Remarks on \(\tilde g_{\alpha}\)-closed sets in topological spaces. (English) Zbl 1207.54030

Jafari, Saeid; Thivagar, M. Lellis; Paul, Nirmala Rebecca

Int. Math. Forum 5, No. 21-24, 1167-1178 (2010).

Summary: In this paper we introduce a new class of sets called \(\tilde g_{\alpha}\)-closed sets in topological spaces. We prove that this class lies between \(\alpha \)-closed sets and \(g\alpha\)-closed sets. We discuss some basic properties of \(\tilde g_{\alpha}\)-closed sets. Applying this we introduce a new space called \(T_{\tilde g_{\alpha}}\)-space.

MSC:

54D10	Lower separation axioms (\(T_0\)–\(T_3\), etc.)
54C08	Weak and generalized continuity
54A05	Topological spaces and generalizations (closure spaces, etc.)

Keywords:

topological spaces; generalized closed sets; \(^{\#}gs\)-closed sets; \(^{\#}gs\)-open sets and \(\alpha \)- closure