Generalization of perfectly continuous, regular set-connected and clopen functions

Abstract

Abstract. Recently the class of almost cl-supercontinuous functions between topological spaces has been studied in some detail. We consider this class of functions from the point of view of change(s) of topology. In particular, we conclude that this class of functions coincides with the usual class of continuous functions when the domain and codomain have been retopologized appropriately. Some of the consequences of this fact are considered in this paper. AMS Classification:Primary 54C60, 54C05, 54C10; Secondary 54D10, 54D20.

Two New Type of Irresolute Functions Via e-open Sets

“…A topological space ( , ) is said to be -1 [6] (resp. -1 [5]) if for each pair of distinct points and of , there exist -open (resp. regular open) sets 1 and 2 such that ∈ 1 and ∈ 2 , ∉ 2 and ∉ 1 .…”

Rδ-Supercontinuous Functions

“…An open subset U of a space X is called r δ -open if for each x P U , there exists a δ-closed set C x such that x P C x Ă U , δT1-spaces are referred to as rT1-spaces by Ekici in [4]. : Earlier R0-spaces were defined by Shanin [27] and rediscovered by Vaidyanathswamy who called them Π1-spaces (see [35], p. 98) and later on by Davis [3].…”

A note on almost delta-semicontinuous functions

“…A space X is said to be r-T 1 [2] if for each pair of distinct points x and y of X, there exist regular open sets A and B containing x and y respectively such that y / ∈ A and x / ∈ B.…”