id	sid	eid	entity	type
ejpam-1245	1	1	4_aljarrah.dvi european journal	ORG
ejpam-1245	1	2	5	CARDINAL
ejpam-1245	1	3	2, 2012	DATE
ejpam-1245	1	4	129	CARDINAL
ejpam-1245	1	5	hussein aljarrah∗	PERSON
ejpam-1245	1	6	mohd salmi	PERSON
ejpam-1245	1	7	md noorani school of mathematical sciences	ORG
ejpam-1245	1	8	universiti kebangsaan malaysia	PERSON
ejpam-1245	1	9	43600	DATE
ejpam-1245	1	10	ukm bangi	PERSON
ejpam-1245	1	11	selangor	GPE
ejpam-1245	1	12	malaysia	GPE
ejpam-1245	2	1	3	CARDINAL
ejpam-1245	2	2	u −	ORG
ejpam-1245	7	1	2010	DATE
ejpam-1245	7	2	54c05	CARDINAL
ejpam-1245	7	3	54c10	CARDINAL
ejpam-1245	8	1	1	CARDINAL
ejpam-1245	10	1	int(a	GPE
ejpam-1245	10	2	cl(a	NORP
ejpam-1245	11	1	4	CARDINAL
ejpam-1245	12	1	7	CARDINAL
ejpam-1245	12	2	⊆	CARDINAL
ejpam-1245	13	1	a⊆ cl(int(cl(a	PERSON
ejpam-1245	15	1	3	CARDINAL
ejpam-1245	17	1	9	CARDINAL
ejpam-1245	18	1	2	CARDINAL
ejpam-1245	19	1	u −	ORG
ejpam-1245	21	1	ωbo(x	GPE
ejpam-1245	22	1	ωb−open, β−open,	DATE
ejpam-1245	25	1	h. aljarrah	PERSON
ejpam-1245	25	2	msn�ukm.my	PERSON
ejpam-1245	25	3	m. noorani	PERSON
ejpam-1245	26	1	129	CARDINAL
ejpam-1245	26	2	2012	DATE
ejpam-1245	27	1	h. aljarrah	PERSON
ejpam-1245	27	2	m. noorani	PERSON
ejpam-1245	28	1	j. pure	PERSON
ejpam-1245	28	2	5	CARDINAL
ejpam-1245	28	3	2012	DATE
ejpam-1245	28	4	129	CARDINAL
ejpam-1245	28	5	1	CARDINAL
ejpam-1245	30	1	6	CARDINAL
ejpam-1245	31	1	9	CARDINAL
ejpam-1245	32	1	ωbo(x	GPE
ejpam-1245	33	1	1	CARDINAL
ejpam-1245	34	1	3	CARDINAL
ejpam-1245	34	2	i. the union of any	ORG
ejpam-1245	34	3	ωβo(x	GPE
ejpam-1245	36	1	ωβo(x	GPE
ejpam-1245	37	1	1	CARDINAL
ejpam-1245	38	1	3	CARDINAL
ejpam-1245	39	1	a∈ωβo(y	ORG
ejpam-1245	40	1	2	CARDINAL
ejpam-1245	41	1	3	CARDINAL
ejpam-1245	43	1	3	CARDINAL
ejpam-1245	44	1	5	CARDINAL
ejpam-1245	46	1	2	CARDINAL
ejpam-1245	46	2	2	CARDINAL
ejpam-1245	47	1	∈	ORG
ejpam-1245	47	2	⊆	CARDINAL
ejpam-1245	48	1	3	CARDINAL
ejpam-1245	49	1	ωβo(x	GPE
ejpam-1245	49	2	⊆ a. theorem 4	DATE
ejpam-1245	51	1	i.	PERSON
ejpam-1245	52	1	ωβo(x	GPE
ejpam-1245	56	1	⊂	GPE
ejpam-1245	57	1	vi	PERSON
ejpam-1245	59	1	vii	PERSON
ejpam-1245	61	1	h. aljarrah	PERSON
