpam-6270	489	2	that	that	SCONJ
ejpam-6270	489	3	m	m	PROPN
ejpam-6270	489	4	is	be	AUX
ejpam-6270	489	5	a	a	DET
ejpam-6270	489	6	b	b	NOUN
ejpam-6270	489	7	-	-	PUNCT
ejpam-6270	489	8	open	open	ADJ
ejpam-6270	489	9	set	set	NOUN
ejpam-6270	489	10	,	,	PUNCT
ejpam-6270	489	11	then	then	ADV
ejpam-6270	489	12	by	by	ADP
ejpam-6270	489	13	lemma	lemma	PROPN
ejpam-6270	489	14	2	2	NUM
ejpam-6270	489	15	,	,	PUNCT
ejpam-6270	489	16	m	m	VERB
ejpam-6270	489	17	=	=	NOUN
ejpam-6270	489	18	m	m	NOUN
ejpam-6270	489	19	∩	∩	NOUN
ejpam-6270	489	20	(	(	PUNCT
ejpam-6270	489	21	int(cl(m	int(cl(m	PROPN
ejpam-6270	489	22	)	)	PUNCT
ejpam-6270	489	23	)	)	PUNCT
ejpam-6270	490	1	∩	∩	ADJ
ejpam-6270	490	2	cl(int(m	cl(int(m	NOUN
ejpam-6270	490	3	)	)	PUNCT
ejpam-6270	490	4	)	)	PUNCT
ejpam-6270	490	5	.	.	PUNCT
ejpam-6270	491	1	from	from	ADP
ejpam-6270	491	2	proposition	proposition	NOUN
ejpam-6270	491	3	25	25	NUM
ejpam-6270	491	4	,	,	PUNCT
ejpam-6270	491	5	we	we	PRON
ejpam-6270	491	6	get	get	VERB
ejpam-6270	491	7	f(m	f(m	PROPN
ejpam-6270	491	8	)	)	PUNCT
ejpam-6270	492	1	=	=	SYM
ejpam-6270	492	2	f(m)∩	f(m)∩	PROPN
ejpam-6270	492	3	(	(	PUNCT
ejpam-6270	492	4	f(int(cl(m	f(int(cl(m	PROPN
ejpam-6270	492	5	)	)	PUNCT
ejpam-6270	492	6	)	)	PUNCT
ejpam-6270	492	7	)	)	PUNCT
ejpam-6270	493	1	∩	∩	NOUN
ejpam-6270	493	2	(	(	PUNCT
ejpam-6270	493	3	fcl(int(m	fcl(int(m	NOUN
ejpam-6270	493	4	)	)	PUNCT
ejpam-6270	493	5	)	)	PUNCT
ejpam-6270	493	6	)	)	PUNCT
ejpam-6270	493	7	.	.	PUNCT
ejpam-6270	494	1	by	by	ADP
ejpam-6270	494	2	corollary	corollary	ADJ
ejpam-6270	494	3	9	9	NUM
ejpam-6270	494	4	,	,	PUNCT
ejpam-6270	494	5	we	we	PRON
ejpam-6270	494	6	get	get	VERB
ejpam-6270	494	7	f(m	f(m	PROPN
ejpam-6270	494	8	)	)	PUNCT
ejpam-6270	495	1	=	=	SYM
ejpam-6270	495	2	f(m)∩	f(m)∩	PROPN
ejpam-6270	495	3	(	(	PUNCT
ejpam-6270	495	4	σint(σcl(f(m	σint(σcl(f(m	NOUN
ejpam-6270	495	5	)	)	PUNCT
ejpam-6270	495	6	)	)	PUNCT
ejpam-6270	495	7	)	)	PUNCT
ejpam-6270	496	1	∩	∩	NOUN
ejpam-6270	496	2	(	(	PUNCT
ejpam-6270	496	3	σcl(σint(f(m	σcl(σint(f(m	NOUN
ejpam-6270	496	4	)	)	PUNCT
ejpam-6270	496	5	)	)	PUNCT
ejpam-6270	496	6	)	)	PUNCT
ejpam-6270	496	7	.	.	PUNCT
ejpam-6270	497	1	hence	hence	ADV
ejpam-6270	497	2	,	,	PUNCT
ejpam-6270	497	3	f(m	f(m	PROPN
ejpam-6270	497	4	)	)	PUNCT
ejpam-6270	497	5	is	be	AUX
ejpam-6270	497	6	a	a	DET
ejpam-6270	497	7	b	b	NOUN
ejpam-6270	497	8	-	-	PUNCT
ejpam-6270	497	9	open	open	ADJ
ejpam-6270	497	10	set	set	NOUN
ejpam-6270	497	11	in	in	ADP
ejpam-6270	497	12	(	(	PUNCT
ejpam-6270	497	13	l(w	l(w	PROPN
ejpam-6270	497	14	)	)	PUNCT
ejpam-6270	497	15	,	,	PUNCT
ejpam-6270	497	16	σ	σ	PROPN
ejpam-6270	497	17	)	)	PUNCT
ejpam-6270	497	18	.	.	PUNCT
ejpam-6270	498	1	reversing	reverse	VERB
ejpam-6270	498	2	the	the	DET
ejpam-6270	498	3	statement	statement	NOUN
ejpam-6270	498	4	,	,	PUNCT
ejpam-6270	498	5	we	we	PRON
ejpam-6270	498	6	get	get	VERB
ejpam-6270	498	7	the	the	DET
ejpam-6270	498	8	result	result	NOUN
ejpam-6270	498	9	.	.	PUNCT
ejpam-6270	499	1	proof	proof	NOUN
ejpam-6270	499	2	.	.	PUNCT
ejpam-6270	500	1	suppose	suppose	VERB
ejpam-6270	500	2	that	that	SCONJ
ejpam-6270	500	3	m	m	PROPN
ejpam-6270	500	4	is	be	AUX
ejpam-6270	500	5	a	a	DET
ejpam-6270	500	6	b	b	NOUN
ejpam-6270	500	7	-	-	PUNCT
ejpam-6270	500	8	open	open	ADJ
ejpam-6270	500	9	set	set	NOUN
ejpam-6270	500	10	,	,	PUNCT
ejpam-6270	500	11	then	then	ADV
ejpam-6270	500	12	by	by	ADP
ejpam-6270	500	13	lemma	lemma	PROPN
ejpam-6270	500	14	2	2	NUM
ejpam-6270	500	15	,	,	PUNCT
ejpam-6270	500	16	m	m	VERB
ejpam-6270	500	17	=	=	NOUN
ejpam-6270	500	18	m	m	NOUN
ejpam-6270	500	19	∩	∩	NOUN
ejpam-6270	500	20	(	(	PUNCT
ejpam-6270	500	21	int(cl(m	int(cl(m	PROPN
ejpam-6270	500	22	)	)	PUNCT
ejpam-6270	500	23	)	)	PUNCT
ejpam-6270	501	1	∩	∩	ADJ
ejpam-6270	501	2	cl(int(m	cl(int(m	NOUN
ejpam-6270	501	3	)	)	PUNCT
ejpam-6270	501	4	)	)	PUNCT
ejpam-6270	501	5	.	.	PUNCT
ejpam-6270	502	1	from	from	ADP
ejpam-6270	502	2	proposition	proposition	NOUN
ejpam-6270	502	3	25	25	NUM
ejpam-6270	502	4	,	,	PUNCT
ejpam-6270	502	5	we	we	PRON
ejpam-6270	502	6	get	get	VERB
ejpam-6270	502	7	f(m	f(m	PROPN
ejpam-6270	502	8	)	)	PUNCT
ejpam-6270	503	1	=	=	SYM
ejpam-6270	503	2	f(m)∩	f(m)∩	PROPN
ejpam-6270	503	3	(	(	PUNCT
ejpam-6270	503	4	f(int(cl(m	f(int(cl(m	PROPN
ejpam-6270	503	5	)	)	PUNCT
ejpam-6270	503	6	)	)	PUNCT
ejpam-6270	503	7	)	)	PUNCT
ejpam-6270	504	1	∩	∩	NOUN
ejpam-6270	504	2	(	(	PUNCT
ejpam-6270	504	3	fcl(int(m	fcl(int(m	NOUN
ejpam-6270	504	4	)	)	PUNCT
ejpam-6270	504	5	)	)	PUNCT
ejpam-6270	504	6	)	)	PUNCT
ejpam-6270	504	7	.	.	PUNCT
ejpam-6270	505	1	by	by	ADP
ejpam-6270	505	2	corollary	corollary	ADJ
ejpam-6270	505	3	9	9	NUM
ejpam-6270	505	4	,	,	PUNCT
ejpam-6270	505	5	we	we	PRON
ejpam-6270	505	6	get	get	VERB
ejpam-6270	505	7	f(m	f(m	PROPN
ejpam-6270	505	8	)	)	PUNCT
ejpam-6270	506	1	=	=	SYM
ejpam-6270	506	2	f(m)∩	f(m)∩	PROPN
ejpam-6270	506	3	(	(	PUNCT
ejpam-6270	506	4	σint(σcl(f(m	σint(σcl(f(m	NOUN
ejpam-6270	506	5	)	)	PUNCT
ejpam-6270	506	6	)	)	PUNCT
