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On a type of generalized open sets. (English) Zbl 1236.54019

Summary: A new class of sets called \(\mu\)-generalized closed (briefly \(\mu g\)-closed) sets in generalized topological spaces is introduced and studied. The class of all \(\mu g\)-closed sets is strictly larger than the class of all \(\mu \)-closed sets (in the sense of Á. Császár). Furthermore, \(g\)-closed sets (in the sense of N. Levine) are a special type of \(\mu g\)-closed sets in a topological space. Some of their properties are investigated here.
Finally, some characterizations of \(\mu \)-regular and \(\mu \)-normal spaces are given.

MSC:

54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
54C08 Weak and generalized continuity
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
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