id	sid	eid	entity	type
cana-1749	1	1	1074	CARDINAL
cana-1749	1	2	32	CARDINAL
cana-1749	1	3	2	CARDINAL
cana-1749	1	4	375	CARDINAL
cana-1749	1	5	karnatak university’s	ORG
cana-1749	1	6	karnatak science college	ORG
cana-1749	1	7	dharwad-580 001	FAC
cana-1749	1	8	karnataka state	GPE
cana-1749	1	9	india	GPE
cana-1749	2	1	02-08-2024	CARDINAL
cana-1749	2	2	11	CARDINAL
cana-1749	2	3	20-09-2024	CARDINAL
cana-1749	4	1	keywordsslight continuity	PERSON
cana-1749	4	2	gpr	ORG
cana-1749	5	1	1982,mashhour	CARDINAL
cana-1749	6	1	9	CARDINAL
cana-1749	7	1	8	CARDINAL
cana-1749	8	1	balasubramanian et al	PERSON
cana-1749	8	2	2011	DATE
cana-1749	8	3	gpr-continuity[2	ORG
cana-1749	8	4	precontinuity[2	ORG
cana-1749	9	1	j.b.	PERSON
cana-1749	10	1	15,16	CARDINAL
cana-1749	10	2	contra	ORG
cana-1749	11	1	gpr	ORG
cana-1749	12	1	contra	NORP
cana-1749	17	1	1.1	CARDINAL
cana-1749	22	1	1.2	CARDINAL
cana-1749	22	2	δ-closed[18	ORG
cana-1749	24	1	1.3	CARDINAL
cana-1749	25	1	⊆	CARDINAL
cana-1749	25	2	k ⊆ u	ORG
cana-1749	25	3	x.	GPE
cana-1749	25	4	1.4	CARDINAL
cana-1749	25	5	gpr-continuous[2	ORG
cana-1749	26	1	gpr	ORG
cana-1749	26	2	1074	CARDINAL
cana-1749	26	3	32	CARDINAL
cana-1749	26	4	2	CARDINAL
cana-1749	26	5	2025	DATE
cana-1749	27	1	376	CARDINAL
cana-1749	27	2	contra	ORG
cana-1749	27	3	15	CARDINAL
cana-1749	27	4	1.5	CARDINAL
cana-1749	28	1	x.	GPE
cana-1749	30	1	1.6[16	CARDINAL
cana-1749	30	2	x. 2	DATE
cana-1749	30	3	2.1	CARDINAL
cana-1749	32	1	2.2	CARDINAL
cana-1749	34	1	x. iii	PERSON
cana-1749	35	1	x.	GPE
cana-1749	35	2	2.3	CARDINAL
cana-1749	36	1	τ)→(y	PERSON
cana-1749	36	2	precontinuity contra	PERSON
cana-1749	36	3	↓ ↓	ORG
cana-1749	36	4	gpr-continuity	ORG
cana-1749	36	5	↑	ORG
cana-1749	37	1	2.3	CARDINAL
cana-1749	39	1		PERSON
cana-1749	40	1	τ)→(y	PERSON
cana-1749	40	2	f(a)=a	NORP
cana-1749	40	3	gpr	ORG
cana-1749	41	1	1074	CARDINAL
cana-1749	41	2	32	CARDINAL
cana-1749	41	3	2	CARDINAL
cana-1749	41	4	2025	DATE
cana-1749	41	5	377	CARDINAL
cana-1749	41	6	τ)→(y	PERSON
cana-1749	41	7	τ)→(y	PERSON
cana-1749	42	1	2.4	CARDINAL
cana-1749	44	1	m={x  r:x	PERSON
cana-1749	44	2	two	CARDINAL
cana-1749	45	1	σ	ORG
cana-1749	45	2	x∉q	PERSON
cana-1749	46	1	contra	NORP
cana-1749	46	2	r\{0}	GPE
cana-1749	47	1	2.5	CARDINAL
cana-1749	49	1	contra	NORP
cana-1749	50	1	2.6	CARDINAL
cana-1749	52	1	gpr	ORG
cana-1749	53	1	2.7	CARDINAL
cana-1749	54	1	f(n	ORG
cana-1749	54	2	x.	GPE
cana-1749	58	1	≠ 	PERSON
cana-1749	59	1	8	CARDINAL
cana-1749	59	2	2.8	CARDINAL
cana-1749	60	1	1074	CARDINAL
cana-1749	60	2	32	CARDINAL
cana-1749	60	3	2	CARDINAL
cana-1749	60	4	378	CARDINAL
cana-1749	61	1	f−1(clq	ORG
