id	sid	eid	entity	type
ejpam-2826	1	1	european journal	ORG
ejpam-2826	2	1	10	CARDINAL
ejpam-2826	2	2	2	CARDINAL
ejpam-2826	2	3	2017	DATE
ejpam-2826	2	4	312	CARDINAL
ejpam-2826	2	5	new york	GPE
ejpam-2826	3	1	s.s.benchalli1	GPE
ejpam-2826	3	2	2,∗	CARDINAL
ejpam-2826	3	3	j.b.toranagatti3	DATE
ejpam-2826	3	4	1,2	CARDINAL
ejpam-2826	3	5	karnatak university	ORG
ejpam-2826	3	6	dharwad	GPE
ejpam-2826	3	7	india	GPE
ejpam-2826	3	8	3	CARDINAL
ejpam-2826	3	9	karnatak university’s	ORG
ejpam-2826	3	10	karnatak college	ORG
ejpam-2826	3	11	dharwad	GPE
ejpam-2826	3	12	india	GPE
ejpam-2826	3	13	4	CARDINAL
ejpam-2826	3	14	dharwad	GPE
ejpam-2826	3	15	india	GPE
ejpam-2826	4	1	contra	ORG
ejpam-2826	4	2	contra	NORP
ejpam-2826	5	1	2010	DATE
ejpam-2826	5	2	54c08	CARDINAL
ejpam-2826	5	3	54c10	CARDINAL
ejpam-2826	5	4	contra	ORG
ejpam-2826	6	1	1	CARDINAL
ejpam-2826	6	2	1996	DATE
ejpam-2826	6	3	contra	NORP
ejpam-2826	7	1	nasef	LANGUAGE
ejpam-2826	8	1	10	CARDINAL
ejpam-2826	8	2	contra	ORG
ejpam-2826	8	3	contra	NORP
ejpam-2826	9	1	functions.these	NORP
ejpam-2826	9	2	contra	ORG
ejpam-2826	10	1	η)(or	ORG
ejpam-2826	11	1	cl(a	NORP
ejpam-2826	11	2	int(a	GPE
ejpam-2826	11	3	ac	ORG
ejpam-2826	12	1	1	CARDINAL
ejpam-2826	13	1	9	CARDINAL
ejpam-2826	13	2	2	CARDINAL
ejpam-2826	13	3	14	CARDINAL
ejpam-2826	14	1	17	CARDINAL
ejpam-2826	14	2	6	CARDINAL
ejpam-2826	15	1	benchalliss@gmail.com(s.s.benchalli),pgpatil01@gmail.com(p.g.patil	WORK_OF_ART
ejpam-2826	16	1	312	CARDINAL
ejpam-2826	16	2	2017	CARDINAL
ejpam-2826	17	1	s.s.benchalli	PERSON
ejpam-2826	18	1	j. pure	PERSON
ejpam-2826	18	2	10	CARDINAL
ejpam-2826	18	3	2	CARDINAL
ejpam-2826	18	4	2017	CARDINAL
ejpam-2826	18	5	312	CARDINAL
ejpam-2826	19	1	4	CARDINAL
ejpam-2826	19	2	a⊆g	PERSON
ejpam-2826	19	3	x.	GPE
ejpam-2826	21	1	2	CARDINAL
ejpam-2826	22	1	contra	NORP
ejpam-2826	22	2	6	CARDINAL
ejpam-2826	22	3	contra	ORG
ejpam-2826	23	1	10	CARDINAL
ejpam-2826	23	2	contra	ORG
ejpam-2826	23	3	13	CARDINAL
ejpam-2826	23	4	rgb	ORG
ejpam-2826	23	5	5	CARDINAL
ejpam-2826	23	6	3	CARDINAL
ejpam-2826	23	7	12	CARDINAL
ejpam-2826	23	8	δ∗-continuous	GPE
ejpam-2826	23	9	contra	ORG
ejpam-2826	23	10	1	CARDINAL
ejpam-2826	23	11	7]if	CARDINAL
ejpam-2826	24	1	3	CARDINAL
ejpam-2826	25	1	5	CARDINAL
ejpam-2826	26	1	1 2	CARDINAL