ejpam-1245	61	2	m. noorani	PERSON
ejpam-1245	62	1	j. pure	PERSON
ejpam-1245	62	2	5	CARDINAL
ejpam-1245	62	3	2012	DATE
ejpam-1245	62	4	129	CARDINAL
ejpam-1245	65	1	⊆	CARDINAL
ejpam-1245	66	1	⊆	CARDINAL
ejpam-1245	67	1	x∈	DATE
ejpam-1245	68	1	1(i	CARDINAL
ejpam-1245	69	1	ii→ iii	PERSON
ejpam-1245	69	2	w	ORG
ejpam-1245	70	1	∈	ORG
ejpam-1245	70	2	⊆	CARDINAL
ejpam-1245	71	1	3	CARDINAL
ejpam-1245	80	1	⊆	CARDINAL
ejpam-1245	80	2	⊆	CARDINAL
ejpam-1245	81	1	x∈	DATE
ejpam-1245	82	1	1(i	CARDINAL
ejpam-1245	83	1	ωβc(x	PERSON
ejpam-1245	84	1	vi	PERSON
ejpam-1245	87	1	vi	PERSON
ejpam-1245	88	1	⊆	CARDINAL
ejpam-1245	90	1	ωβo(x	GPE
ejpam-1245	90	2	∈	ORG
ejpam-1245	90	3	6=	CARDINAL
ejpam-1245	92	1	2	CARDINAL
ejpam-1245	92	2	6=	CARDINAL
ejpam-1245	93	1	φ	ORG
ejpam-1245	95	1	4	CARDINAL
ejpam-1245	97	1	5	CARDINAL
ejpam-1245	103	1	6⊂	CARDINAL
ejpam-1245	104	1	6=	CARDINAL
ejpam-1245	105	1	2	CARDINAL
ejpam-1245	108	1	⊆	CARDINAL
ejpam-1245	114	1	ωβo(x	GPE
ejpam-1245	115	1	ωβfr	PERSON
ejpam-1245	116	1	⊆	CARDINAL
ejpam-1245	117	1	1	CARDINAL
ejpam-1245	118	1	⊆	CARDINAL
ejpam-1245	122	1	ωβo(x	GPE
ejpam-1245	124	1	h. aljarrah	PERSON
ejpam-1245	124	2	m. noorani	PERSON
ejpam-1245	125	1	j. pure	PERSON
ejpam-1245	125	2	5	CARDINAL
ejpam-1245	125	3	2012	DATE
ejpam-1245	125	4	129	CARDINAL
ejpam-1245	127	1	∈	ORG
ejpam-1245	128	1	∈	ORG
ejpam-1245	128	2	⊆	CARDINAL
ejpam-1245	132	1	↓ ↓ ↓	ORG
ejpam-1245	133	1	0,1	CARDINAL
ejpam-1245	133	2	φ	ORG
ejpam-1245	135	1	1 x ∈	QUANTITY
ejpam-1245	135	2	0	CARDINAL
ejpam-1245	135	3	∈q	ORG
ejpam-1245	136	1	2	CARDINAL
ejpam-1245	136	2	1,2,3	CARDINAL
ejpam-1245	136	3	φ	PERSON
ejpam-1245	136	4	1	CARDINAL
ejpam-1245	136	5	2	CARDINAL
ejpam-1245	136	6	1,2	CARDINAL
ejpam-1245	136	7	φ	ORG
ejpam-1245	138	1	1,2	CARDINAL
ejpam-1245	138	2	3	CARDINAL
ejpam-1245	139	1	3	CARDINAL
ejpam-1245	141	1	φ	ORG
ejpam-1245	145	1	∈	ORG
ejpam-1245	145	2	0,2)∩q	CARDINAL
ejpam-1245	146	1	1	CARDINAL
ejpam-1245	149	1	ωβo(x	GPE
ejpam-1245	151	1	∩a	GPE
ejpam-1245	151	2	ωβo(x	GPE
ejpam-1245	152	1	1	CARDINAL
ejpam-1245	154	1	∩a	GPE
ejpam-1245	154	2	ωβo(a	CARDINAL
ejpam-1245	156	1	h. aljarrah	PERSON
