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\(\mathcal{I}_\mathbf{g}^*\)-closed sets via ideal topological spaces. (English) Zbl 1452.54001

Summary: In this paper, aspects of generalized continuity and generalized closedness are explored. The standard material on the notions of \(*g\)-open, \(\mathbf{g}\)-open sets and some definitions and results that are needed are presented first. Then the class of \(\mathcal{I}_\mathbf{g}^*\)-closed sets is introduced and its fundamental properties are studied. Also, \(\mathcal{I}_\mathbf{g}^*\)-regular, \(^*\)-additive, \(^*\)-multiplicative, \(\mathcal{I}_\mathbf{g}^*\)-additive, and \(\mathcal{I}_\mathbf{g}^*\)-multiplicative spaces are introduced and their properties are investigated.

MSC:

54A05 Topological spaces and generalizations (closure spaces, etc.)
54C08 Weak and generalized continuity
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References:

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