ejpam-2826	27	1	2	CARDINAL
ejpam-2826	27	2	contra	NORP
ejpam-2826	28	1	4	CARDINAL
ejpam-2826	29	1	contra	NORP
ejpam-2826	29	2	contra	NORP
ejpam-2826	29	3	1	CARDINAL
ejpam-2826	30	1	contra	NORP
ejpam-2826	30	2	contra	NORP
ejpam-2826	32	1	2	CARDINAL
ejpam-2826	33	1	contra	NORP
ejpam-2826	33	2	contra	NORP
ejpam-2826	34	1	contra	NORP
ejpam-2826	34	2	contra	NORP
ejpam-2826	34	3	1	CARDINAL
ejpam-2826	34	4	1	CARDINAL
ejpam-2826	35	1	1	CARDINAL
ejpam-2826	35	2	2	CARDINAL
ejpam-2826	36	1	s.s.benchalli	PERSON
ejpam-2826	37	1	j. pure	PERSON
ejpam-2826	37	2	10	CARDINAL
ejpam-2826	37	3	2	CARDINAL
ejpam-2826	37	4	2017	CARDINAL
ejpam-2826	37	5	312	CARDINAL
ejpam-2826	37	6	314	CARDINAL
ejpam-2826	39	1	τ={x	ORG
ejpam-2826	40	1	contra	NORP
ejpam-2826	40	2	contra	NORP
ejpam-2826	40	3	contra	NORP
ejpam-2826	40	4	x.	GPE
ejpam-2826	40	5	3	CARDINAL
ejpam-2826	41	1	contra	NORP
ejpam-2826	41	2	contra	NORP
ejpam-2826	41	3	rgb	ORG
ejpam-2826	42	1	rgb	ORG
ejpam-2826	43	1	2	CARDINAL
ejpam-2826	44	1	3	CARDINAL
ejpam-2826	46	1	2	CARDINAL
ejpam-2826	47	1	τ={x	ORG
ejpam-2826	48	1	f(a)=a	NORP
ejpam-2826	48	2	f(b	GPE
ejpam-2826	48	3	f(c)=c	PERSON
ejpam-2826	49	1	contra	NORP
ejpam-2826	49	2	rgb	ORG
ejpam-2826	49	3	contra	NORP
ejpam-2826	50	1	4	CARDINAL
ejpam-2826	52	1	contra	NORP
ejpam-2826	52	2	contra	NORP
ejpam-2826	53	1	1 2 -space	DATE
ejpam-2826	53	2	contra	NORP
ejpam-2826	53	3	contra	NORP
ejpam-2826	54	1	proof:(i	PERSON
ejpam-2826	54	2	contra	NORP
ejpam-2826	55	1	contra	NORP
ejpam-2826	56	1	converse	PERSON
ejpam-2826	57	1	ii)suppose x	PERSON
ejpam-2826	57	2	1 2	DATE
ejpam-2826	57	3	contra	NORP
ejpam-2826	59	1	contra	NORP
ejpam-2826	60	1	converse	PERSON
ejpam-2826	60	2	2	CARDINAL
ejpam-2826	60	3	5	CARDINAL
ejpam-2826	61	1	5	CARDINAL
ejpam-2826	62	1	6=	CARDINAL
ejpam-2826	62	2	1	CARDINAL
ejpam-2826	63	1	8	CARDINAL
ejpam-2826	63	2	x∈ker(a	DATE
ejpam-2826	64	1	x.	GPE
ejpam-2826	64	2	ker(a)⊆ker(b	GPE
ejpam-2826	65	1	6	CARDINAL
ejpam-2826	65	2	contra	NORP
ejpam-2826	66	1	j. pure	PERSON
ejpam-2826	66	2	10	CARDINAL
ejpam-2826	66	3	2	CARDINAL
ejpam-2826	66	4	2017	CARDINAL
ejpam-2826	66	5	312	CARDINAL
ejpam-2826	68	1	f(a)⊆b	LANGUAGE
ejpam-2826	68	2	f−1(g)⊆h	CARDINAL
ejpam-2826	72	1	gx	ORG
ejpam-2826	74	1	x.	GPE
ejpam-2826	77	1	f⊆f−1(y	ORG