ejpam-6270	506	7	)	)	PUNCT
ejpam-6270	507	1	∩	∩	NOUN
ejpam-6270	507	2	(	(	PUNCT
ejpam-6270	507	3	σcl(σint(f(m	σcl(σint(f(m	NOUN
ejpam-6270	507	4	)	)	PUNCT
ejpam-6270	507	5	)	)	PUNCT
ejpam-6270	507	6	)	)	PUNCT
ejpam-6270	507	7	.	.	PUNCT
ejpam-6270	508	1	hence	hence	ADV
ejpam-6270	508	2	,	,	PUNCT
ejpam-6270	508	3	f(m	f(m	PROPN
ejpam-6270	508	4	)	)	PUNCT
ejpam-6270	508	5	is	be	AUX
ejpam-6270	508	6	a	a	DET
ejpam-6270	508	7	b	b	NOUN
ejpam-6270	508	8	-	-	PUNCT
ejpam-6270	508	9	open	open	ADJ
ejpam-6270	508	10	set	set	NOUN
ejpam-6270	508	11	in	in	ADP
ejpam-6270	508	12	(	(	PUNCT
ejpam-6270	508	13	l(w	l(w	PROPN
ejpam-6270	508	14	)	)	PUNCT
ejpam-6270	508	15	,	,	PUNCT
ejpam-6270	508	16	σ	σ	PROPN
ejpam-6270	508	17	)	)	PUNCT
ejpam-6270	508	18	.	.	PUNCT
ejpam-6270	509	1	proposition	proposition	NOUN
ejpam-6270	509	2	29	29	NUM
ejpam-6270	509	3	.	.	PUNCT
ejpam-6270	510	1	let	let	VERB
ejpam-6270	510	2	w	w	NOUN
ejpam-6270	510	3	be	be	AUX
ejpam-6270	510	4	a	a	DET
ejpam-6270	510	5	positive	positive	ADJ
ejpam-6270	510	6	implicative	implicative	ADJ
ejpam-6270	510	7	tbd	tbd	NOUN
ejpam-6270	510	8	-	-	PUNCT
ejpam-6270	510	9	algebra	algebra	NOUN
ejpam-6270	510	10	.	.	PUNCT
ejpam-6270	511	1	then	then	ADV
ejpam-6270	511	2	(	(	PUNCT
ejpam-6270	511	3	l(w	l(w	PROPN
ejpam-6270	511	4	)	)	PUNCT
ejpam-6270	511	5	,	,	PUNCT
ejpam-6270	511	6	◦	◦	NOUN
ejpam-6270	511	7	,	,	PUNCT
ejpam-6270	511	8	σ	σ	PROPN
ejpam-6270	511	9	)	)	PUNCT
ejpam-6270	511	10	is	be	AUX
ejpam-6270	511	11	a	a	DET
ejpam-6270	511	12	tbd	tbd	NOUN
ejpam-6270	511	13	-	-	PUNCT
ejpam-6270	511	14	algebra	algebra	NOUN
ejpam-6270	511	15	.	.	PUNCT
ejpam-6270	512	1	proof	proof	NOUN
ejpam-6270	512	2	.	.	PUNCT
ejpam-6270	513	1	suppose	suppose	VERB
ejpam-6270	513	2	that	that	SCONJ
ejpam-6270	513	3	lζ	lζ	ADV
ejpam-6270	513	4	,	,	PUNCT
ejpam-6270	513	5	lη	lη	PROPN
ejpam-6270	513	6	are	be	AUX
ejpam-6270	513	7	any	any	DET
ejpam-6270	513	8	elements	element	NOUN
ejpam-6270	513	9	in	in	ADP
ejpam-6270	513	10	l(w	l(w	NOUN
ejpam-6270	513	11	)	)	PUNCT
ejpam-6270	513	12	and	and	CCONJ
ejpam-6270	513	13	f(w	f(w	PROPN
ejpam-6270	513	14	)	)	PUNCT
ejpam-6270	513	15	is	be	AUX
ejpam-6270	513	16	a	a	DET
ejpam-6270	513	17	σ	σ	NOUN
ejpam-6270	513	18	-	-	PUNCT
ejpam-6270	513	19	open	open	ADJ
ejpam-6270	513	20	set	set	NOUN
ejpam-6270	513	21	having	having	AUX
ejpam-6270	513	22	lζ	lζ	VERB
ejpam-6270	513	23	◦	◦	NOUN
ejpam-6270	513	24	lη	lη	NOUN
ejpam-6270	514	1	=	=	NOUN
ejpam-6270	514	2	lζ⊙η	lζ⊙η	PROPN
ejpam-6270	514	3	.	.	PUNCT
ejpam-6270	515	1	then	then	ADV
ejpam-6270	515	2	,	,	PUNCT
ejpam-6270	515	3	w	w	PROPN
ejpam-6270	515	4	is	be	AUX
ejpam-6270	515	5	an	an	DET
ejpam-6270	515	6	open	open	ADJ
ejpam-6270	515	7	set	set	NOUN
ejpam-6270	515	8	having	have	VERB
ejpam-6270	515	9	ζ	ζ	PROPN
ejpam-6270	515	10	⊙	⊙	PROPN
ejpam-6270	515	11	η	η	PROPN
ejpam-6270	515	12	in	in	ADP
ejpam-6270	515	13	w	w	PROPN
ejpam-6270	515	14	,	,	PUNCT
ejpam-6270	515	15	since	since	SCONJ
ejpam-6270	515	16	w	w	NOUN
ejpam-6270	515	17	is	be	AUX
ejpam-6270	515	18	a	a	DET
ejpam-6270	515	19	tbd	tbd	NOUN
ejpam-6270	515	20	-	-	PUNCT
ejpam-6270	515	21	algebra	algebra	NOUN
ejpam-6270	515	22	,	,	PUNCT
ejpam-6270	515	23	so	so	SCONJ
ejpam-6270	515	24	there	there	PRON
ejpam-6270	515	25	exist	exist	VERB
ejpam-6270	515	26	b	b	X
ejpam-6270	515	27	-	-	PUNCT
ejpam-6270	515	28	open	open	ADJ
ejpam-6270	515	29	sets	set	NOUN
ejpam-6270	515	30	u	u	NOUN
ejpam-6270	515	31	and	and	CCONJ
ejpam-6270	515	32	v	v	ADP
ejpam-6270	515	33	containing	contain	VERB
ejpam-6270	515	34	ζ	ζ	NOUN
ejpam-6270	515	35	and	and	CCONJ
ejpam-6270	515	36	η	η	PROPN
ejpam-6270	515	37	respectively	respectively	ADV
ejpam-6270	515	38	such	such	ADJ
ejpam-6270	515	39	that	that	SCONJ
ejpam-6270	515	40	u	u	PROPN
ejpam-6270	515	41	⊙	⊙	VERB
ejpam-6270	515	42	v	v	ADP
ejpam-6270	515	43	⊆	⊆	NUM
ejpam-6270	515	44	w	w	NOUN
ejpam-6270	515	45	.	.	PUNCT
ejpam-6270	516	1	therefore	therefore	ADV
ejpam-6270	516	2	,	,	PUNCT
ejpam-6270	516	3	f(u	f(u	PROPN
ejpam-6270	516	4	⊙	⊙	PROPN
ejpam-6270	516	5	v	v	NOUN
ejpam-6270	516	6	)	)	PUNCT
ejpam-6270	516	7	⊆	⊆	NUM
ejpam-6270	516	8	f(w	f(w	PROPN
ejpam-6270	516	9	)	)	PUNCT
ejpam-6270	516	10	.	.	PUNCT
ejpam-6270	517	1	since	since	SCONJ
ejpam-6270	517	2	w	w	PROPN
ejpam-6270	517	3	is	be	AUX
ejpam-6270	517	4	positive	positive	ADJ
ejpam-6270	517	5	implicative	implicative	ADJ
ejpam-6270	517	6	,	,	PUNCT
ejpam-6270	517	7	and	and	CCONJ
ejpam-6270	517	8	by	by	ADP
ejpam-6270	517	9	proposition	proposition	NOUN
ejpam-6270	517	10	26	26	NUM
ejpam-6270	517	11	,	,	PUNCT
ejpam-6270	517	12	f(u	f(u	PROPN
ejpam-6270	517	13	⊙	⊙	PROPN
ejpam-6270	517	14	v	v	NOUN
ejpam-6270	517	15	)	)	PUNCT
ejpam-6270	517	16	=	=	SYM
ejpam-6270	517	17	f(u	f(u	PROPN
ejpam-6270	517	18	)	)	PUNCT
ejpam-6270	517	19	◦	◦	NOUN
ejpam-6270	517	20	f(v	f(v	PROPN
ejpam-6270	517	21	)	)	PUNCT
ejpam-6270	517	22	⊆	⊆	X
ejpam-6270	517	23	f(w	f(w	PROPN
ejpam-6270	517	24	)	)	PUNCT
ejpam-6270	517	25	.	.	PUNCT
ejpam-6270	518	1	by	by	ADP
