id	sid	eid	entity	type
cana-4781	1	1	1074	CARDINAL
cana-4781	1	2	32	CARDINAL
cana-4781	1	3	3 (	CARDINAL
cana-4781	1	4	879	CARDINAL
cana-4781	2	1	1	CARDINAL
cana-4781	2	2	r. selvi	PERSON
cana-4781	3	1	2	CARDINAL
cana-4781	3	2	1	CARDINAL
cana-4781	4	1	22211202092003	DATE
cana-4781	4	2	627802	DATE
cana-4781	4	3	manonmaniam sundaranar university	ORG
cana-4781	4	4	627012	DATE
cana-4781	6	1	2	CARDINAL
cana-4781	6	2	627802	DATE
cana-4781	6	3	manonmaniam sundaranar university	ORG
cana-4781	6	4	627012	DATE
cana-4781	7	1	12-01-2025	CARDINAL
cana-4781	7	2	15-02-2025	CARDINAL
cana-4781	7	3	01-03-2025	CARDINAL
cana-4781	12	1	2020	DATE
cana-4781	12	2	20e32	CARDINAL
cana-4781	12	3	22c05	CARDINAL
cana-4781	12	4	22d05	CARDINAL
cana-4781	13	1	14	CARDINAL
cana-4781	13	2	1982	DATE
cana-4781	14	1	more than 30 years	DATE
cana-4781	15	1	1994	DATE
cana-4781	15	2	biswas	ORG
cana-4781	15	3	3	CARDINAL
cana-4781	17	1	2016	CARDINAL
cana-4781	18	1	13	CARDINAL
cana-4781	23	1	2	CARDINAL
cana-4781	23	2	2.1	CARDINAL
cana-4781	24	1	4	CARDINAL
cana-4781	25	1	mailto:tamilarasiparamasivan@gmail.com	ORG
cana-4781	25	2	1074	CARDINAL
cana-4781	25	3	32	CARDINAL
cana-4781	25	4	3 (	CARDINAL
cana-4781	25	5	880	CARDINAL
cana-4781	25	6	g̅	GPE
cana-4781	26	1	x∗e	DATE
cana-4781	26	2	e∗x	GPE
cana-4781	27	1	∈	ORG
cana-4781	27	2	∃ y ∈	PERSON
cana-4781	27	3	2.2	CARDINAL
cana-4781	28	1	4	CARDINAL
cana-4781	30	1	∈	ORG
cana-4781	30	2	x-1 ∈	ORG
cana-4781	30	3	2.3	CARDINAL
cana-4781	31	1	13	CARDINAL
cana-4781	31	2	two	CARDINAL
cana-4781	33	1	f(x	ORG
cana-4781	35	1	= x-1	PERSON
cana-4781	35	2	2.4	CARDINAL
cana-4781	36	1	4	CARDINAL
cana-4781	36	2	𝑅1	GPE
cana-4781	36	3	𝑅2	DATE
cana-4781	36	4	two	CARDINAL
cana-4781	36	5	∗	CARDINAL
cana-4781	37	1	𝑈1	PRODUCT
cana-4781	37	2	𝐺2 ⊂ 𝑈2	ORG
cana-4781	38	1	𝐺1	CARDINAL
cana-4781	38	2	𝐺2	CARDINAL
cana-4781	38	3	𝐺1	CARDINAL
cana-4781	38	4	𝐺1	MONEY
cana-4781	38	5	𝜑(𝑥 ∗ 𝑦	ORG
cana-4781	38	6	𝜑(𝑦	PERSON
cana-4781	39	1	𝐺1	CARDINAL
cana-4781	39	2	𝐺2	CARDINAL
cana-4781	40	1	2.5	CARDINAL
cana-4781	41	1	1	CARDINAL
cana-4781	41	2	𝐺1	CARDINAL
cana-4781	41	3	𝐺2 ̅̅	ORG
cana-4781	41	4	𝐺2	CARDINAL
cana-4781	41	5	𝐺1	CARDINAL
cana-4781	41	6	𝐺1	CARDINAL
cana-4781	42	1	2.6	CARDINAL
cana-4781	43	1	1	CARDINAL
cana-4781	43	2	𝐺1	CARDINAL
cana-4781	43	3	1𝐺1	CARDINAL
cana-4781	44	1	2.7	CARDINAL
cana-4781	45	1	1	CARDINAL
cana-4781	45	2	𝐺1	CARDINAL
cana-4781	45	3	𝐺2	CARDINAL
cana-4781	46	1	∶ φ(𝑔	PERSON
cana-4781	47	1	φ	PERSON
cana-4781	48	1	2.8	CARDINAL
cana-4781	49	1	12	CARDINAL
cana-4781	49	2	g̅	GPE
cana-4781	50	1	2.9	CARDINAL
cana-4781	51	1	16	CARDINAL
cana-4781	51	2	𝐺ℜ	ORG
cana-4781	52	1	𝐺ℜ	ORG
cana-4781	52	2	1074	CARDINAL
cana-4781	52	3	32	CARDINAL
cana-4781	52	4	3 (	CARDINAL
cana-4781	52	5	881	CARDINAL
cana-4781	52	6	2.10	CARDINAL
cana-4781	53	1	16	CARDINAL
cana-4781	53	2	𝐺ℜ	ORG
cana-4781	53	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	53	4	two	CARDINAL
cana-4781	53	5	𝐺ℜ × 𝐺ℜ	ORG
cana-4781	53	6	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	53	7	f(x	ORG
cana-4781	53	8	𝐺ℜ × 𝐺ℜ	ORG
cana-4781	54	1	= x-1	PERSON
cana-4781	54	2	𝐺ℜ	ORG
cana-4781	54	3	2.11	CARDINAL
cana-4781	55	1	16	CARDINAL
cana-4781	55	2	𝐺ℜ	ORG
cana-4781	56	1	u ⊆ 𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	56	2	𝐺ℜ	GPE
cana-4781	56	3	⊆	CARDINAL
cana-4781	56	4	2.12	CARDINAL
cana-4781	57	1	17	CARDINAL
cana-4781	57	2	𝐺ℜ	ORG
cana-4781	57	3	𝐺ℜ	ORG
cana-4781	57	4	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	57	5	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	58	1	𝐺ℜ	GPE