ejpam-2826	78	1	f−1(g)⊆x-f.	DATE
ejpam-2826	81	1	f(u)⊆f	GPE
ejpam-2826	82	1	x.	ORG
ejpam-2826	82	2	y /∈ ker(f(a	PERSON
ejpam-2826	83	1	1	CARDINAL
ejpam-2826	86	1	f−1(b)⊆x	ORG
ejpam-2826	87	1	δgbcl(f−1(b)))⊆ ker(f	ORG
ejpam-2826	89	1	1	CARDINAL
ejpam-2826	91	1	2	CARDINAL
ejpam-2826	92	1	16	CARDINAL
ejpam-2826	93	1	7	CARDINAL
ejpam-2826	94	1	4]if	CARDINAL
ejpam-2826	94	2	a⊆x	ORG
ejpam-2826	95	1	8	CARDINAL
ejpam-2826	96	1	a⊆x	ORG
ejpam-2826	97	1	3	CARDINAL
ejpam-2826	98	1	s.s.benchalli	GPE
ejpam-2826	99	1	j. pure	PERSON
ejpam-2826	99	2	10	CARDINAL
ejpam-2826	99	3	2	CARDINAL
ejpam-2826	99	4	2017	CARDINAL
ejpam-2826	99	5	312	CARDINAL
ejpam-2826	100	1	7	CARDINAL
ejpam-2826	100	2	bcl(a)⊆a	DATE
ejpam-2826	101	1	a⊆int(cl(a)).hence	ORG
ejpam-2826	102	1	ii)→(i	NORP
ejpam-2826	102	2	8	CARDINAL
ejpam-2826	103	1	8	CARDINAL
ejpam-2826	103	2	bcl(a)⊆a	DATE
ejpam-2826	105	1	lemma	ORG
ejpam-2826	105	2	9	CARDINAL
ejpam-2826	106	1	contra	NORP
ejpam-2826	106	2	δ∗-continuous	GPE
ejpam-2826	106	3	contra	NORP
ejpam-2826	107	1	5	CARDINAL
ejpam-2826	108	1	16	CARDINAL
ejpam-2826	109	1	6	CARDINAL
ejpam-2826	110	1	16	CARDINAL
ejpam-2826	110	2	10	CARDINAL
ejpam-2826	112	1	11	CARDINAL
ejpam-2826	114	1	10	CARDINAL
ejpam-2826	115	1	q-set.again	GPE
ejpam-2826	115	2	10	CARDINAL
ejpam-2826	118	1	7	CARDINAL
ejpam-2826	119	1	3	CARDINAL
ejpam-2826	121	1	10	CARDINAL
ejpam-2826	122	1	s.s.benchalli	PERSON
ejpam-2826	123	1	j. pure	PERSON
ejpam-2826	123	2	10	CARDINAL
ejpam-2826	123	3	2	CARDINAL
ejpam-2826	123	4	2017	CARDINAL
ejpam-2826	123	5	312	CARDINAL
ejpam-2826	123	6	317	CARDINAL
ejpam-2826	123	7	12	CARDINAL
ejpam-2826	124	1	δ∗-continuous	GPE
ejpam-2826	124	2	contra	NORP
ejpam-2826	124	3	contra	NORP
ejpam-2826	125	1	7	CARDINAL
ejpam-2826	126	1	x.	GPE
ejpam-2826	126	2	13	CARDINAL
ejpam-2826	127	1	contra	NORP
ejpam-2826	128	1	f	PERSON
ejpam-2826	128	2	contra	NORP
ejpam-2826	128	3	x.	GPE
ejpam-2826	128	4	8	CARDINAL
ejpam-2826	129	1	11	CARDINAL
ejpam-2826	129	2	x.	GPE
ejpam-2826	129	3	14	DATE
ejpam-2826	130	1	contra	NORP
ejpam-2826	131	1	contra	NORP
ejpam-2826	131	2	x.	GPE
ejpam-2826	131	3	cl(v)=cl(int(v))⊆v	PERSON
ejpam-2826	133	1	15	CARDINAL
ejpam-2826	135	1	contra	NORP
ejpam-2826	139	1	contra	NORP
ejpam-2826	142	1	f(x	ORG