ejpam-6270	518	2	proposition	proposition	NOUN
ejpam-6270	518	3	27	27	NUM
ejpam-6270	518	4	,	,	PUNCT
ejpam-6270	518	5	f(u	f(u	PROPN
ejpam-6270	518	6	)	)	PUNCT
ejpam-6270	518	7	and	and	CCONJ
ejpam-6270	518	8	f(v	f(v	PROPN
ejpam-6270	518	9	)	)	PUNCT
ejpam-6270	518	10	are	be	AUX
ejpam-6270	518	11	b	b	ADJ
ejpam-6270	518	12	-	-	PUNCT
ejpam-6270	518	13	open	open	ADJ
ejpam-6270	518	14	sets	set	NOUN
ejpam-6270	518	15	in	in	ADP
ejpam-6270	518	16	(	(	PUNCT
ejpam-6270	518	17	l(w	l(w	PROPN
ejpam-6270	518	18	)	)	PUNCT
ejpam-6270	518	19	,	,	PUNCT
ejpam-6270	518	20	◦	◦	NOUN
ejpam-6270	518	21	,	,	PUNCT
ejpam-6270	518	22	σ	σ	NOUN
ejpam-6270	518	23	)	)	PUNCT
ejpam-6270	518	24	containing	contain	VERB
ejpam-6270	518	25	lζ	lζ	ADV
ejpam-6270	518	26	and	and	CCONJ
ejpam-6270	518	27	lη	lη	NOUN
ejpam-6270	518	28	respectively	respectively	ADV
ejpam-6270	518	29	,	,	PUNCT
ejpam-6270	518	30	hence	hence	ADV
ejpam-6270	518	31	the	the	DET
ejpam-6270	518	32	proof	proof	NOUN
ejpam-6270	518	33	.	.	PUNCT
ejpam-6270	519	1	m.	m.	NOUN
ejpam-6270	519	2	w.	w.	PROPN
ejpam-6270	519	3	abdulqader	abdulqader	PROPN
ejpam-6270	519	4	,	,	PUNCT
ejpam-6270	519	5	a.	a.	PROPN
ejpam-6270	519	6	b.	b.	PROPN
ejpam-6270	519	7	khalaf	khalaf	PROPN
ejpam-6270	519	8	/	/	SYM
ejpam-6270	519	9	eur	eur	PROPN
ejpam-6270	519	10	.	.	PUNCT
ejpam-6270	520	1	j.	j.	PROPN
ejpam-6270	520	2	pure	pure	PROPN
ejpam-6270	520	3	appl	appl	PROPN
ejpam-6270	520	4	.	.	PROPN
ejpam-6270	520	5	math	math	PROPN
ejpam-6270	520	6	,	,	PUNCT
ejpam-6270	520	7	18	18	NUM
ejpam-6270	520	8	(	(	PUNCT
ejpam-6270	520	9	3	3	NUM
ejpam-6270	520	10	)	)	PUNCT
ejpam-6270	520	11	(	(	PUNCT
ejpam-6270	520	12	2025	2025	NUM
ejpam-6270	520	13	)	)	PUNCT
ejpam-6270	520	14	,	,	PUNCT
ejpam-6270	520	15	6270	6270	NUM
ejpam-6270	520	16	16	16	NUM
ejpam-6270	520	17	of	of	ADP
ejpam-6270	520	18	17	17	NUM
ejpam-6270	520	19	example	example	NOUN
ejpam-6270	520	20	6	6	NUM
ejpam-6270	520	21	.	.	PUNCT
ejpam-6270	520	22	consider	consider	VERB
ejpam-6270	520	23	the	the	DET
ejpam-6270	520	24	d	d	NOUN
ejpam-6270	520	25	-	-	PUNCT
ejpam-6270	520	26	algebra	algebra	NOUN
ejpam-6270	520	27	(	(	PUNCT
ejpam-6270	520	28	w,⊙,ω	w,⊙,ω	PROPN
ejpam-6270	520	29	)	)	PUNCT
ejpam-6270	520	30	in	in	ADP
ejpam-6270	520	31	example	example	NOUN
ejpam-6270	520	32	1	1	NUM
ejpam-6270	520	33	,	,	PUNCT
ejpam-6270	520	34	the	the	DET
ejpam-6270	520	35	operation	operation	NOUN
ejpam-6270	520	36	(	(	PUNCT
ejpam-6270	520	37	◦	◦	NOUN
ejpam-6270	520	38	)	)	PUNCT
ejpam-6270	520	39	defined	define	VERB
ejpam-6270	520	40	on	on	ADP
ejpam-6270	520	41	l(w	l(w	NOUN
ejpam-6270	520	42	)	)	PUNCT
ejpam-6270	520	43	is	be	AUX
ejpam-6270	520	44	given	give	VERB
ejpam-6270	520	45	as	as	SCONJ
ejpam-6270	520	46	follows	follow	VERB
ejpam-6270	520	47	:	:	PUNCT
ejpam-6270	520	48	◦	◦	NOUN
ejpam-6270	520	49	l0	l0	NOUN
ejpam-6270	520	50	lα	lα	NOUN
ejpam-6270	520	51	lβ	lβ	PROPN
ejpam-6270	520	52	lγ	lγ	PROPN
ejpam-6270	520	53	l0	l0	PROPN
ejpam-6270	520	54	l0	l0	PROPN
ejpam-6270	520	55	l0	l0	PROPN
ejpam-6270	520	56	l0	l0	PROPN
ejpam-6270	520	57	l0	l0	PROPN
ejpam-6270	520	58	lα	lα	PROPN
ejpam-6270	520	59	lα	lα	PROPN
ejpam-6270	520	60	l0	l0	PROPN
ejpam-6270	520	61	l0	l0	PROPN
ejpam-6270	520	62	lα	lα	ADP
ejpam-6270	520	63	lβ	lβ	ADP
ejpam-6270	520	64	lβ	lβ	PROPN
ejpam-6270	520	65	lβ	lβ	PROPN
ejpam-6270	520	66	l0	l0	PROPN
ejpam-6270	520	67	l0	l0	PROPN
ejpam-6270	521	1	lγ	lγ	ADP
ejpam-6270	521	2	lγ	lγ	ADP
ejpam-6270	521	3	lγ	lγ	ADP
ejpam-6270	521	4	lγ	lγ	ADP
ejpam-6270	521	5	l0	l0	PROPN
ejpam-6270	521	6	table	table	NOUN
ejpam-6270	521	7	2	2	NUM
ejpam-6270	521	8	:	:	PUNCT
ejpam-6270	521	9	the	the	DET
ejpam-6270	521	10	d	d	NOUN
ejpam-6270	521	11	-	-	PUNCT
ejpam-6270	521	12	algebra	algebra	NOUN
ejpam-6270	521	13	(	(	PUNCT
ejpam-6270	521	14	l(w	l(w	PROPN
ejpam-6270	521	15	)	)	PUNCT
ejpam-6270	521	16	,	,	PUNCT
ejpam-6270	521	17	◦	◦	NOUN
ejpam-6270	521	18	,	,	PUNCT
ejpam-6270	521	19	σ	σ	PROPN
ejpam-6270	521	20	)	)	PUNCT
ejpam-6270	521	21	from	from	ADP
ejpam-6270	521	22	proposition	proposition	NOUN
ejpam-6270	521	23	27	27	NUM
ejpam-6270	521	24	and	and	CCONJ
ejpam-6270	521	25	the	the	DET
ejpam-6270	521	26	definition	definition	NOUN
ejpam-6270	521	27	of	of	ADP
ejpam-6270	521	28	ω	ω	PROPN
ejpam-6270	521	29	,	,	PUNCT
ejpam-6270	521	30	we	we	PRON
ejpam-6270	521	31	obtain	obtain	VERB
ejpam-6270	521	32	that	that	DET
ejpam-6270	521	33	σ	σ	NOUN
ejpam-6270	521	34	=	=	SYM
ejpam-6270	521	35	{	{	PUNCT
ejpam-6270	521	36	φ	φ	NOUN
ejpam-6270	521	37	,	,	PUNCT
ejpam-6270	521	38	lα	lα	ADJ
ejpam-6270	521	39	,	,	PUNCT
ejpam-6270	521	40	lγ	lγ	ADV
ejpam-6270	521	41	,	,	PUNCT
ejpam-6270	521	42	l{α	l{α	PROPN
ejpam-6270	521	43	,	,	PUNCT
ejpam-6270	521	44	γ},l(w	γ},l(w	ADJ
ejpam-6270	521	45	)	)	PUNCT
ejpam-6270	521	46	}	}	PUNCT
ejpam-6270	521	47	.	.	PUNCT
ejpam-6270	522	1	by	by	ADP
ejpam-6270	522	2	routine	routine	ADJ
ejpam-6270	522	3	calculation	calculation	NOUN
ejpam-6270	522	4	,	,	PUNCT
ejpam-6270	522	5	we	we	PRON
