β* - Compactness and β* - Connectedness

In 2014 Mubarki, Al-Rshudi, and Al-Juhani introduced and studied the notion of a set in general topology called β * - open sets and investigated its fundamental properties and studied the relationships between β * - open set and other topological sets including β * - continuity in topological spaces. The objective of this paper is to introduce the new concepts called β * - compact space, countably β * - compact space, β * - Lindelof space, almost β * - compact space, mildly β * - compact space and β * - connected space in general topology and investigate several properties and characterizations of these new concepts in topological spaces.