cana-4781	58	2	0	CARDINAL
cana-4781	59	1	2.13	CARDINAL
cana-4781	60	1	x.	GPE
cana-4781	60	2	x.	GPE
cana-4781	60	3	2.14	CARDINAL
cana-4781	61	1	5	CARDINAL
cana-4781	61	2	x.	GPE
cana-4781	61	3	2.15	CARDINAL
cana-4781	62	1	16	CARDINAL
cana-4781	62	2	𝐻ℜ	ORG
cana-4781	62	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	62	4	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	63	1	2.16	CARDINAL
cana-4781	64	1	16	CARDINAL
cana-4781	64	2	2.17	CARDINAL
cana-4781	65	1	5	CARDINAL
cana-4781	65	2	∈	ORG
cana-4781	65	3	⊆	CARDINAL
cana-4781	65	4	2.18	CARDINAL
cana-4781	66	1	5	CARDINAL
cana-4781	66	2	∈ 𝑌	ORG
cana-4781	66	3	𝑈 ⊂ 𝑋	ORG
cana-4781	66	4	𝑓−1(𝑉	CARDINAL
cana-4781	67	1	𝐺ℜ	ORG
cana-4781	67	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	67	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	67	4	3	CARDINAL
cana-4781	67	5	3.1	CARDINAL
cana-4781	68	1	𝐺ℜ	ORG
cana-4781	68	2	𝐺ℜ	ORG
cana-4781	68	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	68	4	𝐴	ORG
cana-4781	68	5	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	69	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	69	2	𝐴 ∩ 𝑀 = ∅	ORG
cana-4781	69	3	𝐺ℜ	GPE
cana-4781	69	4	𝐴𝑉	GPE
cana-4781	69	5	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	69	6	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	69	7	𝑎𝑈𝑎 ∩ 𝑀 = ∅	ORG
cana-4781	69	8	2.9	CARDINAL
cana-4781	69	9	𝐺ℜ	GPE
cana-4781	69	10	𝑉𝑎𝑉𝑎 ⊆ 𝑈𝑎.	ORG
cana-4781	69	11	𝐴	ORG
cana-4781	69	12	⋃ 𝑎𝑎∈𝐴	PERSON
cana-4781	69	13	𝐴 ⊆	ORG
cana-4781	70	1	𝑏 ∈ 𝐴	ORG
cana-4781	70	2	∈	ORG
cana-4781	70	3	⊆	CARDINAL
cana-4781	70	4	⊆	CARDINAL
cana-4781	70	5	𝑎𝑉𝑎𝑉𝑎	ORG
cana-4781	70	6	⊆	PRODUCT
cana-4781	70	7	𝑎𝑈𝑎	PRODUCT
cana-4781	70	8	𝐴𝑉	GPE
cana-4781	70	9	1074	CARDINAL
cana-4781	70	10	32	CARDINAL
cana-4781	70	11	3 (	CARDINAL
cana-4781	70	12	882	CARDINAL
cana-4781	70	13	3.2	CARDINAL
cana-4781	71	1	second	ORDINAL
cana-4781	71	2	𝐺ℜ	ORG
cana-4781	71	3	𝐺ℜ	ORG
cana-4781	71	4	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	72	1	𝐴	ORG
cana-4781	72	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	72	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	73	1	𝑀𝐴	ORG
cana-4781	73	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	74	1	𝐴	ORG
cana-4781	75	1	3.1	CARDINAL
cana-4781	75	2	𝐺ℜ	GPE
cana-4781	75	3	∩ 𝑀	PERSON
cana-4781	75	4	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	76	1	𝑀𝐴	ORG
cana-4781	76	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	77	1	3.3	CARDINAL
cana-4781	78	1	𝐺ℜ	ORG
cana-4781	78	2	𝐺ℜ	ORG
cana-4781	78	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	79	1	𝐴	ORG
cana-4781	79	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	80	1	⊆	CARDINAL
cana-4781	80	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	80	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	81	1	2.10	CARDINAL
cana-4781	81	2	𝐺ℜ	GPE
cana-4781	81	3	0	CARDINAL
cana-4781	82	1	𝐴	ORG
cana-4781	82	2	𝐴 ⊆ 𝑈𝑀	ORG
cana-4781	82	3	𝐴.	ORG
cana-4781	83	1	2.11	CARDINAL
cana-4781	83	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	84	1	⊆	CARDINAL
cana-4781	84	2	𝑈3 ⊆	MONEY
cana-4781	84	3	3.4	CARDINAL
cana-4781	85	1	𝐺ℜ	ORG
cana-4781	85	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	85	3	𝐻ℜ	ORG
cana-4781	85	4	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	86	1	𝐻ℜ	ORG
cana-4781	86	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	86	3	𝐻ℜ	ORG