ejpam-6270	522	6	can	can	AUX
ejpam-6270	522	7	show	show	VERB
ejpam-6270	522	8	that	that	SCONJ
ejpam-6270	522	9	(	(	PUNCT
ejpam-6270	522	10	l(w	l(w	NOUN
ejpam-6270	522	11	)	)	PUNCT
ejpam-6270	522	12	,	,	PUNCT
ejpam-6270	522	13	◦	◦	NOUN
ejpam-6270	522	14	,	,	PUNCT
ejpam-6270	522	15	σ	σ	PROPN
ejpam-6270	522	16	)	)	PUNCT
ejpam-6270	522	17	is	be	AUX
ejpam-6270	522	18	a	a	DET
ejpam-6270	522	19	tbd	tbd	NOUN
ejpam-6270	522	20	-	-	PUNCT
ejpam-6270	522	21	algebra	algebra	NOUN
ejpam-6270	522	22	but	but	CCONJ
ejpam-6270	522	23	(	(	PUNCT
ejpam-6270	522	24	w,⊙,ω	w,⊙,ω	PROPN
ejpam-6270	522	25	)	)	PUNCT
ejpam-6270	522	26	is	be	AUX
ejpam-6270	522	27	not	not	PART
ejpam-6270	522	28	positive	positive	ADJ
ejpam-6270	522	29	implicative	implicative	NOUN
ejpam-6270	522	30	because	because	SCONJ
ejpam-6270	522	31	(	(	PUNCT
ejpam-6270	522	32	α⊙	α⊙	NOUN
ejpam-6270	522	33	γ)⊙	γ)⊙	NOUN
ejpam-6270	522	34	(	(	PUNCT
ejpam-6270	522	35	β	β	PROPN
ejpam-6270	522	36	⊙	⊙	PROPN
ejpam-6270	522	37	γ	γ	PROPN
ejpam-6270	522	38	)	)	PUNCT
ejpam-6270	522	39	=	=	SYM
ejpam-6270	522	40	α	α	PROPN
ejpam-6270	522	41	̸=	̸=	PROPN
ejpam-6270	522	42	(	(	PUNCT
ejpam-6270	522	43	α⊙	α⊙	NOUN
ejpam-6270	522	44	β)⊙	β)⊙	NOUN
ejpam-6270	522	45	γ	γ	X
ejpam-6270	522	46	=	=	SYM
ejpam-6270	522	47	0	0	NUM
ejpam-6270	522	48	.	.	NOUN
ejpam-6270	522	49	4	4	NUM
ejpam-6270	522	50	.	.	X
ejpam-6270	522	51	conclusions	conclusion	NOUN
ejpam-6270	522	52	in	in	ADP
ejpam-6270	522	53	this	this	DET
ejpam-6270	522	54	paper	paper	NOUN
ejpam-6270	522	55	,	,	PUNCT
ejpam-6270	522	56	we	we	PRON
ejpam-6270	522	57	applied	apply	VERB
ejpam-6270	522	58	the	the	DET
ejpam-6270	522	59	family	family	NOUN
ejpam-6270	522	60	of	of	ADP
ejpam-6270	522	61	b	b	NOUN
ejpam-6270	522	62	-	-	PUNCT
ejpam-6270	522	63	open	open	ADJ
ejpam-6270	522	64	sets	set	NOUN
ejpam-6270	522	65	in	in	ADP
ejpam-6270	522	66	topological	topological	ADJ
ejpam-6270	522	67	spaces	space	NOUN
ejpam-6270	522	68	to	to	PART
ejpam-6270	522	69	define	define	VERB
ejpam-6270	522	70	the	the	DET
ejpam-6270	522	71	concept	concept	NOUN
ejpam-6270	522	72	of	of	ADP
ejpam-6270	522	73	b	b	NOUN
ejpam-6270	522	74	-	-	PUNCT
ejpam-6270	522	75	topological	topological	ADJ
ejpam-6270	522	76	d	d	NOUN
ejpam-6270	522	77	-	-	NOUN
ejpam-6270	522	78	algebra	algebra	NOUN
ejpam-6270	522	79	.	.	PUNCT
ejpam-6270	523	1	through	through	ADP
ejpam-6270	523	2	this	this	DET
ejpam-6270	523	3	work	work	NOUN
ejpam-6270	523	4	,	,	PUNCT
ejpam-6270	523	5	we	we	PRON
ejpam-6270	523	6	reviewed	review	VERB
ejpam-6270	523	7	the	the	DET
ejpam-6270	523	8	basics	basic	NOUN
ejpam-6270	523	9	necessary	necessary	ADJ
ejpam-6270	523	10	for	for	ADP
ejpam-6270	523	11	studying	study	VERB
ejpam-6270	523	12	this	this	DET
ejpam-6270	523	13	new	new	ADJ
ejpam-6270	523	14	topological	topological	ADJ
ejpam-6270	523	15	algebra	algebra	NOUN
ejpam-6270	523	16	.	.	PUNCT
ejpam-6270	524	1	we	we	PRON
ejpam-6270	524	2	also	also	ADV
ejpam-6270	524	3	provided	provide	VERB
ejpam-6270	524	4	proofs	proof	NOUN
ejpam-6270	524	5	for	for	ADP
ejpam-6270	524	6	several	several	ADJ
ejpam-6270	524	7	issues	issue	NOUN
ejpam-6270	524	8	related	relate	VERB
ejpam-6270	524	9	to	to	ADP
ejpam-6270	524	10	continuity	continuity	NOUN
ejpam-6270	524	11	,	,	PUNCT
ejpam-6270	524	12	separation	separation	NOUN
ejpam-6270	524	13	axioms	axiom	NOUN
ejpam-6270	524	14	,	,	PUNCT
ejpam-6270	524	15	and	and	CCONJ
ejpam-6270	524	16	other	other	ADJ
ejpam-6270	524	17	concepts	concept	NOUN
ejpam-6270	524	18	.	.	PUNCT
ejpam-6270	525	1	this	this	PRON
ejpam-6270	525	2	paves	pave	VERB
ejpam-6270	525	3	the	the	DET
ejpam-6270	525	4	way	way	NOUN
ejpam-6270	525	5	for	for	ADP
ejpam-6270	525	6	future	future	ADJ
ejpam-6270	525	7	studies	study	NOUN
ejpam-6270	525	8	related	relate	VERB
ejpam-6270	525	9	to	to	ADP
ejpam-6270	525	10	topological	topological	ADJ
ejpam-6270	525	11	d	d	NOUN
ejpam-6270	525	12	-	-	PUNCT
ejpam-6270	525	13	algebras	algebra	VERB
ejpam-6270	525	14	by	by	ADP
ejpam-6270	525	15	applying	apply	VERB
ejpam-6270	525	16	various	various	ADJ
ejpam-6270	525	17	types	type	NOUN
ejpam-6270	525	18	of	of	ADP
ejpam-6270	525	19	nearly	nearly	ADV
ejpam-6270	525	20	open	open	ADJ
ejpam-6270	525	21	sets	set	NOUN
ejpam-6270	525	22	.	.	PUNCT
ejpam-6270	526	1	moreover	moreover	ADV
ejpam-6270	526	2	,	,	PUNCT
ejpam-6270	526	3	d	d	X
ejpam-6270	526	4	-	-	PUNCT
ejpam-6270	526	5	algebras	algebras	PROPN
ejpam-6270	526	6	can	can	AUX
ejpam-6270	526	7	be	be	AUX
ejpam-6270	526	8	studied	study	VERB
ejpam-6270	526	9	in	in	ADP
ejpam-6270	526	10	supratopological	supratopological	ADJ
ejpam-6270	526	11	spaces	space	NOUN
ejpam-6270	526	12	.	.	PUNCT
ejpam-6270	527	1	references	reference	NOUN
ejpam-6270	527	2	[	[	X
ejpam-6270	527	3	1	1	X
ejpam-6270	527	4	]	]	PUNCT
ejpam-6270	527	5	d.	d.	PROPN
ejpam-6270	527	6	andrijevic	andrijevic	VERB
ejpam-6270	527	7	.	.	PUNCT
ejpam-6270	528	1	on	on	ADP
ejpam-6270	528	2	b	b	X
ejpam-6270	528	3	-	-	PUNCT
ejpam-6270	528	4	open	open	ADJ