ejpam-1245	156	2	m. noorani	PERSON
ejpam-1245	157	1	j. pure	PERSON
ejpam-1245	157	2	5	CARDINAL
ejpam-1245	157	3	2012	DATE
ejpam-1245	157	4	129	CARDINAL
ejpam-1245	157	5	4	CARDINAL
ejpam-1245	158	1	0,1	CARDINAL
ejpam-1245	158	2	φ	ORG
ejpam-1245	158	3	1	CARDINAL
ejpam-1245	160	1	1 x ∈	CARDINAL
ejpam-1245	162	1	∈	ORG
ejpam-1245	162	2	1	CARDINAL
ejpam-1245	164	1	5	CARDINAL
ejpam-1245	164	2	0,1	CARDINAL
ejpam-1245	164	3	φ	ORG
ejpam-1245	164	4	1	CARDINAL
ejpam-1245	166	1	1 x	QUANTITY
ejpam-1245	166	2	2	CARDINAL
ejpam-1245	166	3	∈q	ORG
ejpam-1245	170	1	5	CARDINAL
ejpam-1245	172	1	2	CARDINAL
ejpam-1245	179	1	∈ωβo(aα	CARDINAL
ejpam-1245	180	1	1	CARDINAL
ejpam-1245	181	1	1(i	CARDINAL
ejpam-1245	182	1	2	CARDINAL
ejpam-1245	187	1	6	CARDINAL
ejpam-1245	188	1	φ	ORG
ejpam-1245	188	2	1	CARDINAL
ejpam-1245	190	1	1 x ∈	QUANTITY
ejpam-1245	190	2	2	CARDINAL
ejpam-1245	190	3	∈q	ORG
ejpam-1245	190	4	h. aljarrah	PERSON
ejpam-1245	190	5	m. noorani	PERSON
ejpam-1245	191	1	j. pure	PERSON
ejpam-1245	191	2	5	CARDINAL
ejpam-1245	191	3	2012	DATE
ejpam-1245	191	4	129	CARDINAL
ejpam-1245	192	1	2	CARDINAL
ejpam-1245	192	2	1	CARDINAL
ejpam-1245	195	1	3	CARDINAL
ejpam-1245	198	1	g(w	ORG
ejpam-1245	199	1	⊆	CARDINAL
ejpam-1245	200	1	u)⊆w	GPE
ejpam-1245	201	1	g(w	ORG
ejpam-1245	201	2	⊆	CARDINAL
ejpam-1245	202	1	3	CARDINAL
ejpam-1245	204	1	7	CARDINAL
ejpam-1245	205	1	φ	ORG
ejpam-1245	206	1	φ	ORG
ejpam-1245	206	2	1	CARDINAL
ejpam-1245	206	3	1,2	CARDINAL
ejpam-1245	206	4	1,2,3	CARDINAL
ejpam-1245	208	1	∈q	ORG
ejpam-1245	209	1	1 x	QUANTITY
ejpam-1245	209	2	3 x	QUANTITY
ejpam-1245	209	3	2	CARDINAL
ejpam-1245	212	1	3	CARDINAL
ejpam-1245	214	1	6	CARDINAL
ejpam-1245	216	1	∈	ORG
ejpam-1245	220	1	3	CARDINAL
ejpam-1245	222	1	h. aljarrah	PERSON
ejpam-1245	222	2	m. noorani	PERSON
ejpam-1245	223	1	j. pure	PERSON
ejpam-1245	223	2	5	CARDINAL
ejpam-1245	223	3	2012	DATE
ejpam-1245	223	4	129	CARDINAL
ejpam-1245	224	1	⊆	CARDINAL
ejpam-1245	224	2	⊆	CARDINAL
ejpam-1245	227	1	⊆	CARDINAL
ejpam-1245	229	1	∩	PERSON
ejpam-1245	230	1	∈	ORG
ejpam-1245	230	2	h)⊆	DATE
ejpam-1245	233	1	6	CARDINAL
ejpam-1245	234	1	8	CARDINAL