cana-4781	86	4	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	88	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	89	1	𝐻ℜ	ORG
cana-4781	90	1	𝐻ℜ	ORG
cana-4781	90	2	⋃ 𝑎𝐻ℜ𝑎∉𝐻ℜ	PERSON
cana-4781	90	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	91	1	𝐻ℜ	ORG
cana-4781	91	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	92	1	3.5	CARDINAL
cana-4781	93	1	𝐺ℜ	ORG
cana-4781	93	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	93	3	𝐺ℜ	ORG
cana-4781	93	4	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	94	1	𝐴	ORG
cana-4781	94	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	94	3	𝐻ℜ	ORG
cana-4781	94	4	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	94	5	𝐻ℜ ⊆ 𝐴.	ORG
cana-4781	94	6	𝐴 ⊆	ORG
cana-4781	94	7	𝐺ℜ	GPE
cana-4781	94	8	𝑉𝑉	ORG
cana-4781	94	9	2.10	CARDINAL
cana-4781	94	10	0	CARDINAL
cana-4781	95	1	𝐻ℜ	ORG
cana-4781	95	2	⋃ 𝑉𝑛 𝑛∈ℕ−{0	PERSON
cana-4781	96	1	𝐻ℜ	ORG
cana-4781	96	2	𝐺ℜ	GPE
cana-4781	96	3	𝐻ℜ ⊆ 𝐴.	ORG
cana-4781	96	4	𝐺ℜ	ORG
cana-4781	96	5	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	96	6	𝐻ℜ	ORG
cana-4781	96	7	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	97	1	𝐻ℜ	ORG
cana-4781	97	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	98	1	𝑏 ∈ 𝑉𝑚	ORG
cana-4781	98	2	0	CARDINAL
cana-4781	99	1	𝐻ℜ	ORG
cana-4781	99	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	100	1	3.4	CARDINAL
cana-4781	100	2	𝐻ℜ	ORG
cana-4781	100	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	101	1	𝐻ℜ	ORG
cana-4781	101	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	102	1	3.6	CARDINAL
cana-4781	103	1	𝐺ℜ	ORG
cana-4781	103	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	103	3	𝐻ℜ	ORG
cana-4781	103	4	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	104	1	𝐻ℜ	ORG
cana-4781	104	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	105	1	𝐻ℜ	ORG
cana-4781	105	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	105	3	𝐻ℜ	ORG
cana-4781	105	4	𝐻ℜ	ORG
cana-4781	105	5	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	106	1	3.4	CARDINAL
cana-4781	106	2	𝐻ℜ	ORG
cana-4781	106	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	107	1	3.7	CARDINAL
cana-4781	108	1	𝐺ℜ	ORG
cana-4781	108	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	108	3	𝐻ℜ	ORG
cana-4781	108	4	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	109	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	109	2	𝐺ℜ ̅̅ ̅̅ 𝐻ℜ⁄	ORG
cana-4781	110	1	1074	CARDINAL
cana-4781	110	2	32	CARDINAL
cana-4781	110	3	3 (	CARDINAL
cana-4781	110	4	883	CARDINAL
cana-4781	110	5	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	111	1	second	ORDINAL
cana-4781	111	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	115	1	𝜑(𝑎	GPE
cana-4781	117	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	118	1	2.14	CARDINAL
cana-4781	119	1	3.8	CARDINAL
cana-4781	120	1	𝐺ℜ	ORG
cana-4781	120	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	121	1	𝐻ℜ	ORG
cana-4781	121	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	121	3	𝐻ℜ	ORG
cana-4781	123	1	𝐺ℜ	ORG
cana-4781	123	2	𝐴	ORG
cana-4781	123	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	123	4	∈	ORG
cana-4781	123	5	𝐺ℜ	ORG
cana-4781	123	6	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	123	7	𝐻ℜ	ORG
cana-4781	123	8	⋃	DATE
cana-4781	123	9	𝑖=1	GPE
cana-4781	123	10	𝐻ℜ	ORG
cana-4781	124	1	3.9	CARDINAL
cana-4781	125	1	𝐺ℜ	ORG
cana-4781	125	2	𝐻ℜ	ORG
cana-4781	125	3	𝐺ℜ	ORG
cana-4781	125	4	𝐻ℜ	ORG