cana-1749	61	2	2.7	CARDINAL
cana-1749	61	3	∈	PRODUCT
cana-1749	62	1	p∈	ORG
cana-1749	63	1	up⊂ f-1	ORG
cana-1749	69	1	iii)→(iv)let	CARDINAL
cana-1749	76	1	x.	GPE
cana-1749	76	2	2.9	CARDINAL
cana-1749	76	3	two	CARDINAL
cana-1749	77	1	2.10	CARDINAL
cana-1749	77	2	d},z=={a	GPE
cana-1749	77	3		PERSON
cana-1749	77	4	ƞ=={z	PERSON
cana-1749	78	1	τ)→(y	PERSON
cana-1749	78	2	f(a)=a	NORP
cana-1749	78	3	g(a)=a	NORP
cana-1749	78	4	g(b)=b	GPE
cana-1749	78	5	g(d	PERSON
cana-1749	79	1	x→z	CARDINAL
cana-1749	82	1	x.	GPE
cana-1749	82	2	2.11	CARDINAL
cana-1749	82	3	two	CARDINAL
cana-1749	85	1	proof:(i	PERSON
cana-1749	85	2	z. then g-1(v	PERSON
cana-1749	86	1	contra δgpcontinuous	ORG
cana-1749	87	1	contra	NORP
cana-1749	89	1	1074	CARDINAL
cana-1749	89	2	32	CARDINAL
cana-1749	89	3	2	CARDINAL
cana-1749	89	4	2025	DATE
cana-1749	89	5	379	CARDINAL
cana-1749	89	6	2.12	CARDINAL
cana-1749	89	7	x→z	CARDINAL
cana-1749	90	1	x.	GPE
cana-1749	90	2	f(f-1(g-1(u)))= g-1(u	GPE
cana-1749	91	1	2.13	CARDINAL
cana-1749	94	1	f(pcl(m	ORG
cana-1749	95	1	pcl	PERSON
cana-1749	98	1	2.14	CARDINAL
cana-1749	98	2	x→x×y	DATE
cana-1749	98	3	g(x)=(x,f(x)	ORG
cana-1749	101	1	u)=	NORP
cana-1749	103	1	2.15	CARDINAL
cana-1749	103	2	5	CARDINAL
cana-1749	105	1	∉	ORG
cana-1749	105	2	⊂	GPE
cana-1749	105	3	x∈ m.	PERSON
cana-1749	106	1	two	CARDINAL
cana-1749	107	1	2.16	CARDINAL
cana-1749	111	1	1074	CARDINAL
cana-1749	111	2	32	CARDINAL
cana-1749	111	3	2	CARDINAL
cana-1749	111	4	380	CARDINAL
cana-1749	113	1	2.17	CARDINAL
cana-1749	114	1	x1 ≠ x2	PERSON
cana-1749	115	1		ORG
cana-1749	115	2	δgpo	PERSON
cana-1749	115	3	1	CARDINAL
cana-1749	115	4	2	DATE
cana-1749	116	1	2.18	CARDINAL
cana-1749	118	1	∈	ORG
cana-1749	118	2	x.	GPE
cana-1749	118	3	≠ g(p	PERSON
cana-1749	122	1	x.	GPE
cana-1749	122	2	2.19	CARDINAL
cana-1749	124	1	y ∉	PERSON
cana-1749	124	2	y=f(x).since f	PERSON
cana-1749	126	1	∉ n.	PERSON
cana-1749	126	2	o	DATE
cana-1749	126	3	n⊂ u	ORG
cana-1749	127	1	f(n)⊂ f(u	PERSON
cana-1749	127	2	f(u	GPE
cana-1749	128	1	2.20	CARDINAL
cana-1749	130	1	x.	GPE
cana-1749	131	1	f⊂ f(v	PERSON
cana-1749	131	2	f(u	PERSON
cana-1749	132	1	2.21	CARDINAL
cana-1749	134	1	 	PERSON
cana-1749	135	1	1074	CARDINAL
cana-1749	135	2	32	CARDINAL
cana-1749	135	3	2	CARDINAL
cana-1749	135	4	381	CARDINAL
cana-1749	135	5	 	PERSON
cana-1749	136	1	i0	ORG
cana-1749	136	2	{f-1	PERSON
cana-1749	137	1	 	PERSON
cana-1749	139	1	2.22	CARDINAL
cana-1749	142	1	two	CARDINAL
cana-1749	143	1	2.23	CARDINAL
cana-1749	143	2	g(f	GPE
cana-1749	143	3	f:(x	ORG
cana-1749	143	4	σ	ORG
cana-1749	143	5	2.24	CARDINAL
cana-1749	143	6	g(f	GPE
cana-1749	143	7	f:(x	ORG
cana-1749	143	8	σ	ORG