ejpam-1245	236	1	ρ	GPE
ejpam-1245	238	1	first	ORDINAL
ejpam-1245	238	2	σ	ORG
ejpam-1245	239	1	∈	ORG
ejpam-1245	240	1	⊆	CARDINAL
ejpam-1245	244	1	∈	ORG
ejpam-1245	245	1	∈	ORG
ejpam-1245	246	1	⊆	CARDINAL
ejpam-1245	250	1	xα	ORG
ejpam-1245	250	2	∈	ORG
ejpam-1245	251	1	∏	CARDINAL
ejpam-1245	251	2	∏	CARDINAL
ejpam-1245	251	3	∏ α∈∆	GPE
ejpam-1245	253	1	first	ORDINAL
ejpam-1245	254	1	∈	ORG
ejpam-1245	254	2	⊆	CARDINAL
ejpam-1245	255	1	σ	ORG
ejpam-1245	256	1	∏	CARDINAL
ejpam-1245	257	1	∏	CARDINAL
ejpam-1245	258	1	∈	ORG
ejpam-1245	259	1	3	CARDINAL
ejpam-1245	260	1	7	DATE
ejpam-1245	261	1	8	CARDINAL
ejpam-1245	262	1	3	CARDINAL
ejpam-1245	262	2	i. x	PERSON
ejpam-1245	262	3	β−lindelőf	GPE
ejpam-1245	266	1	β−lindelőf	GPE
ejpam-1245	268	1	ωβ−	DATE
ejpam-1245	269	1	β−lindelőf	GPE
ejpam-1245	269	2	8	CARDINAL
ejpam-1245	273	1	vα1 , vα2	PERSON
ejpam-1245	277	1	5	CARDINAL
ejpam-1245	279	1	β−lindelőf	GPE
ejpam-1245	279	2	lindelőf.	GPE
ejpam-1245	279	3	h. aljarrah	PERSON
ejpam-1245	279	4	m. noorani	PERSON
ejpam-1245	280	1	j. pure	PERSON
ejpam-1245	280	2	5	CARDINAL
ejpam-1245	280	3	2012	DATE
ejpam-1245	280	4	129	CARDINAL
ejpam-1245	280	5	3	CARDINAL
ejpam-1245	280	6	7	CARDINAL
ejpam-1245	281	1	ωβo(y	PRODUCT
ejpam-1245	281	2	σ	ORG
ejpam-1245	281	3	ωβo(x	GPE
ejpam-1245	283	1	8	CARDINAL
ejpam-1245	284	1	1,2	CARDINAL
ejpam-1245	284	2	2	CARDINAL
ejpam-1245	286	1	1	CARDINAL
ejpam-1245	288	1	9	CARDINAL
ejpam-1245	290	1	i.	PERSON
ejpam-1245	291	1	σ	ORG
ejpam-1245	293	1	ωβ−	DATE
ejpam-1245	296	1	∈	ORG
ejpam-1245	299	1	⊆	CARDINAL
ejpam-1245	300	1	∈	ORG
ejpam-1245	300	2	3	CARDINAL
ejpam-1245	300	3	σ	ORG
ejpam-1245	300	4	⊆	CARDINAL
ejpam-1245	300	5	∈	ORG
ejpam-1245	301	1	⊆	CARDINAL
ejpam-1245	301	2	⊆	CARDINAL
ejpam-1245	302	1	3	CARDINAL
ejpam-1245	305	1	⊆	CARDINAL
ejpam-1245	308	1	ωβo(y	MONEY
ejpam-1245	308	2	σ	ORG
ejpam-1245	310	1	3	CARDINAL
ejpam-1245	310	2	⊆	CARDINAL
ejpam-1245	310	3	1(i	CARDINAL
ejpam-1245	310	4	x∈a	PERSON
ejpam-1245	310	5	ωβo(x	GPE
ejpam-1245	311	1	10	CARDINAL
ejpam-1245	312	1	σ	ORG
ejpam-1245	312	2	i. f	PERSON
ejpam-1245	313	1	h. aljarrah	PERSON
ejpam-1245	313	2	m. noorani	PERSON
