Renuka Devi, V.; Sivaraj, D. A decomposition of continuity via ideals. (English) Zbl 1164.54329 Acta Math. Hung. 118, No. 1-2, 53-59 (2008). Summary: A new class of sets in ideal topological spaces is introduced and using these sets, a decomposition of continuity is given. Cited in 2 Documents MSC: 54C08 Weak and generalized continuity 54C10 Special maps on topological spaces (open, closed, perfect, etc.) Keywords:\(\alpha\)-\({\mathcal I}\)-open; pre-\({\mathcal I}\)-open; semi-\({\mathcal I}\)-open; \(\delta\)-\({\mathcal I}\)-open; \({\mathcal I}\)-locally closed; \(A_{\mathcal I}\)-set; \(C_{\mathcal I}\)-set; \(\alpha\)-\({\mathcal I}\)-continuity; pre-\({\mathcal I}\)-continuity; semi-\({\mathcal I}\)-continuity; \(\delta\)-\({\mathcal I}\)-continuity; \({\mathcal I}LC\)-continuity; \(A_{\mathcal I}\)-continuity PDFBibTeX XMLCite \textit{V. Renuka Devi} and \textit{D. Sivaraj}, Acta Math. Hung. 118, No. 1--2, 53--59 (2008; Zbl 1164.54329) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.