cana-1749	144	1	2.25	CARDINAL
cana-1749	144	2	f:(x	ORG
cana-1749	144	3	σ	ORG
cana-1749	144	4	g(f	GPE
cana-1749	145	1	f(x	ORG
cana-1749	145	2	f(x)∈u	GPE
cana-1749	145	3	y∈v	DATE
cana-1749	145	4	g(f	GPE
cana-1749	146	1	2.26	CARDINAL
cana-1749	146	2	f:(x	ORG
cana-1749	146	3	σ	ORG
cana-1749	146	4	g(f	GPE
cana-1749	147	1	f(x	ORG
cana-1749	147	2	o	DATE
cana-1749	147	3	f(x)∈	ORG
cana-1749	148	1	g(f	GPE
cana-1749	150	1	1	CARDINAL
cana-1749	150	2	acta mathematica hungarica	PERSON
cana-1749	150	3	52,2002	CARDINAL
cana-1749	151	1	2	CARDINAL
cana-1749	151	2	s.balasubramanian	NORP
cana-1749	151	3	m. lakshmi sarada	PERSON
cana-1749	151	4	gpr	ORG
cana-1749	151	5	scientia magna	ORG
cana-1749	152	1	4652,2011	CARDINAL
cana-1749	153	1	3	CARDINAL
cana-1749	153	2	contemporary mathematical sciences	ORG
cana-1749	153	3	292,2016	CARDINAL
cana-1749	154	1	1074	CARDINAL
cana-1749	154	2	32	CARDINAL
cana-1749	154	3	2	CARDINAL
cana-1749	154	4	382	CARDINAL
cana-1749	155	1	4	CARDINAL
cana-1749	155	2	n.el-deeb	PERSON
cana-1749	155	3	mathematique de la societe des sciences mathematiques de roumanie	ORG
cana-1749	156	1	5	CARDINAL
cana-1749	156	2	de mathematica	PERSON
cana-1749	156	3	vol.9 pp.21-31,2005	PERSON
cana-1749	157	1	6	CARDINAL
cana-1749	157	2	indian	NORP
cana-1749	158	1	7	CARDINAL
cana-1749	158	2	8	CARDINAL
cana-1749	159	1	8	CARDINAL
cana-1749	159	2	r. c. jain	PERSON
cana-1749	159	3	d.	NORP
cana-1749	159	4	meerut university	ORG
cana-1749	159	5	meerut	GPE
cana-1749	159	6	india	GPE
cana-1749	159	7	1980	DATE
cana-1749	159	8	9	CARDINAL
cana-1749	159	9	j. umehara	PERSON
cana-1749	160	1	science kochi university series	ORG
cana-1749	160	2	pp.33-42,1996	PRODUCT
cana-1749	161	1	10	CARDINAL
cana-1749	161	2	a. s. mashhour	PERSON
cana-1749	161	3	m. e. abd	PERSON
cana-1749	162	1	s. n. el-deeb	PERSON
cana-1749	162	2	egypt	GPE
cana-1749	163	1	11	CARDINAL
cana-1749	163	2	annales academiae scientiarum	ORG
cana-1749	164	1	i. mathematica	PERSON
cana-1749	164	2	vol.3	ORG
cana-1749	165	1	185-205,1977	DATE
cana-1749	166	1	12	CARDINAL
cana-1749	166	2	pacific journal	ORG
cana-1749	167	1	169-185,1974	TIME
cana-1749	168	1	13	CARDINAL
cana-1749	168	2	american	NORP
cana-1749	169	1	14	CARDINAL
cana-1749	169	2	kyungpook mathematical journal	ORG
cana-1749	169	3	87	CARDINAL
cana-1749	170	1	15	CARDINAL
cana-1749	171	1	16	CARDINAL
cana-1749	171	2	contra delta generalized	ORG
cana-1749	171	3	pp.283288, 2018	ORG
cana-1749	172	1	17	CARDINAL
cana-1749	172	2	the aligarh bulletin	ORG
cana-1749	173	1	18	CARDINAL
cana-1749	173	2	n.v.veliko	ORG
cana-1749	173	3	american mathematical society translations	ORG