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.