cana-4781	125	5	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	125	6	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	126	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	126	2	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	127	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	127	2	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	127	3	𝜋	PRODUCT
cana-4781	128	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	128	2	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	128	3	𝜋	ORG
cana-4781	129	1	𝜋	ORG
cana-4781	129	2	𝜋	PRODUCT
cana-4781	130	1	⊆	CARDINAL
cana-4781	130	2	𝐻ℜ	ORG
cana-4781	130	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	131	1	𝜋	PERSON
cana-4781	132	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	134	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	134	2	𝒦𝜋	PERSON
cana-4781	134	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	135	1	𝜋	PERSON
cana-4781	136	1	𝜋	PRODUCT
cana-4781	137	1	3.10	CARDINAL
cana-4781	138	1	𝐺ℜ	ORG
cana-4781	138	2	𝐺ℜ	ORG
cana-4781	138	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	139	1	𝐴 ⊆ 𝐺ℜ	ORG
cana-4781	140	1	∩ 𝐺ℜ	PERSON
cana-4781	141	1	𝐺ℜ	ORG
cana-4781	141	2	𝐺ℜ	ORG
cana-4781	141	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	141	4	𝐺ℜ	GPE
cana-4781	141	5	⊆	CARDINAL
cana-4781	141	6	∩ 𝐺ℜ	PERSON
cana-4781	141	7	𝑖𝑛𝑡(𝐴	PERSON
cana-4781	141	8	3.11	CARDINAL
cana-4781	142	1	𝐺ℜ	ORG
cana-4781	142	2	𝐻ℜ	ORG
cana-4781	142	3	two	CARDINAL
cana-4781	142	4	𝐺ℜ	ORG
cana-4781	142	5	𝐻ℜ	ORG
cana-4781	142	6	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	142	7	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	143	1	𝜋	PRODUCT
cana-4781	143	2	𝐻ℜ	ORG
cana-4781	143	3	𝐺ℜ	ORG
cana-4781	144	1	𝜋	PERSON
cana-4781	146	1	𝐺ℜ	ORG
cana-4781	146	2	𝐺ℜ	GPE
cana-4781	146	3	⊆	CARDINAL
cana-4781	146	4	∈	ORG
cana-4781	148	1	𝐺ℜ	ORG
cana-4781	148	2	𝐺ℜ	ORG
cana-4781	148	3	⋃	PERSON
cana-4781	149	1	𝜋	PERSON
cana-4781	149	2	𝜋(𝐺ℜ	GPE
cana-4781	149	3	⋃ 𝜋(𝑥𝑖𝑐𝑙(𝑁𝑖∈ℕ	PERSON
cana-4781	149	4	𝐻ℜ	ORG
cana-4781	149	5	𝜋(𝑥𝑖) 𝜋(𝑐𝑙(𝑁𝑖∈ℕ	DATE
cana-4781	150	1	𝐻ℜ	ORG
cana-4781	150	2	1074	CARDINAL
cana-4781	150	3	32	CARDINAL
cana-4781	150	4	3 (	CARDINAL
cana-4781	150	5	884	CARDINAL
cana-4781	151	1	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	151	2	𝐻ℜ ∩ 𝑦𝑖 𝜋(𝑐𝑙(𝑁	ORG
cana-4781	151	3	𝐻ℜ	ORG
cana-4781	151	4	𝑖𝑛𝑡(𝐻ℜ	DATE
cana-4781	152	1	≠ ∅	PERSON
cana-4781	152	2	3.10	CARDINAL
cana-4781	152	3	𝑖𝑛𝑡(𝜋(𝑐𝑙(𝑁	ORG
cana-4781	153	1	⊆	CARDINAL
cana-4781	153	2	𝐻ℜ	ORG
cana-4781	153	3	𝑉 ⊆ 𝜋(𝑐𝑙(𝑁	ORG
cana-4781	154	1	𝜋(𝑛	PRODUCT
cana-4781	154	2	𝑒′ ∈ 𝑣−1𝑉 ⊆ 𝑣−1𝜋(𝑐𝑙(𝑁	ORG
cana-4781	155	1	𝜋(𝑛−1)𝜋(𝑐𝑙(𝑁	CARDINAL
cana-4781	156	1	⊆	CARDINAL
cana-4781	156	2	⊆	CARDINAL
cana-4781	156	3	⊆	CARDINAL
cana-4781	157	1	𝜋	PERSON
cana-4781	158	1	4	CARDINAL
cana-4781	158	2	topological	ORG
cana-4781	158	3	4.1	CARDINAL
cana-4781	159	1	𝐺ℜ	ORG
cana-4781	159	2	𝐻ℜ	ORG
cana-4781	159	3	𝐺ℜ	ORG
cana-4781	159	4	𝐻ℜ	ORG
cana-4781	159	5	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	159	6	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	160	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	160	2	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	161	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	161	2	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	163	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	163	2	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	164	1	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	165	1	𝑉−1𝑉	NORP
cana-4781	166	1	𝑉−1𝑉 ⊆	ORG
cana-4781	167	1	⊆	CARDINAL
