Infra -α- Compact and Infra -α- Connected Spaces

In 2016 Hakeem A. Othman and Md. Hanif Page introduced a new notion of set in general topology called an infra -α- open set and investigated its fundamental properties and studied the relationship between infra -α- open set and other topological sets. The objective of this paper is to introduce the new concepts called infra -α- compact space, countably infra -α- compact space, infra -α- Lindelof space, almost infra -α- compact space, mildly infra -α- compact space and infra -α- connected space in general topology and investigate several properties and characterizations of these new concepts in topological spaces.