ejpam-6270	528	5	set	set	NOUN
ejpam-6270	528	6	.	.	PUNCT
ejpam-6270	529	1	mat	mat	PROPN
ejpam-6270	529	2	.	.	PROPN
ejpam-6270	529	3	vesink	vesink	PROPN
ejpam-6270	529	4	,	,	PUNCT
ejpam-6270	529	5	48:59–64	48:59–64	PROPN
ejpam-6270	529	6	,	,	PUNCT
ejpam-6270	529	7	1996	1996	NUM
ejpam-6270	529	8	.	.	PUNCT
ejpam-6270	530	1	[	[	X
ejpam-6270	530	2	2	2	NUM
ejpam-6270	530	3	]	]	PUNCT
ejpam-6270	530	4	a.	a.	NOUN
ejpam-6270	530	5	y.	y.	PROPN
ejpam-6270	530	6	al	al	PROPN
ejpam-6270	530	7	-	-	PUNCT
ejpam-6270	530	8	etik	etik	NOUN
ejpam-6270	530	9	.	.	PUNCT
ejpam-6270	531	1	a	a	DET
ejpam-6270	531	2	study	study	NOUN
ejpam-6270	531	3	of	of	ADP
ejpam-6270	531	4	some	some	DET
ejpam-6270	531	5	types	type	NOUN
ejpam-6270	531	6	of	of	ADP
ejpam-6270	531	7	mappings	mapping	NOUN
ejpam-6270	531	8	on	on	ADP
ejpam-6270	531	9	topological	topological	ADJ
ejpam-6270	531	10	spaces	space	NOUN
ejpam-6270	531	11	.	.	PUNCT
ejpam-6270	532	1	master	master	NOUN
ejpam-6270	532	2	’s	’s	PART
ejpam-6270	532	3	thesis	thesis	NOUN
ejpam-6270	532	4	,	,	PUNCT
ejpam-6270	532	5	tanta	tanta	PROPN
ejpam-6270	532	6	university	university	PROPN
ejpam-6270	532	7	,	,	PUNCT
ejpam-6270	532	8	1997	1997	NUM
ejpam-6270	532	9	.	.	PUNCT
ejpam-6270	533	1	[	[	X
ejpam-6270	533	2	3	3	NUM
ejpam-6270	533	3	]	]	PUNCT
ejpam-6270	533	4	m.	m.	NOUN
ejpam-6270	533	5	caldas	caldas	PROPN
ejpam-6270	533	6	and	and	CCONJ
ejpam-6270	533	7	s.	s.	PROPN
ejpam-6270	533	8	jafari	jafari	PROPN
ejpam-6270	533	9	.	.	PUNCT
ejpam-6270	534	1	on	on	ADP
ejpam-6270	534	2	some	some	DET
ejpam-6270	534	3	applications	application	NOUN
ejpam-6270	534	4	of	of	ADP
ejpam-6270	534	5	b	b	NOUN
ejpam-6270	534	6	-	-	PUNCT
ejpam-6270	534	7	open	open	ADJ
ejpam-6270	534	8	sets	set	NOUN
ejpam-6270	534	9	in	in	ADP
ejpam-6270	534	10	topological	topological	ADJ
ejpam-6270	534	11	spaces	space	NOUN
ejpam-6270	534	12	.	.	PUNCT
ejpam-6270	535	1	kochi	kochi	PROPN
ejpam-6270	535	2	j.	j.	PROPN
ejpam-6270	535	3	math	math	PROPN
ejpam-6270	535	4	.	.	PUNCT
ejpam-6270	535	5	,	,	PUNCT
ejpam-6270	535	6	2:11–19	2:11–19	PROPN
ejpam-6270	535	7	,	,	PUNCT
ejpam-6270	535	8	2007	2007	NUM
ejpam-6270	535	9	.	.	PUNCT
ejpam-6270	536	1	[	[	X
ejpam-6270	536	2	4	4	X
ejpam-6270	536	3	]	]	PUNCT
ejpam-6270	536	4	j.	j.	PROPN
ejpam-6270	536	5	neggers	neggers	PROPN
ejpam-6270	536	6	and	and	CCONJ
ejpam-6270	536	7	h.	h.	PROPN
ejpam-6270	536	8	s.	s.	PROPN
ejpam-6270	536	9	kim	kim	PROPN
ejpam-6270	536	10	.	.	PUNCT
ejpam-6270	537	1	on	on	ADP
ejpam-6270	537	2	d	d	PROPN
ejpam-6270	537	3	-	-	PUNCT
ejpam-6270	537	4	algebras	algebras	PROPN
ejpam-6270	537	5	.	.	PUNCT
ejpam-6270	538	1	mathematica	mathematica	PROPN
ejpam-6270	538	2	slovaca	slovaca	PROPN
ejpam-6270	538	3	,	,	PUNCT
ejpam-6270	538	4	49(1):19–26	49(1):19–26	NUM
ejpam-6270	538	5	,	,	PUNCT
ejpam-6270	538	6	1999	1999	NUM
ejpam-6270	538	7	.	.	PUNCT
ejpam-6270	539	1	[	[	X
ejpam-6270	539	2	5	5	X
ejpam-6270	539	3	]	]	PUNCT
ejpam-6270	539	4	d.	d.	PROPN
ejpam-6270	539	5	s.	s.	PROPN
ejpam-6270	539	6	lee	lee	PROPN
ejpam-6270	539	7	and	and	CCONJ
ejpam-6270	539	8	d.	d.	PROPN
ejpam-6270	539	9	n.	n.	PROPN
ejpam-6270	539	10	ryu	ryu	PROPN
ejpam-6270	539	11	.	.	PUNCT
ejpam-6270	539	12	notes	note	NOUN
ejpam-6270	539	13	on	on	ADP
ejpam-6270	539	14	topological	topological	ADJ
ejpam-6270	539	15	bck	bck	PROPN
ejpam-6270	539	16	-	-	PUNCT
ejpam-6270	539	17	algebras	algebras	PROPN
ejpam-6270	539	18	.	.	PUNCT
ejpam-6270	540	1	sci	sci	PROPN
ejpam-6270	540	2	.	.	PROPN
ejpam-6270	540	3	math	math	PROPN
ejpam-6270	540	4	.	.	PUNCT
ejpam-6270	540	5	,	,	PUNCT
ejpam-6270	540	6	1:231–235	1:231–235	NUM
ejpam-6270	540	7	,	,	PUNCT
ejpam-6270	540	8	1998	1998	NUM
ejpam-6270	540	9	.	.	PUNCT
ejpam-6270	541	1	[	[	X
ejpam-6270	541	2	6	6	NUM
ejpam-6270	541	3	]	]	PUNCT
ejpam-6270	541	4	a.	a.	NOUN
ejpam-6270	541	5	kh	kh	PROPN
ejpam-6270	541	6	.	.	PUNCT
ejpam-6270	542	1	hasan	hasan	PROPN
ejpam-6270	542	2	.	.	PUNCT
ejpam-6270	543	1	a	a	DET
ejpam-6270	543	2	topology	topology	NOUN
ejpam-6270	543	3	on	on	ADP
ejpam-6270	543	4	d	d	NOUN
ejpam-6270	543	5	-	-	NOUN
ejpam-6270	543	6	algebra	algebra	NOUN
ejpam-6270	543	7	via	via	ADP
ejpam-6270	543	8	dual	dual	ADJ
ejpam-6270	543	9	stabilizers	stabilizer	NOUN
ejpam-6270	543	10	.	.	PUNCT
ejpam-6270	544	1	journal	journal	PROPN
ejpam-6270	544	2	of	of	ADP
ejpam-6270	544	3	physics	physics	PROPN
ejpam-6270	544	4	:	:	PUNCT
ejpam-6270	544	5	conference	conference	NOUN
ejpam-6270	544	6	series	series	NOUN
ejpam-6270	544	7	,	,	PUNCT
ejpam-6270	544	8	1660	1660	NUM
ejpam-6270	544	9	(	(	PUNCT
ejpam-6270	544	10	2020	2020	NUM
ejpam-6270	544	11	)	)	PUNCT
ejpam-6270	544	12	012103:1–4	012103:1–4	NOUN
ejpam-6270	544	13	,	,	PUNCT
ejpam-6270	544	14	2020	2020	NUM
ejpam-6270	544	15	.	.	PUNCT
ejpam-6270	545	1	[	[	X
ejpam-6270	545	2	7	7	NUM
ejpam-6270	545	3	]	]	PUNCT
ejpam-6270	545	4	a.	a.	PROPN
ejpam-6270	545	5	b.	b.	PROPN
ejpam-6270	545	6	khalaf	khalaf	PROPN
ejpam-6270	545	7	and	and	CCONJ
ejpam-6270	545	8	n.	n.	PROPN