cana-4781	167	2	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	169	1	𝑓(𝑎	ORG
cana-4781	169	2	⊆	CARDINAL
cana-4781	169	3	𝑁.	ORG
cana-4781	169	4	𝑉 ⊆ 𝑓(𝑈	ORG
cana-4781	169	5	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	170	1	⊆	CARDINAL
cana-4781	170	2	⊆	CARDINAL
cana-4781	172	1	4.2	CARDINAL
cana-4781	173	1	𝐺ℜ	ORG
cana-4781	173	2	𝐻ℜ	ORG
cana-4781	174	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	175	1	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	175	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	175	3	𝑔(𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	176	1	𝒦𝑓 ⊆ 𝒦𝑔	ORG
cana-4781	176	2	𝒦𝑔	GPE
cana-4781	176	3	𝑔.	TIME
cana-4781	176	4	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	176	5	𝐺ℜ	ORG
cana-4781	176	6	𝐻ℜ	ORG
cana-4781	176	7	𝐺ℜ	ORG
cana-4781	176	8	𝐻ℜ	ORG
cana-4781	176	9	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	176	10	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	176	11	𝐾ℜ ̅̅ ̅̅	ORG
cana-4781	177	1	⊆	CARDINAL
cana-4781	177	2	𝑓−1(𝑉	MONEY
cana-4781	177	3	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	177	4	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	178	1	∘	DATE
cana-4781	179	1	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	180	1	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	180	2	⊆	CARDINAL
cana-4781	182	1	⊆	CARDINAL
cana-4781	182	2	ℎ(𝑉	ORG
cana-4781	183	1	⊆	CARDINAL
cana-4781	183	2	𝐾ℜ ̅̅ ̅̅	ORG
cana-4781	184	1	4.3	CARDINAL
cana-4781	185	1	𝐺ℜ	ORG
cana-4781	185	2	𝐻ℜ	ORG
cana-4781	185	3	𝐺ℜ	ORG
cana-4781	185	4	𝐻ℜ	ORG
cana-4781	185	5	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	185	6	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	185	7	𝐾ℜ ̅̅ ̅̅	ORG
cana-4781	186	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	187	1	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	187	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	187	3	𝑔(𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	188	1	𝒦𝑓 ⊆ 𝒦𝑔	ORG
cana-4781	188	2	𝒦𝑔	GPE
cana-4781	188	3	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	188	4	1074	CARDINAL
cana-4781	188	5	32	CARDINAL
cana-4781	188	6	3 (	CARDINAL
cana-4781	188	7	885	CARDINAL
cana-4781	188	8	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	188	9	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	192	1	4.4	CARDINAL
cana-4781	193	1	𝐺ℜ	ORG
cana-4781	193	2	𝐻ℜ	ORG
cana-4781	193	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	193	4	𝐾ℜ ̅̅ ̅̅	ORG
cana-4781	194	1	𝐺ℜ	ORG
cana-4781	194	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	195	1	𝐻ℜ	ORG
cana-4781	195	2	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	196	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	196	2	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	197	1	𝐺ℜ ̅̅	ORG
cana-4781	197	2	𝐻ℜ	ORG
cana-4781	197	3	ℳ⁄	PERSON
cana-4781	198	1	𝜌(𝑎	DATE
cana-4781	199	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	199	2	𝐺ℜ ̅̅	ORG
cana-4781	199	3	𝐻ℜ	ORG
cana-4781	199	4	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	199	5	ℳ⁄	PERSON
cana-4781	200	1	∘	CARDINAL
cana-4781	200	2	𝜇′	PRODUCT
cana-4781	201	1	∈ 𝐺ℜ ̅̅	ORG
cana-4781	202	1	𝜌(𝑎	DATE
cana-4781	202	2	𝜌(𝑎	DATE
cana-4781	202	3	∈	ORG
cana-4781	204	1	5	CARDINAL
cana-4781	204	2	5.1	CARDINAL
cana-4781	205	1	𝐺ℜ	ORG
cana-4781	205	2	𝐻ℜ	ORG
