Abstract
The concept of αδ-closed sets was introduced in the research paper “On Strongly-αδ-Super-Irresolute Functions In Topological Spaces. The aim of this paper is to consider and characterize αδ-irresolute and αδ-continuous functions via the concept of αδ-closed sets and to relate these concepts to the classes of αδ-compact spaces and αδ0-connected spaces.
Highlights
Closedness is a basic concept for the study and investigation of topological spaces
We will continue the study of αδ-closed sets and associated function with introducing and characterizing αδ- continuous and αδ-irresolute functions
We introduce the concepts of strong - αδ- continuity, perfect - αδ- continuity, αδO-compactness and αδ-connectedness, and study their behaviour under αδ-continuous functions
Summary
Closedness is a basic concept for the study and investigation of topological spaces. This concept has been generalized and studied by many authors from different points of views. A subset A of a space X is said to be (a) An α-generalized closed [9] (αg-closed) set if αcl(A) ⊆ Uwhenever A ⊆ U and U is α-open in (X, τ). The union of all πg-open sets, [15] each contained in a set S in a topological space X is called the πginterior of S and it is denoted by πg-int(S).
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