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A decomposition of continuity via ideals. (English) Zbl 1164.54329

Summary: A new class of sets in ideal topological spaces is introduced and using these sets, a decomposition of continuity is given.

MSC:

54C08 Weak and generalized continuity
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
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References:

[1] A. Açikgöz, T. Noiri and Ş. Yüksel, On {\(\alpha\)}-I-open sets and decomposition of {\(\alpha\)}-continuity, Acta Math. Hungar., 102 (2004), 349–357. · Zbl 1047.54010 · doi:10.1023/B:AMHU.0000024685.84429.e9
[2] J. Dontchev, On pre-I-open sets and a decomposition of I-continuity, Banyan Math. J., 2 (1996).
[3] J. Dontchev, M. Ganster and D. Rose, Ideal resolvability, Topology and its Applications, 93 (1999), 1–16. · Zbl 0955.54001 · doi:10.1016/S0166-8641(97)00257-5
[4] E. Hatir and T. Noiri, On decomposition of continuity via idealization, Acta Math. Hungar., 96 (2002), 341–349. · Zbl 1012.54019 · doi:10.1023/A:1019760901169
[5] D. Janković and T. R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97 (1990), 295–310. · Zbl 0723.54005 · doi:10.2307/2324512
[6] A. Keskin, T. Noiri and Ş. Yüksel, Idealization of a decomposition theorem, Acta Math. Hungar., 102 (2004), 269–277. · Zbl 1047.54011 · doi:10.1023/B:AMHU.0000024677.08811.6a
[7] K. Kuratowski, Topology, Vol. I, Academic Press (New York, 1966).
[8] V. Renuka Devi, D. Sivaraj and T. Tamizh Chelvam, Codense and completely codense ideals, Acta Math. Hungar., 108 (2005), 197–205. · Zbl 1100.54001 · doi:10.1007/s10474-005-0220-0
[9] R. Vaidyanathaswamy, The localization theory in set topology, Proc. Indian Acad. Sci. Math. Sci., 20 (1945), 51–61. · Zbl 0061.39308
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