cana-4781	205	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	206	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	206	2	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	206	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	207	1	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	208	1	𝜌(𝑎	DATE
cana-4781	210	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	210	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	212	1	𝑎𝑏−1 ∈ 𝒦𝜌.	PERSON
cana-4781	212	2	𝜌(𝑎)𝜌(𝑏)−1 = 𝜌(𝑎𝑏−1	ORG
cana-4781	212	3	𝑒′	GPE
cana-4781	212	4	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	213	1	one-one	CARDINAL
cana-4781	217	1	𝜌(𝑎	DATE
cana-4781	217	2	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	222	1	1074	CARDINAL
cana-4781	222	2	32	CARDINAL
cana-4781	222	3	3 (	CARDINAL
cana-4781	222	4	886	CARDINAL
cana-4781	222	5	φ	ORG
cana-4781	222	6	∘	CARDINAL
cana-4781	222	7	𝜇−1	ORG
cana-4781	223	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	224	1	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	225	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	230	1	5.2	CARDINAL
cana-4781	231	1	theorem ii	PERSON
cana-4781	231	2	𝐺ℜ	ORG
cana-4781	231	3	𝐻ℜ	ORG
cana-4781	232	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	232	2	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	232	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	232	4	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	232	5	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	233	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	236	1	𝐻ℜ	ORG
cana-4781	237	1	𝐻ℜ	ORG
cana-4781	238	1	𝐻ℜ	ORG
cana-4781	239	1	∘	DATE
cana-4781	239	2	𝐻ℜ	ORG
cana-4781	239	3	ℒ⁄	PERSON
cana-4781	240	1	𝜌′	PRODUCT
cana-4781	240	2	∘	DATE
cana-4781	240	3	𝜌′	PRODUCT
cana-4781	241	1	𝜇(𝜌(𝑎	PERSON
cana-4781	242	1	∶	ORG
cana-4781	243	1	∶	ORG
cana-4781	244	1	5.1	CARDINAL
cana-4781	244	2	𝐺ℜ ̅̅	ORG
cana-4781	244	3	ℳ⁄	PERSON
cana-4781	244	4	𝐻ℜ	ORG
cana-4781	245	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	246	1	𝐻ℜ	ORG
cana-4781	249	1	𝜌(𝑎	DATE
cana-4781	250	1	∶	ORG
cana-4781	251	1	𝐻ℜ	ORG
cana-4781	252	1	𝐻ℜ	ORG
cana-4781	253	1	5.1	CARDINAL
cana-4781	253	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	254	1	𝐻ℜ	ORG
cana-4781	255	1	5.3	CARDINAL
cana-4781	256	1	theorem iii	PERSON
cana-4781	256	2	𝐺ℜ	ORG
cana-4781	256	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	257	1	𝐻ℜ	ORG
cana-4781	257	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	257	3	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	257	4	𝐻ℜ ̅̅ ̅̅ ℒ ℒ⁄	ORG
cana-4781	257	5	𝜑(𝐻ℜ	DATE
cana-4781	257	6	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	257	7	𝐺ℜ ̅̅	ORG
cana-4781	257	8	ℒ⁄	PERSON
cana-4781	257	9	𝜑(𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	257	10	𝐺ℜ ̅̅	ORG
cana-4781	258	1	𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	259	1	𝐻ℜ ̅̅ ̅̅ ℒ	ORG
cana-4781	259	2	𝜑(𝐻ℜ	DATE
cana-4781	259	3	𝜑(𝑎	PERSON
cana-4781	262	1	𝜑(𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	263	1	𝐺ℜ ̅̅	ORG
cana-4781	263	2	𝜑(𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	263	3	𝐺ℜ ̅̅	ORG
cana-4781	264	1	∈ 𝐻ℜ ̅̅ ̅̅	ORG
cana-4781	264	2	5.1	CARDINAL
cana-4781	264	3	𝐻ℜ ̅̅ ̅̅ ℒ ℒ⁄	ORG
cana-4781	264	4	𝜑(𝐻ℜ	DATE
cana-4781	265	1	6	CARDINAL
cana-4781	265	2	6.1	CARDINAL
cana-4781	266	1	𝐺ℜ	ORG
cana-4781	266	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	266	3	𝐻ℜ	ORG
cana-4781	266	4	𝐻ℜ	ORG
cana-4781	266	5	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	266	6	𝐾ℜ\𝐺ℜ ̅̅ ̅̅ /𝐻ℜ	ORG
cana-4781	268	1	∈ 𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	268	2	1074	CARDINAL