ejpam-6270	545	9	k.	k.	PROPN
ejpam-6270	545	10	ahmed	ahmed	PROPN
ejpam-6270	545	11	.	.	PUNCT
ejpam-6270	546	1	on	on	ADP
ejpam-6270	546	2	pre	pre	ADJ
ejpam-6270	546	3	-	-	ADJ
ejpam-6270	546	4	topological	topological	ADJ
ejpam-6270	546	5	bck	bck	NOUN
ejpam-6270	546	6	-	-	PUNCT
ejpam-6270	546	7	algebras	algebras	PROPN
ejpam-6270	546	8	.	.	PUNCT
ejpam-6270	547	1	journal	journal	PROPN
ejpam-6270	547	2	of	of	ADP
ejpam-6270	547	3	algebra	algebra	PROPN
ejpam-6270	547	4	and	and	CCONJ
ejpam-6270	547	5	related	related	ADJ
ejpam-6270	547	6	topics	topic	NOUN
ejpam-6270	547	7	,	,	PUNCT
ejpam-6270	547	8	11:65–80	11:65–80	PROPN
ejpam-6270	547	9	,	,	PUNCT
ejpam-6270	547	10	2023	2023	NUM
ejpam-6270	547	11	.	.	PUNCT
ejpam-6270	548	1	[	[	X
ejpam-6270	548	2	8	8	NUM
ejpam-6270	548	3	]	]	PUNCT
ejpam-6270	548	4	a.	a.	PROPN
ejpam-6270	548	5	b.	b.	PROPN
ejpam-6270	548	6	khalaf	khalaf	PROPN
ejpam-6270	548	7	and	and	CCONJ
ejpam-6270	548	8	f.	f.	PROPN
ejpam-6270	548	9	w.	w.	PROPN
ejpam-6270	548	10	ali	ali	PROPN
ejpam-6270	548	11	.	.	PUNCT
ejpam-6270	549	1	on	on	ADP
ejpam-6270	549	2	s	s	NOUN
ejpam-6270	549	3	-	-	ADJ
ejpam-6270	549	4	topological	topological	ADJ
ejpam-6270	549	5	bck	bck	NOUN
ejpam-6270	549	6	-	-	PUNCT
ejpam-6270	549	7	algebra	algebra	NOUN
ejpam-6270	549	8	.	.	PUNCT
ejpam-6270	550	1	journal	journal	NOUN
ejpam-6270	550	2	of	of	ADP
ejpam-6270	550	3	university	university	PROPN
ejpam-6270	550	4	of	of	ADP
ejpam-6270	550	5	duhok	duhok	NOUN
ejpam-6270	550	6	,	,	PUNCT
ejpam-6270	550	7	23(1):199–208	23(1):199–208	NOUN
ejpam-6270	550	8	,	,	PUNCT
ejpam-6270	550	9	2020	2020	NUM
ejpam-6270	550	10	.	.	PUNCT
ejpam-6270	551	1	[	[	X
ejpam-6270	551	2	9	9	NUM
ejpam-6270	551	3	]	]	PUNCT
ejpam-6270	551	4	a.	a.	PROPN
ejpam-6270	551	5	b.	b.	PROPN
ejpam-6270	551	6	khalaf	khalaf	PROPN
ejpam-6270	551	7	.	.	PUNCT
ejpam-6270	552	1	on	on	ADP
ejpam-6270	552	2	weak	weak	ADJ
ejpam-6270	552	3	topological	topological	ADJ
ejpam-6270	552	4	bck	bck	NOUN
ejpam-6270	552	5	-	-	PUNCT
ejpam-6270	552	6	algebras	algebras	PROPN
ejpam-6270	552	7	.	.	PUNCT
ejpam-6270	553	1	journal	journal	PROPN
ejpam-6270	553	2	of	of	ADP
ejpam-6270	553	3	interdisciplinary	interdisciplinary	ADJ
ejpam-6270	553	4	mathematics	mathematic	NOUN
ejpam-6270	553	5	,	,	PUNCT
ejpam-6270	553	6	25(6):1621–1641	25(6):1621–1641	NUM
ejpam-6270	553	7	,	,	PUNCT
ejpam-6270	553	8	2022	2022	NUM
ejpam-6270	553	9	.	.	PUNCT
ejpam-6270	554	1	m.	m.	NOUN
ejpam-6270	554	2	w.	w.	PROPN
ejpam-6270	554	3	abdulqader	abdulqader	PROPN
ejpam-6270	554	4	,	,	PUNCT
ejpam-6270	554	5	a.	a.	PROPN
ejpam-6270	554	6	b.	b.	PROPN
ejpam-6270	554	7	khalaf	khalaf	PROPN
ejpam-6270	554	8	/	/	SYM
ejpam-6270	554	9	eur	eur	PROPN
ejpam-6270	554	10	.	.	PUNCT
ejpam-6270	555	1	j.	j.	PROPN
ejpam-6270	555	2	pure	pure	PROPN
ejpam-6270	555	3	appl	appl	PROPN
ejpam-6270	555	4	.	.	PROPN
ejpam-6270	555	5	math	math	PROPN
ejpam-6270	555	6	,	,	PUNCT
ejpam-6270	555	7	18	18	NUM
ejpam-6270	555	8	(	(	PUNCT
ejpam-6270	555	9	3	3	NUM
ejpam-6270	555	10	)	)	PUNCT
ejpam-6270	555	11	(	(	PUNCT
ejpam-6270	555	12	2025	2025	NUM
ejpam-6270	555	13	)	)	PUNCT
ejpam-6270	555	14	,	,	PUNCT
ejpam-6270	555	15	6270	6270	NUM
ejpam-6270	555	16	17	17	NUM
ejpam-6270	555	17	of	of	ADP
ejpam-6270	555	18	17	17	NUM
ejpam-6270	555	19	[	[	SYM
ejpam-6270	555	20	10	10	NUM
ejpam-6270	555	21	]	]	PUNCT
ejpam-6270	555	22	t.	t.	PROPN
ejpam-6270	555	23	m.	m.	PROPN
ejpam-6270	555	24	al	al	PROPN
ejpam-6270	555	25	-	-	PUNCT
ejpam-6270	555	26	shami	shami	PROPN
ejpam-6270	555	27	,	,	PUNCT
ejpam-6270	555	28	abdelwaheb	abdelwaheb	PROPN
ejpam-6270	555	29	mhemdi	mhemdi	PROPN
ejpam-6270	555	30	,	,	PUNCT
ejpam-6270	555	31	mohammed	mohammed	PROPN
ejpam-6270	555	32	jameel	jameel	PROPN
ejpam-6270	555	33	,	,	PUNCT
ejpam-6270	555	34	and	and	CCONJ
ejpam-6270	555	35	mohamed	mohamed	PROPN
ejpam-6270	555	36	abouhawwash	abouhawwash	PROPN
ejpam-6270	555	37	.	.	PUNCT
ejpam-6270	556	1	supra	supra	PROPN
ejpam-6270	556	2	b	b	PROPN
ejpam-6270	556	3	limit	limit	NOUN
ejpam-6270	556	4	points	point	NOUN
ejpam-6270	556	5	and	and	CCONJ
ejpam-6270	556	6	supra	supra	PROPN
ejpam-6270	556	7	b	b	PROPN
ejpam-6270	556	8	separation	separation	NOUN
ejpam-6270	556	9	axioms	axiom	VERB
ejpam-6270	556	10	.	.	PUNCT
ejpam-6270	557	1	european	european	ADJ
ejpam-6270	557	2	journal	journal	PROPN
ejpam-6270	557	3	of	of	ADP
ejpam-6270	557	4	pure	pure	ADJ
ejpam-6270	557	5	and	and	CCONJ
ejpam-6270	557	6	applied	applied	ADJ
ejpam-6270	557	7	mathematics	mathematic	NOUN
ejpam-6270	557	8	,	,	PUNCT
ejpam-6270	557	9	15(1):15–29	15(1):15–29	NUM
ejpam-6270	557	10	,	,	PUNCT
ejpam-6270	557	11	2022	2022	NUM
ejpam-6270	557	12	.	.	PUNCT
ejpam-6270	558	1	[	[	X
ejpam-6270	558	2	11	11	NUM
ejpam-6270	558	3	]	]	PUNCT
ejpam-6270	558	4	r.	r.	PROPN
ejpam-6270	558	5	abu	abu	PROPN
ejpam-6270	558	6	-	-	PUNCT
ejpam-6270	558	7	gdairi	gdairi	PROPN
ejpam-6270	558	8	,	,	PUNCT
ejpam-6270	558	9	m.	m.	NOUN
ejpam-6270	558	10	al	al	PROPN
ejpam-6270	558	11	-	-	PUNCT