ejpam-2826	142	2	x∈x}⊆x×y	PRODUCT
ejpam-2826	142	3	g(f	ORG
ejpam-2826	143	1	9	CARDINAL
ejpam-2826	144	1	g(f	GPE
ejpam-2826	144	2	contra	NORP
ejpam-2826	144	3	u×v)∩g(f)=φ	ORG
ejpam-2826	145	1	16	CARDINAL
ejpam-2826	146	1	g(f	GPE
ejpam-2826	146	2	contra	NORP
ejpam-2826	146	3	f(u)∩v	ORG
ejpam-2826	147	1	17	CARDINAL
ejpam-2826	148	1	contra	NORP
ejpam-2826	148	2	g(f	GPE
ejpam-2826	148	3	contra	NORP
ejpam-2826	149	1	6	CARDINAL
ejpam-2826	149	2	f(x)∈a	CARDINAL
ejpam-2826	150	1	contra	NORP
ejpam-2826	150	2	f(u)⊆cl(a	ORG
ejpam-2826	152	1	g(f	GPE
ejpam-2826	152	2	contra	NORP
ejpam-2826	153	1	s.s.benchalli	PERSON
ejpam-2826	154	1	j. pure	PERSON
ejpam-2826	154	2	10	CARDINAL
ejpam-2826	154	3	2	CARDINAL
ejpam-2826	154	4	2017	CARDINAL
ejpam-2826	154	5	312	CARDINAL
ejpam-2826	154	6	322 318	CARDINAL
ejpam-2826	154	7	18	CARDINAL
ejpam-2826	155	1	g(f	GPE
ejpam-2826	155	2	contra	NORP
ejpam-2826	155	3	x×y	PRODUCT
ejpam-2826	156	1	6	CARDINAL
ejpam-2826	156	2	f(x)∈u	GPE
ejpam-2826	157	1	g(f	GPE
ejpam-2826	157	2	contra	NORP
ejpam-2826	158	1	19	CARDINAL
ejpam-2826	159	1	x→x×y	DATE
ejpam-2826	159	2	g(x)=(x,f(x)	ORG
ejpam-2826	160	1	contra	NORP
ejpam-2826	160	2	contra	NORP
ejpam-2826	161	1	x×u	ORG
ejpam-2826	162	1	contra	NORP
ejpam-2826	163	1	x.	GPE
ejpam-2826	164	1	contra	NORP
ejpam-2826	165	1	20	CARDINAL
ejpam-2826	166	1	contra	NORP
ejpam-2826	166	2	f(u)⊆v	GPE
ejpam-2826	167	1	f(x)∈v	ORG
ejpam-2826	167	2	x∈f−1(v	NORP
ejpam-2826	168	1	contra	NORP
ejpam-2826	168	2	x.	GPE
ejpam-2826	170	1	10	CARDINAL
ejpam-2826	171	1	16	CARDINAL
ejpam-2826	172	1	21	DATE
ejpam-2826	173	1	a∪b	PRODUCT
ejpam-2826	173	2	x.	GPE
ejpam-2826	173	3	x.	GPE
ejpam-2826	173	4	a⊆g	GPE
ejpam-2826	173	5	b⊆g	GPE
ejpam-2826	173	6	bcl(b)⊆g	ORG
ejpam-2826	174	1	bcl(m)=cl(m	ORG
ejpam-2826	174	2	m⊆x.therefore	PRODUCT
ejpam-2826	175	1	1	CARDINAL
ejpam-2826	176	1	x.	GPE
ejpam-2826	176	2	22	CARDINAL
ejpam-2826	177	1	23	CARDINAL
ejpam-2826	178	1	contra	NORP
ejpam-2826	178	2	k={x∈x	LAW
ejpam-2826	178	3	x.	GPE
ejpam-2826	178	4	6	CARDINAL
ejpam-2826	178	5	f(x)∈u	GPE
ejpam-2826	178	6	g(x)∈v	ORG
ejpam-2826	179	1	contra	NORP
ejpam-2826	179	2	x.	GPE
ejpam-2826	183	1	5	CARDINAL
ejpam-2826	184	1	x.	GPE
ejpam-2826	184	2	11	DATE
ejpam-2826	185	1	two	CARDINAL
ejpam-2826	186	1	24	CARDINAL