cana-4781	268	3	32	CARDINAL
cana-4781	268	4	3 (	CARDINAL
cana-4781	268	5	887	CARDINAL
cana-4781	268	6	6.2	CARDINAL
cana-4781	269	1	𝐺ℜ	ORG
cana-4781	269	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	269	3	𝐻ℜ	ORG
cana-4781	269	4	𝐻ℜ	ORG
cana-4781	269	5	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	269	6	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	272	1	∩ 𝐾ℜ𝑦𝐻ℜ	PERSON
cana-4781	272	2	∈	ORG
cana-4781	272	3	∈	ORG
cana-4781	272	4	⊆	CARDINAL
cana-4781	272	5	6.3	CARDINAL
cana-4781	273	1	𝐻ℜ	ORG
cana-4781	273	2	𝐺ℜ	ORG
cana-4781	273	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	273	4	𝐻ℜ	ORG
cana-4781	273	5	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	274	1	𝐴	ORG
cana-4781	274	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	275	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	275	2	𝜑(𝐵	GPE
cana-4781	276	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	277	1	𝐴	ORG
cana-4781	278	1	𝐴 ⊆	ORG
cana-4781	279	1	⋃	DATE
cana-4781	279	2	⋃	PRODUCT
cana-4781	280	1	𝐵	ORG
cana-4781	280	2	𝜑(𝐵	GPE
cana-4781	280	3	⋃	DATE
cana-4781	281	1	6.4	CARDINAL
cana-4781	282	1	𝐺ℜ	ORG
cana-4781	282	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	282	3	𝐺ℜ	ORG
cana-4781	282	4	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	283	1	𝐻ℜ	ORG
cana-4781	283	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	283	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	284	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	285	1	𝐻ℜ	ORG
cana-4781	285	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	285	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	286	1	3.2	CARDINAL
cana-4781	286	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	286	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	287	1	6.5	CARDINAL
cana-4781	288	1	𝐻ℜ	ORG
cana-4781	288	2	𝐺ℜ	ORG
cana-4781	288	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	288	4	𝐻ℜ	ORG
cana-4781	288	5	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	289	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	289	2	𝐻ℜ	ORG
cana-4781	289	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	289	4	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	290	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	291	1	𝜑−1𝜑(𝑈	PERSON
cana-4781	292	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	294	1	6.6	CARDINAL
cana-4781	295	1	𝐻ℜ	ORG
cana-4781	295	2	𝐺ℜ	ORG
cana-4781	295	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	295	4	𝐻ℜ	ORG
cana-4781	295	5	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	297	1	∈	ORG
cana-4781	297	2	∈ 𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	298	1	4.2	CARDINAL
cana-4781	299	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	299	2	⊆	CARDINAL
cana-4781	299	3	⊆	CARDINAL
cana-4781	299	4	3.3	CARDINAL
cana-4781	299	5	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	299	6	⊆	CARDINAL
cana-4781	299	7	∈	ORG
cana-4781	299	8	𝑁𝐾ℜ ⊆	ORG
cana-4781	299	9	⊆	CARDINAL
cana-4781	299	10	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	300	1	⊆	CARDINAL
cana-4781	300	2	⊆	CARDINAL
cana-4781	301	1	1074	CARDINAL
cana-4781	301	2	32	CARDINAL
cana-4781	301	3	3 (	CARDINAL
cana-4781	301	4	888	CARDINAL
cana-4781	301	5	6.7	CARDINAL
cana-4781	302	1	𝐻ℜ	ORG
cana-4781	302	2	𝐺ℜ	ORG
cana-4781	302	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	302	4	𝐻ℜ	ORG
cana-4781	302	5	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	303	1	𝐺ℜ ̅̅ ̅̅ /𝐻ℜ	ORG
