Ideal and some applications of simply open sets
DOI:
https://doi.org/10.24297/jam.v13i3.6204Keywords:
Ideal, simply open sets, simply continuous, strongly simply continu- ous and dual simply continuous functionsAbstract
Recently there has been some interest in the notion of a locally closed subset of a topo- logical space. In this paper, we introduce a useful characterizations of simply open sets in terms of the ideal of nowhere dense set. Also, we study a new notion of functions in topo- logical spaces known as dual simply-continuous functions and some of their fundamental properties are investigated. Finally, a new type of simply open sets is introduced.
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References
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[2] D. Andrijevic, Some properties of the topology of -sets, Mat. Vesnik 36(1984), 1-10.
[3] P. Bhattacharya and B.K. Lahirir, Semi-generalized closed sets in topology, Indian J. Math., 29(1987), no. 3, 375-382.
[4] N. Biswas, On some mappings in topological spaces, Bull.Cal. Math. Soc.61(1969),127-135.
[5] J. Borsik and J. Dobous, On decompositions of quasicontinuity, Real Analysis Exchange, Vo. 16 (1990-1991), 292-305.
[6] N. Bourbaki, General Topology, Part 1, Addison Wesly, Rending, Mass., 1966.
[7] M. Caldes and J. Dontchev, G.^sô€€€sets and G._sô€€€sets, Mem.Fac. Sci.Kochi. Univ. (Math.) 21(2000), 21-30.
[8] C. Chattopadhyay and U.K. Roy, -sets, irresolvable space, Math., Slovaca, 42(1992), no.3,
371-378.
[9] S.G. Crossley and S.K. Hildebrand, semi-topological properties, Fund. Math, 74(1972), 233-254.
[10] J. Dontchev, The characterization of some peculiar topological spaces via A - and B -sets, Acta Math. Hunger., 67(3)(1995), 67-71.
[11] J. Dontchev and M. Ganster, A decomposition of irresoluteness, Acta Math. Hungarica
77(1-2)(1997), 41-46.
[12] A.G. El'kin, Decomposition of spaces, Soviet Math. Dokl., 10(1969), 521-525.
[13] J. Ewert, On quasi-continuous and cliquish maps with values in uniform spaces, Bull. Acad. Polon. Sci., 32(1984), 81-88.
[14] J. Foran and P. Liebnitz, A characterization of almost resolvable spaces, Rend. Circ. Mat. Palermo, Serie II, Tomo XL (1991), 136-141.
[15] M. Ganster, I.L. Reilly and M.K. Vamanamurthy, Remarks on locally closed sets, Math. Pannonica, 3(2)(1992), 107-113.
[16] D.S Jankoivic, On locally irreducible spcaes, Ann. Soc. Sci. Bruxelles Ser. I, 97(1983), no.2, 59-72.
[17] K. Kuratowski, Topology, Vol. I, Academic press, New york, 1966.
[18] N. Levine, semi-open set and semi-continuty in topological spaces, Amr. Math. Monthly, 70(1963), 36-41.
[19] S.N. Maheshwari and R. Prasad, On R0ô€€€spaces, Portugal Math., 34(1975), 213-217.
[20] S. Marcus, Suvless functions quasicontinouns au sens de S. Kempists, Collage. Math. 8(1961), 47-53.
[21] A.S. Mashhour, M.E. Abd El-Monsef and S.N. El-Deeb, On precontinuous and weak pre- continuous mappings, Proc. Math. Phys. Soc. Egypt, 53(1982), 47-53.
[22] A.S. Mashhour, I.A. Hasanein and S.N. El-Deeb, ô€€€continous and ô€€€open mappings, Acta Math. Hungar., 47(1983), 213-218.
[23] A. Neubrunnova, On transnite sequences of certain types of functions, Acta Fac.Rer. Natur. Univ. Com. Math., 30(1975), 121-126.
[24] O. Njastad, On some classes of nearly open sets, Pacic J. Math., 15(1965), 961-970.
[25] T. Noiri, Semi-normal spaces and some functions, Acta Math. Hungar,65(3)(1994),305-311.
[26] M.H. Stone, Applications of the Theory of Boolean Rings to General Topology, TAMS,41(1937),375-381.
[27] A.H. Stone, Absolutely FG-spaces, Proc. Amer. Math. Soc., 80(1980), 515-520.
[28] P. Sundaram and K. Balachandran, Semi-generalized locally closed sets in topological spaces, preprint.
[29] J.P. Thomas, Maximal connected topologies, J. Austral Math. Soc. Ser.A,8(1968), 700-705.
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Published
2017-07-30
How to Cite
Nasefa, A. A., & Mareay, R. (2017). Ideal and some applications of simply open sets. JOURNAL OF ADVANCES IN MATHEMATICS, 13(3), 7264–7271. https://doi.org/10.24297/jam.v13i3.6204
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