Sα-Connectedness in Topological Spaces

Abstract

In this paper, connectedness of a class of S_α-open sets in a topological space X is introduced. The connectedness of this class on X, called S_α-connectedness, turns out to be equivalent to connectedness of X when X is locally indiscrete or with finite α-topology. The S_α-continuous and S_α-irresolute mappings are defined and their relationship with other mappings such as continuous mappings and semi-continuous mappings are discussed. An intermediate value theorem is obtained. The hyperconnected spaces constitute a subclass of the class of S_α-connected spaces.

Key words and phrases. α-connected, hyperconnected, semi-connected, S_α-connected.

2010 Mathematics Subject Classification. 54A05, 54D05