Abstract
By using a notion of soft alpha-open sets, we generalize the concepts of soft compact and soft Lindelof spaces. We define the concepts of soft alpha-compact, soft alpha-Lindelof, almost (approximately, mildly) soft alpha-compact and almost (approximately, mildly) soft alpha-Lindelof spaces. We present two new kinds of the finite intersection property and utilize them to characterize almost soft alpha-compact and approximately soft alpha-compact spaces. To elucidate the relationships among the introduced spaces and to illustrate our main results, we supply several interesting examples. Also, we point out that the initiated spaces are preserved under soft alpha-irresolute mappings and we investigate certain of results which associate an extended soft topology with the introduced soft spaces. In the end, we conclude some findings which associate the introduced spaces with some soft topological notions such as soft alpha-connectedness, soft alpha-T-2-spaces, soft alpha-partition and soft subspaces.