Almost soft compact and approximately soft Lindelöf spaces

Abstract

The concepts of almost soft compact (almost soft Lindelöf), approximately soft Lindelöf and mildly soft compact (mildly soft Lindelöf) spaces are initiated and investigated in this work. Their characterizations and main properties are established and the relationships among them are illustrated with the help of examples. The sufficient conditions for the equivalent between almost soft Lindelöf and approximately soft Lindelöf spaces; and for the equivalent among soft Lindelöf, almost soft Lindelöf, approximately soft Lindelöf and mildly soft Lindelöf spaces are given. The image of the introduced types of soft compact and soft Lindelöf spaces under soft continuous mappings are studied; and the mutual relations between them and their parametric topological spaces are probed. Some results which associate soft hyperconnectedness and soft connectedness, respectively with almost soft compactness and mildly soft compactness are verified. This study is concluded by providing an illustrative diagram for the interrelations among the initiated soft compact and soft Lindelöf spaces.

Keywords

• Almost soft compactness
• approximately soft Lindelöfness
• mildly soft compactness
• soft locally finite and soft partition topological spaces