ejpam-6270	558	12	shamiri	shamiri	PROPN
ejpam-6270	558	13	,	,	PUNCT
ejpam-6270	558	14	s.	s.	PROPN
ejpam-6270	558	15	saleh	saleh	PROPN
ejpam-6270	558	16	,	,	PUNCT
ejpam-6270	558	17	and	and	CCONJ
ejpam-6270	558	18	t.	t.	PROPN
ejpam-6270	558	19	m.	m.	PROPN
ejpam-6270	558	20	al	al	PROPN
ejpam-6270	558	21	-	-	PUNCT
ejpam-6270	558	22	shami	shami	PROPN
ejpam-6270	558	23	.	.	PUNCT
ejpam-6270	559	1	on	on	ADP
ejpam-6270	559	2	b	b	X
ejpam-6270	559	3	-	-	PUNCT
ejpam-6270	559	4	open	open	ADJ
ejpam-6270	559	5	sets	set	NOUN
ejpam-6270	559	6	via	via	ADP
ejpam-6270	559	7	infra	infra	NOUN
ejpam-6270	559	8	soft	soft	ADJ
ejpam-6270	559	9	topological	topological	ADJ
ejpam-6270	559	10	spaces	space	NOUN
ejpam-6270	559	11	.	.	PUNCT
ejpam-6270	560	1	european	european	ADJ
ejpam-6270	560	2	journal	journal	PROPN
ejpam-6270	560	3	of	of	ADP
ejpam-6270	560	4	pure	pure	ADJ
ejpam-6270	560	5	and	and	CCONJ
ejpam-6270	560	6	applied	applied	ADJ
ejpam-6270	560	7	mathematics	mathematic	NOUN
ejpam-6270	560	8	,	,	PUNCT
ejpam-6270	560	9	15(4):1455–1471	15(4):1455–1471	NUM
ejpam-6270	560	10	,	,	PUNCT
ejpam-6270	560	11	2022	2022	NUM
ejpam-6270	560	12	.	.	PUNCT
ejpam-6270	561	1	[	[	X
ejpam-6270	561	2	12	12	NUM
ejpam-6270	561	3	]	]	PUNCT
ejpam-6270	561	4	t.	t.	PROPN
ejpam-6270	561	5	m.	m.	PROPN
ejpam-6270	561	6	al	al	PROPN
ejpam-6270	561	7	-	-	PUNCT
ejpam-6270	561	8	shami	shami	PROPN
ejpam-6270	561	9	,	,	PUNCT
ejpam-6270	561	10	ea	ea	X
ejpam-6270	561	11	abo	abo	NOUN
ejpam-6270	561	12	-	-	PUNCT
ejpam-6270	561	13	tabl	tabl	NOUN
ejpam-6270	561	14	,	,	PUNCT
ejpam-6270	561	15	baravan	baravan	PROPN
ejpam-6270	561	16	assad	assad	PROPN
ejpam-6270	561	17	,	,	PUNCT
ejpam-6270	561	18	and	and	CCONJ
ejpam-6270	561	19	mohamed	mohamed	PROPN
ejpam-6270	561	20	arahet	arahet	PROPN
ejpam-6270	561	21	.	.	PUNCT
ejpam-6270	562	1	limit	limit	VERB
ejpam-6270	562	2	points	point	NOUN
ejpam-6270	562	3	and	and	CCONJ
ejpam-6270	562	4	separation	separation	NOUN
ejpam-6270	562	5	axioms	axiom	NOUN
ejpam-6270	562	6	with	with	ADP
ejpam-6270	562	7	respect	respect	NOUN
ejpam-6270	562	8	to	to	ADP
ejpam-6270	562	9	supra	supra	PROPN
ejpam-6270	562	10	semi	semi	ADJ
ejpam-6270	562	11	-	-	ADJ
ejpam-6270	562	12	open	open	ADJ
ejpam-6270	562	13	sets	set	NOUN
ejpam-6270	562	14	.	.	PUNCT
ejpam-6270	563	1	european	european	ADJ
ejpam-6270	563	2	journal	journal	PROPN
ejpam-6270	563	3	of	of	ADP
ejpam-6270	563	4	pure	pure	ADJ
ejpam-6270	563	5	and	and	CCONJ
ejpam-6270	563	6	applied	applied	ADJ
ejpam-6270	563	7	mathematics	mathematic	NOUN
ejpam-6270	563	8	,	,	PUNCT
ejpam-6270	563	9	13(3):427–443	13(3):427–443	PROPN
ejpam-6270	563	10	,	,	PUNCT
ejpam-6270	563	11	2020	2020	NUM
ejpam-6270	563	12	.	.	PUNCT
ejpam-6270	564	1	[	[	X
ejpam-6270	564	2	13	13	NUM
ejpam-6270	564	3	]	]	X
ejpam-6270	564	4	r.	r.	PROPN
ejpam-6270	564	5	engelking	engelke	VERB
ejpam-6270	564	6	.	.	PUNCT
ejpam-6270	565	1	general	general	ADJ
ejpam-6270	565	2	topology	topology	PROPN
ejpam-6270	565	3	.	.	PUNCT
ejpam-6270	566	1	pwn	pwn	NOUN
ejpam-6270	566	2	-	-	PUNCT
ejpam-6270	566	3	polish	polish	ADJ
ejpam-6270	566	4	scientific	scientific	ADJ
ejpam-6270	566	5	publishers	publisher	NOUN
ejpam-6270	566	6	,	,	PUNCT
ejpam-6270	566	7	1976	1976	NUM
ejpam-6270	566	8	.	.	PUNCT
ejpam-6270	567	1	[	[	X
ejpam-6270	567	2	14	14	NUM
ejpam-6270	567	3	]	]	X
ejpam-6270	567	4	n.	n.	PROPN
ejpam-6270	567	5	levine	levine	PROPN
ejpam-6270	567	6	.	.	PUNCT
ejpam-6270	568	1	semi	semi	ADJ
ejpam-6270	568	2	-	-	ADJ
ejpam-6270	568	3	open	open	ADJ
ejpam-6270	568	4	sets	set	NOUN
ejpam-6270	568	5	and	and	CCONJ
ejpam-6270	568	6	semi	semi	ADJ
ejpam-6270	568	7	-	-	NOUN
ejpam-6270	568	8	continuity	continuity	NOUN
ejpam-6270	568	9	in	in	ADP
ejpam-6270	568	10	topological	topological	ADJ
ejpam-6270	568	11	spaces	space	NOUN
ejpam-6270	568	12	.	.	PUNCT
ejpam-6270	569	1	amer	amer	PROPN
ejpam-6270	569	2	.	.	PUNCT
ejpam-6270	569	3	math	math	PROPN
ejpam-6270	569	4	.	.	PUNCT
ejpam-6270	570	1	monthly	monthly	ADJ
ejpam-6270	570	2	,	,	PUNCT
ejpam-6270	570	3	70:36–41	70:36–41	NUM
ejpam-6270	570	4	,	,	PUNCT
ejpam-6270	570	5	1963	1963	NUM
ejpam-6270	570	6	.	.	PUNCT
ejpam-6270	571	1	[	[	X
ejpam-6270	571	2	15	15	NUM
ejpam-6270	571	3	]	]	X
ejpam-6270	571	4	a.	a.	NOUN
ejpam-6270	571	5	s.	s.	PROPN
ejpam-6270	571	6	mashhour	mashhour	PROPN
ejpam-6270	571	7	.	.	PUNCT
ejpam-6270	572	1	on	on	ADP
ejpam-6270	572	2	pre	pre	ADJ
ejpam-6270	572	3	-	-	ADJ
ejpam-6270	572	4	continuous	continuous	ADJ
ejpam-6270	572	5	and	and	CCONJ
ejpam-6270	572	6	weak	weak	ADJ
ejpam-6270	572	7	pre	pre	ADJ
ejpam-6270	572	8	-	-	ADJ
ejpam-6270	572	9	continuous	continuous	ADJ
ejpam-6270	572	10	mappings	mapping	NOUN
ejpam-6270	572	11	.	.	PUNCT
ejpam-6270	573	1	proc	proc	NOUN
ejpam-6270	573	2	.	.	PUNCT
ejpam-6270	574	1	math	math	NOUN
ejpam-6270	574	2	.	.	PUNCT
ejpam-6270	575	1	phys	phy	NOUN
ejpam-6270	575	2	.	.	PUNCT
ejpam-6270	576	1	soc	soc	PROPN
ejpam-6270	576	2	.	.	PUNCT
ejpam-6270	577	1	egypt	egypt	PROPN
ejpam-6270	577	2	.	.	PROPN