ejpam-1245	314	1	j. pure	PERSON
ejpam-1245	314	2	5	CARDINAL
ejpam-1245	314	3	2012	DATE
ejpam-1245	314	4	129	CARDINAL
ejpam-1245	315	1	σ	ORG
ejpam-1245	319	1	σ	ORG
ejpam-1245	321	1	−1	DATE
ejpam-1245	322	1	ωβc(x	PERSON
ejpam-1245	322	2	⊆	CARDINAL
ejpam-1245	324	1	⊆	CARDINAL
ejpam-1245	325	1	⊆	CARDINAL
ejpam-1245	326	1	⊆	CARDINAL
ejpam-1245	328	1	∈	ORG
ejpam-1245	328	2	u)∩(y−v	ORG
ejpam-1245	328	3	6=	CARDINAL
ejpam-1245	330	1	∈	ORG
ejpam-1245	331	1	2	CARDINAL
ejpam-1245	332	1	ωβo(y	PRODUCT
ejpam-1245	332	2	σ	ORG
ejpam-1245	332	3	6=	CARDINAL
ejpam-1245	333	1	φ	ORG
ejpam-1245	334	1	11	CARDINAL
ejpam-1245	342	1	ωβo(x	GPE
ejpam-1245	344	1	⊆	CARDINAL
ejpam-1245	348	1	∈	ORG
ejpam-1245	349	1	∈	ORG
ejpam-1245	349	2	⊆	CARDINAL
ejpam-1245	351	1	5	CARDINAL
ejpam-1245	355	1	ωβo(y	PRODUCT
ejpam-1245	355	2	σ	ORG
ejpam-1245	355	3	g(w	ORG
ejpam-1245	355	4	⊆	CARDINAL
ejpam-1245	356	1	∈	ORG
ejpam-1245	356	2	g(w	ORG
ejpam-1245	356	3	⊆	CARDINAL
ejpam-1245	358	1	6	CARDINAL
ejpam-1245	360	1	1	CARDINAL
ejpam-1245	360	2	σ	ORG
ejpam-1245	361	1	12	CARDINAL
ejpam-1245	362	1	σ	ORG
ejpam-1245	363	1	ωβo(y	PRODUCT
ejpam-1245	363	2	σ	ORG
ejpam-1245	363	3	σ	ORG
ejpam-1245	363	4	⊆	CARDINAL
ejpam-1245	363	5	σ	ORG
ejpam-1245	365	1	h. aljarrah	PERSON
ejpam-1245	365	2	m. noorani	PERSON
ejpam-1245	366	1	j. pure	PERSON
ejpam-1245	366	2	5	CARDINAL
ejpam-1245	366	3	2012	DATE
ejpam-1245	366	4	129	CARDINAL
ejpam-1245	366	5	140	CARDINAL
ejpam-1245	366	6	6	CARDINAL
ejpam-1245	367	1	ωβo(y	PRODUCT
ejpam-1245	367	2	σ	ORG
ejpam-1245	368	1	u ∈ωβo(y	ORG
ejpam-1245	368	2	3	CARDINAL
ejpam-1245	369	1	⊆	CARDINAL
ejpam-1245	371	1	−1(cl(u))⊆	DATE
ejpam-1245	372	1	10	CARDINAL
ejpam-1245	373	1	3	CARDINAL
ejpam-1245	373	2	aljarrah	ORG
ejpam-1245	373	3	two	CARDINAL
ejpam-1245	373	4	∈	ORG
ejpam-1245	373	5	13	CARDINAL
ejpam-1245	376	1	two	CARDINAL
ejpam-1245	378	1	∩ v2	PERSON
ejpam-1245	381	1	ωβo(x	GPE
ejpam-1245	383	1	8	CARDINAL
ejpam-1245	391	1	σ	ORG
ejpam-1245	392	1	ωβo(x	GPE
ejpam-1245	397	1	4.	CARDINAL
ejpam-1245	397	2	9	CARDINAL
ejpam-1245	400	1	ωβo(y	PRODUCT
ejpam-1245	400	2	σ	ORG
ejpam-1245	401	1	σ	ORG
