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New notions in ideal topological space. (English) Zbl 1431.54003

Summary: In this paper, we apply the notion of \(I^{\ast\ast\alpha}_g\)-closed sets to present and study a new class of locally closed sets called \(I^{\ast\ast\alpha}_g\)-locally closed sets in ideal topological spaces along with their several characterizations and mutual relationships between the new notion and other locally closed sets. Further we introduce \(I^{\ast\ast\alpha}_g\)-submaximal spaces and some properties of such notion are investigated.

MSC:

54A05 Topological spaces and generalizations (closure spaces, etc.)
54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
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