ejpam-2826	187	1	contra	NORP
ejpam-2826	188	1	s.s.benchalli	PERSON
ejpam-2826	189	1	j. pure	PERSON
ejpam-2826	189	2	10	CARDINAL
ejpam-2826	189	3	2	CARDINAL
ejpam-2826	189	4	2017	CARDINAL
ejpam-2826	189	5	312	CARDINAL
ejpam-2826	189	6	contra	NORP
ejpam-2826	193	1	25	CARDINAL
ejpam-2826	194	1	contra	NORP
ejpam-2826	195	1	contra	NORP
ejpam-2826	198	1	contra	NORP
ejpam-2826	198	2	x.	GPE
ejpam-2826	201	1	26	CARDINAL
ejpam-2826	203	1	contra	NORP
ejpam-2826	204	1	two	CARDINAL
ejpam-2826	207	1	12	CARDINAL
ejpam-2826	208	1	4	CARDINAL
ejpam-2826	209	1	27	CARDINAL
ejpam-2826	211	1	contra	NORP
ejpam-2826	212	1	f(x	ORG
ejpam-2826	212	2	6	CARDINAL
ejpam-2826	213	1	6	CARDINAL
ejpam-2826	213	2	w	ORG
ejpam-2826	214	1	contra	NORP
ejpam-2826	215	1	a∩b⊆f−1(cl(v))∩f−1(cl(w))=f−1(φ)=φ	ORG
ejpam-2826	217	1	2	CARDINAL
ejpam-2826	218	1	contra	NORP
ejpam-2826	220	1	13	CARDINAL
ejpam-2826	221	1	14	CARDINAL
ejpam-2826	222	1	s.s.benchalli	PERSON
ejpam-2826	223	1	j. pure	PERSON
ejpam-2826	223	2	10	CARDINAL
ejpam-2826	223	3	2	CARDINAL
ejpam-2826	223	4	2017	CARDINAL
ejpam-2826	223	5	312	CARDINAL
ejpam-2826	223	6	322 320	CARDINAL
ejpam-2826	223	7	28	CARDINAL
ejpam-2826	224	1	contra	NORP
ejpam-2826	225	1	two	CARDINAL
ejpam-2826	226	1	f(x	PRODUCT
ejpam-2826	226	2	6	CARDINAL
ejpam-2826	229	1	14	DATE
ejpam-2826	230	1	14	CARDINAL
ejpam-2826	231	1	15	CARDINAL
ejpam-2826	232	1	4	CARDINAL
ejpam-2826	233	1	29	CARDINAL
ejpam-2826	234	1	contra	NORP
ejpam-2826	235	1	x.	ORG
ejpam-2826	235	2	f(f	ORG
ejpam-2826	235	3	f(e)⊆u	DATE
ejpam-2826	235	4	f(f)⊆v	GPE
ejpam-2826	236	1	f⊆f−1(v	ORG
ejpam-2826	237	1	contra	NORP
ejpam-2826	239	1	3	CARDINAL
ejpam-2826	240	1	two	CARDINAL
ejpam-2826	240	2	contra	NORP
ejpam-2826	242	1	3	CARDINAL
ejpam-2826	243	1	τ={x	ORG
ejpam-2826	243	2	φ,{a},{b},{a	GPE
ejpam-2826	243	3	g(b)=c	PERSON
ejpam-2826	243	4	g(c)=a	PERSON
ejpam-2826	243	5	contra	NORP
ejpam-2826	243	6	x→z	CARDINAL
ejpam-2826	243	7	contra	NORP
ejpam-2826	243	8	x.	GPE
ejpam-2826	243	9	30	DATE
ejpam-2826	244	1	two	CARDINAL
ejpam-2826	245	1	contra	NORP
ejpam-2826	245	2	contra	NORP
ejpam-2826	246	1	contra	NORP
ejpam-2826	246	2	contra	NORP
ejpam-2826	247	1	contra	NORP
ejpam-2826	247	2	contra	NORP
ejpam-2826	248	1	contra	NORP
ejpam-2826	248	2	contra	NORP