ejpam-1245	405	1	9	CARDINAL
ejpam-1245	406	1	1,2,3	CARDINAL
ejpam-1245	406	2	φ	ORG
ejpam-1245	406	3	1	CARDINAL
ejpam-1245	406	4	2	CARDINAL
ejpam-1245	406	5	1,2	CARDINAL
ejpam-1245	407	1	3	CARDINAL
ejpam-1245	407	2	∈	ORG
ejpam-1245	409	1	8	CARDINAL
ejpam-1245	410	1	ωβo(y	PRODUCT
ejpam-1245	410	2	σ	ORG
ejpam-1245	411	1	w ⊂	ORG
ejpam-1245	412	1	14	DATE
ejpam-1245	414	1	a))⊆	ORG
ejpam-1245	415	1	139	CARDINAL
ejpam-1245	418	1	∈	ORG
ejpam-1245	418	2	σ	ORG
ejpam-1245	431	1	∈	ORG
ejpam-1245	435	1	ρ	GPE
ejpam-1245	439	1	10	CARDINAL
ejpam-1245	440	1	1,2	CARDINAL
ejpam-1245	440	2	2	CARDINAL
ejpam-1245	442	1	1 x ∈	QUANTITY
ejpam-1245	442	2	2	CARDINAL
ejpam-1245	442	3	∈q	ORG
ejpam-1245	444	1	11	CARDINAL
ejpam-1245	445	1	1,2	CARDINAL
ejpam-1245	445	2	1	CARDINAL
ejpam-1245	447	1	2	CARDINAL
ejpam-1245	447	2	1	CARDINAL
ejpam-1245	449	1	12	CARDINAL
ejpam-1245	450	1	8	CARDINAL
ejpam-1245	451	1	the malaysian ministry of science	ORG
ejpam-1245	452	1	ukm-st-06-frgs0146-2010	PERSON
ejpam-1245	453	1	k al-zoubi	PERSON
ejpam-1245	455	1	al-yarmouk	PERSON
ejpam-1245	455	2	12(1):119–131	DATE
ejpam-1245	455	3	2003	DATE
ejpam-1245	456	1	2	CARDINAL
ejpam-1245	456	2	k al-zoubi	PERSON
ejpam-1245	458	1	al-manarah journal	ORG
ejpam-1245	458	2	9(2):169–179, 2003	DATE
ejpam-1245	459	1	3	CARDINAL
ejpam-1245	460	1	ωβ−	DATE
ejpam-1245	462	1	140	CARDINAL
ejpam-1245	462	2	4	CARDINAL
ejpam-1245	464	1	48:59–64, 1996	DATE
ejpam-1245	465	1	5	CARDINAL
ejpam-1245	469	1	74(3):233–254	CARDINAL
ejpam-1245	469	2	1972	DATE
ejpam-1245	470	1	6	CARDINAL
ejpam-1245	472	1	dirasat	PERSON
ejpam-1245	472	2	1996	DATE
ejpam-1245	473	1	s el deeb	PERSON
ejpam-1245	473	2	mahmoud	PERSON
ejpam-1245	475	1	bull	ORG
ejpam-1245	476	1	fac	ORG
ejpam-1245	477	1	sci	ORG
ejpam-1245	477	2	assiut univ.	ORG
ejpam-1245	477	3	12:77–90, 1983	DATE
ejpam-1245	478	1	8	CARDINAL
ejpam-1245	480	1	internat	PERSON
ejpam-1245	481	1	j. math	PERSON
ejpam-1245	483	1	sci.	ORG
ejpam-1245	483	2	2002	DATE
ejpam-1245	484	1	9	CARDINAL
ejpam-1245	484	2	al-omari	PERSON
ejpam-1245	487	1	j. pure	PERSON
ejpam-1245	487	2	1:3–9,	DATE
ejpam-1245	487	3	2008	DATE