ejpam-6270	577	3	,	,	PUNCT
ejpam-6270	577	4	53:47–53	53:47–53	NUM
ejpam-6270	577	5	,	,	PUNCT
ejpam-6270	577	6	1982	1982	NUM
ejpam-6270	577	7	.	.	PUNCT
ejpam-6270	578	1	[	[	X
ejpam-6270	578	2	16	16	NUM
ejpam-6270	578	3	]	]	PUNCT
ejpam-6270	578	4	j.	j.	PROPN
ejpam-6270	578	5	dontchev	dontchev	PROPN
ejpam-6270	578	6	.	.	PUNCT
ejpam-6270	579	1	survey	survey	NOUN
ejpam-6270	579	2	on	on	ADP
ejpam-6270	579	3	preopen	preopen	ADJ
ejpam-6270	579	4	sets	set	NOUN
ejpam-6270	579	5	.	.	PUNCT
ejpam-6270	580	1	arxivmath/9810177	arxivmath/9810177	PROPN
ejpam-6270	580	2	math.gn	math.gn	PROPN
ejpam-6270	580	3	,	,	PUNCT
ejpam-6270	580	4	pages	page	NOUN
ejpam-6270	580	5	1–18	1–18	NUM
ejpam-6270	580	6	,	,	PUNCT
ejpam-6270	580	7	1998	1998	NUM
ejpam-6270	580	8	.	.	PUNCT
ejpam-6270	581	1	[	[	X
ejpam-6270	581	2	17	17	NUM
ejpam-6270	581	3	]	]	PUNCT
ejpam-6270	581	4	a.	a.	NOUN
ejpam-6270	581	5	gupta	gupta	PROPN
ejpam-6270	581	6	and	and	CCONJ
ejpam-6270	581	7	r.	r.	PROPN
ejpam-6270	581	8	d.	d.	PROPN
ejpam-6270	581	9	sarma	sarma	PROPN
ejpam-6270	581	10	.	.	PUNCT
ejpam-6270	581	11	ps	ps	NOUN
ejpam-6270	581	12	-	-	PUNCT
ejpam-6270	581	13	regular	regular	ADJ
ejpam-6270	581	14	sets	set	NOUN
ejpam-6270	581	15	in	in	ADP
ejpam-6270	581	16	topology	topology	NOUN
ejpam-6270	581	17	and	and	CCONJ
ejpam-6270	581	18	generalized	generalized	ADJ
ejpam-6270	581	19	topology	topology	NOUN
ejpam-6270	581	20	.	.	PUNCT
ejpam-6270	582	1	journal	journal	PROPN
ejpam-6270	582	2	of	of	ADP
ejpam-6270	582	3	mathematics	mathematic	NOUN
ejpam-6270	582	4	,	,	PUNCT
ejpam-6270	582	5	2014(1):274592	2014(1):274592	NUM
ejpam-6270	582	6	,	,	PUNCT
ejpam-6270	582	7	2014	2014	NUM
ejpam-6270	582	8	.	.	PUNCT
ejpam-6270	583	1	[	[	X
ejpam-6270	583	2	18	18	NUM
ejpam-6270	583	3	]	]	PUNCT
ejpam-6270	583	4	p.	p.	NOUN
ejpam-6270	583	5	muangkarn	muangkarn	PROPN
ejpam-6270	583	6	,	,	PUNCT
ejpam-6270	583	7	c.	c.	PROPN
ejpam-6270	583	8	suanoom	suanoom	NOUN
ejpam-6270	583	9	,	,	PUNCT
ejpam-6270	583	10	and	and	CCONJ
ejpam-6270	583	11	a.	a.	NOUN
ejpam-6270	583	12	iampan	iampan	PROPN
ejpam-6270	583	13	.	.	PUNCT
ejpam-6270	584	1	new	new	ADJ
ejpam-6270	584	2	derivations	derivation	NOUN
ejpam-6270	584	3	of	of	ADP
ejpam-6270	584	4	d	d	NOUN
ejpam-6270	584	5	-	-	PUNCT
ejpam-6270	584	6	algebras	algebras	PROPN
ejpam-6270	584	7	based	base	VERB
ejpam-6270	584	8	on	on	ADP
ejpam-6270	584	9	endomorphisms	endomorphism	NOUN
ejpam-6270	584	10	.	.	PUNCT
ejpam-6270	585	1	international	international	ADJ
ejpam-6270	585	2	journal	journal	NOUN
ejpam-6270	585	3	of	of	ADP
ejpam-6270	585	4	mathematics	mathematic	NOUN
ejpam-6270	585	5	and	and	CCONJ
ejpam-6270	585	6	computer	computer	NOUN
ejpam-6270	585	7	science	science	NOUN
ejpam-6270	585	8	,	,	PUNCT
ejpam-6270	585	9	17(3):1025–1032	17(3):1025–1032	NUM
ejpam-6270	585	10	,	,	PUNCT
ejpam-6270	585	11	2022	2022	NUM
ejpam-6270	585	12	.	.	PUNCT
ejpam-6270	586	1	[	[	X
ejpam-6270	586	2	19	19	NUM
ejpam-6270	586	3	]	]	PUNCT
ejpam-6270	586	4	b.	b.	PROPN
ejpam-6270	586	5	l.	l.	PROPN
ejpam-6270	586	6	meng	meng	PROPN
ejpam-6270	586	7	.	.	PUNCT
ejpam-6270	587	1	atoms	atom	NOUN
ejpam-6270	587	2	in	in	ADP
ejpam-6270	587	3	ci	ci	NOUN
ejpam-6270	587	4	-	-	PUNCT
ejpam-6270	587	5	algebras	algebras	PROPN
ejpam-6270	587	6	and	and	CCONJ
ejpam-6270	587	7	singular	singular	PROPN
ejpam-6270	587	8	ci	ci	NOUN
ejpam-6270	587	9	-	-	PUNCT
ejpam-6270	587	10	algebras	algebras	PROPN
ejpam-6270	587	11	.	.	PUNCT
ejpam-6270	588	1	scientiae	scientiae	PROPN
ejpam-6270	588	2	mathematicae	mathematicae	VERB
ejpam-6270	588	3	japonicae	japonicae	PROPN
ejpam-6270	588	4	online	online	PROPN
ejpam-6270	588	5	,	,	PUNCT
ejpam-6270	588	6	e-2010	e-2010	PROPN
ejpam-6270	588	7	,	,	PUNCT
ejpam-6270	588	8	319–324	319–324	NUM
ejpam-6270	588	9	,	,	PUNCT
ejpam-6270	588	10	online:319–324	online:319–324	NUM
ejpam-6270	588	11	,	,	PUNCT
ejpam-6270	588	12	2010	2010	NUM
ejpam-6270	588	13	.	.	PUNCT
ejpam-6270	589	1	[	[	X
ejpam-6270	589	2	20	20	NUM
ejpam-6270	589	3	]	]	PUNCT
ejpam-6270	589	4	s.	s.	PROPN
ejpam-6270	589	5	s.	s.	PROPN
ejpam-6270	589	6	ahn	ahn	PROPN
ejpam-6270	589	7	and	and	CCONJ
ejpam-6270	589	8	k.	k.	PROPN
ejpam-6270	589	9	s.	s.	PROPN
ejpam-6270	589	10	so	so	ADV
ejpam-6270	589	11	.	.	PUNCT
ejpam-6270	590	1	on	on	ADP
ejpam-6270	590	2	kernels	kernel	NOUN
ejpam-6270	590	3	and	and	CCONJ
ejpam-6270	590	4	annihilators	annihilator	NOUN
ejpam-6270	590	5	of	of	ADP
ejpam-6270	590	6	left	left	ADJ
ejpam-6270	590	7	-	-	PUNCT
ejpam-6270	590	8	regular	regular	ADJ
ejpam-6270	590	9	mappings	mapping	NOUN
ejpam-6270	590	10	in	in	ADP
ejpam-6270	590	11	d	d	NOUN
ejpam-6270	590	12	-	-	PUNCT
ejpam-6270	590	13	algebras	algebras	X
ejpam-6270	590	14	.	.	PUNCT
ejpam-6270	591	1	honan	honan	PROPN
ejpam-6270	591	2	mathematical	mathematical	PROPN
ejpam-6270	591	3	journal	journal	PROPN
ejpam-6270	591	4	,	,	PUNCT
ejpam-6270	591	5	4:645–658	4:645–658	PROPN
ejpam-6270	591	6	,	,	PUNCT
ejpam-6270	591	7	2008	2008	NUM
ejpam-6270	591	8	.	.	PUNCT