cana-4781	305	1	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	305	2	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	307	1	∘ 𝜑∗.	DATE
cana-4781	308	1	∈ 𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	310	1	preimage	ORG
cana-4781	310	2	⊆	CARDINAL
cana-4781	310	3	𝐺ℜ ̅̅ ̅̅	ORG
cana-4781	311	1	𝐺ℜ ̅̅ ̅̅ /𝐻ℜ	ORG
cana-4781	311	2	2.16	CARDINAL
cana-4781	312	1	𝐺ℜ ̅̅	ORG
cana-4781	313	1	⊆	CARDINAL
cana-4781	313	2	⊆	CARDINAL
cana-4781	313	3	𝐾ℜ𝑥𝑈 ⊆ 𝜑∗−1(𝑁	ORG
cana-4781	313	4	⊆	CARDINAL
cana-4781	313	5	∈	ORG
cana-4781	316	1	⊆	CARDINAL
cana-4781	316	2	𝑁.	NORP
cana-4781	318	1	1	CARDINAL
cana-4781	318	2	alaa altassan	PERSON
cana-4781	318	3	nof alharbi	ORG
cana-4781	319	1	gen. topol	PERSON
cana-4781	320	1	21	DATE
cana-4781	320	2	295	CARDINAL
cana-4781	321	1	2	CARDINAL
cana-4781	321	2	skii av	PERSON
cana-4781	321	3	atlantis press	ORG
cana-4781	321	4	world sci	ORG
cana-4781	321	5	paris	GPE
cana-4781	321	6	2008	DATE
cana-4781	322	1	3	CARDINAL
cana-4781	326	1	ac	ORG
cana-4781	326	2	42(1994	CARDINAL
cana-4781	326	3	251254	DATE
cana-4781	327	1	4	CARDINAL
cana-4781	327	2	han	NORP
cana-4781	327	3	daoguo li	PERSON
cana-4781	327	4	lijun sun	PERSON
cana-4781	328	1	2005	DATE
cana-4781	328	2	104113	DATE
cana-4781	329	1	5	CARDINAL
cana-4781	330	1	berlin	GPE
cana-4781	330	2	1989	DATE
cana-4781	331	1	6	CARDINAL
cana-4781	331	2	lin	PERSON
cana-4781	331	3	qianqian sun	PERSON
cana-4781	331	4	yujin lin	PERSON
cana-4781	331	5	jinjin li	PERSON
cana-4781	331	6	2021	CARDINAL
cana-4781	331	7	25	CARDINAL
cana-4781	331	8	3441 3453	DATE
cana-4781	332	1	7	CARDINAL
cana-4781	332	2	james r. munkres	PERSON
cana-4781	332	3	second	ORDINAL
cana-4781	332	4	pearson india education services pvt. ltd, chennai	ORG
cana-4781	333	1	8	CARDINAL
cana-4781	333	2	joseph a. gallian	PERSON
cana-4781	333	3	ninth	ORDINAL
cana-4781	333	4	cengage learning	ORG
cana-4781	333	5	india	GPE
cana-4781	333	6	delhi	GPE
cana-4781	334	1	9	CARDINAL
cana-4781	334	2	philip a. dowerk	PERSON
cana-4781	334	3	266	CARDINAL
cana-4781	334	4	2019	CARDINAL
cana-4781	334	5	106858	DATE
cana-4781	335	1	1074	CARDINAL
cana-4781	335	2	32	CARDINAL
cana-4781	335	3	3 (	CARDINAL
cana-4781	336	1	889	CARDINAL
cana-4781	337	1	10	CARDINAL
cana-4781	337	2	wiley eastern limited	ORG
cana-4781	337	3	india	GPE
cana-4781	337	4	1983	DATE
cana-4781	338	1	11	CARDINAL
cana-4781	338	2	mikhail tkaccnko	PERSON
cana-4781	338	3	86(1998	DATE
cana-4781	338	4	179	CARDINAL
cana-4781	339	1	12	CARDINAL
cana-4781	339	2	alaa altassan	PERSON
cana-4781	339	3	2019	DATE
cana-4781	339	4	17	CARDINAL
cana-4781	339	5	1750-1755	CARDINAL
cana-4781	340	1	13	CARDINAL
cana-4781	340	2	abdullah f. ozcan	PERSON
cana-4781	340	3	topological	ORG
cana-4781	340	4	topol	PERSON
cana-4781	341	1	2016	CARDINAL
cana-4781	341	2	4	CARDINAL
cana-4781	341	3	31	CARDINAL
cana-4781	342	1	14	CARDINAL
cana-4781	343	1	11	CARDINAL
cana-4781	343	2	5, 1982	DATE
cana-4781	343	3	341	CARDINAL
cana-4781	344	1	15	CARDINAL
cana-4781	344	2	wen-li liu	PERSON
cana-4781	344	3	lei mou	PERSON
cana-4781	344	4	algebraic	PERSON
cana-4781	344	5	27	CARDINAL
cana-4781	344	6	57-61	CARDINAL
cana-4781	344	7	2023	CARDINAL
cana-4781	345	1	16	CARDINAL
cana-4781	346	1	selvi	GPE
cana-4781	347	1	the indian academy of mathematics	ORG
cana-4781	348	1	17	CARDINAL
cana-4781	349	1	selvi	GPE
cana-4781	350	1	virudhunagar hindu	NORP
cana-4781	350	2	senthikumara nadar college	ORG
cana-4781	350	3	2025	DATE
cana-4781	350	4	82-89	CARDINAL