ejpam-2826	248	3	proof:(i	PERSON
ejpam-2826	248	4	z.	PERSON
ejpam-2826	248	5	contra	NORP
ejpam-2826	249	1	contra	NORP
ejpam-2826	251	1	31	CARDINAL
ejpam-2826	252	1	contra	NORP
ejpam-2826	253	1	x→z	CARDINAL
ejpam-2826	253	2	contra	NORP
ejpam-2826	255	1	contra	NORP
ejpam-2826	255	2	f−1(g−1(v	PERSON
ejpam-2826	256	1	x.	GPE
ejpam-2826	256	2	contra	NORP
ejpam-2826	257	1	321	CARDINAL
ejpam-2826	257	2	the university grants commission	ORG
ejpam-2826	257	3	new delhi	GPE
ejpam-2826	257	4	india	GPE
ejpam-2826	257	5	ugc sap drs-iii	ORG
ejpam-2826	257	6	29th feb 2016	DATE
ejpam-2826	257	7	karnatak university	ORG
ejpam-2826	257	8	dharwad	GPE
ejpam-2826	257	9	india	GPE
ejpam-2826	258	1	1	CARDINAL
ejpam-2826	258	2	26(2008),53-64	DATE
ejpam-2826	259	1	2	CARDINAL
ejpam-2826	259	2	mat.vesnic	ORG
ejpam-2826	259	3	59	CARDINAL
ejpam-2826	260	1	3	CARDINAL
ejpam-2826	260	2	14(1974),131	CARDINAL
ejpam-2826	261	1	4	CARDINAL
ejpam-2826	261	2	j	PERSON
ejpam-2826	261	3	s.r.vighneshi	ORG
ejpam-2826	261	4	23(2016),1117-1131	DATE
ejpam-2826	262	1	5	CARDINAL
ejpam-2826	262	2	440	CARDINAL
ejpam-2826	263	1	6	CARDINAL
ejpam-2826	263	2	contra	NORP
ejpam-2826	263	3	310	CARDINAL
ejpam-2826	264	1	7	CARDINAL
ejpam-2826	264	2	n.el-deeb	PERSON
ejpam-2826	265	1	soc.sci.math.r.s.roumanie	GPE
ejpam-2826	265	2	27(1983),311	CARDINAL
ejpam-2826	266	1	8	CARDINAL
ejpam-2826	266	2	contra	NORP
ejpam-2826	268	1	budapest	GPE
ejpam-2826	270	1	34	CARDINAL
ejpam-2826	271	1	9	CARDINAL
ejpam-2826	271	2	s. n. el-deeb	PERSON
ejpam-2826	271	3	egypt,53(1982),47-53	DATE
ejpam-2826	272	1	10	CARDINAL
ejpam-2826	272	2	contra	NORP
ejpam-2826	272	3	24(2005),471	CARDINAL
ejpam-2826	273	1	11	CARDINAL
ejpam-2826	274	1	205	CARDINAL
ejpam-2826	275	1	12	CARDINAL
ejpam-2826	275	2	indian	NORP
ejpam-2826	276	1	13	CARDINAL
ejpam-2826	276	2	contra	NORP
ejpam-2826	276	3	97(2014),161	CARDINAL
ejpam-2826	277	1	322	CARDINAL
ejpam-2826	278	1	14	CARDINAL
ejpam-2826	278	2	non-archimedean	NORP
ejpam-2826	278	3	185	CARDINAL
ejpam-2826	279	1	15	CARDINAL
ejpam-2826	279	2	381	CARDINAL
ejpam-2826	280	1	16	CARDINAL
ejpam-2826	280	2	contra	NORP
ejpam-2826	280	3	communication,4(2016),260-269	PRODUCT
ejpam-2826	281	1	17	CARDINAL
ejpam-2826	281	2	n.v.veliko	ORG
ejpam-2826	281	3	118	CARDINAL