Characterizations of M – Compactness and M – Connectedness in Topological Spaces

Abstract

In 2011 A.I. El-Maghrabi and M.A. Al-Johani defined a new notion of set in general topology called an M– open set and investigated its fundamental properties and studied the relations between M– open set and other topological sets. The collection of all M−open sets in a topological space is a supra topology on X. We will extend the concepts of compactness and connectedness to M–compactness and M–connectedness respectively in supra topological spaces and will investigate their relationships among them as well as their characterizations by making use of generalized mappings including M–continuous and M–irresolute functions. The objective of this paper is to introduce the new concepts called M–compact space, M–Lindelof space, countably M–compact space, almost M–compact space, mildly M–compact space and M–connected space in general topology and investigate several properties and characterizations of these new notions.