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  • Author or Editor: T. Noiri x
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Abstract  

A subset A of a topological space X is said to be β-open [1] if A ⊂ Cl (Int (Cl (A))). A function f : XY is said to be β-irresolute [4] if for every β-open set V of Y, f-1(V) is β-open in X. In this paper we introduce weak and strong forms of β-irresolute functions and obtain several basic properties of such functions.

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Abstract  

We introduce a new class of functions called strongly θ-precontinuous functions which is stronger than precontinuous functions and investigate their properties.

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Abstract

A new kind of sets called generalized μ-closed (briefly g μ-closed) sets are introduced and studied in a topological space by using the concept of generalized open sets introduced by Á. Császár. The class of all g μ-closed sets is strictly larger than the class of all μ-closed sets. Furthermore, g-closed sets (in the sense of N. Levine [17]) is a special type of g μ-closed sets in a topological space. Some of their properties are investigated. Finally, some characterizations of μ g-regular and μ g-normal spaces have been given.

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