Some generalized forms of soft compactness and soft Lindel¨ofness via soft α-open sets

Abstract

By using a notion of soft α-open sets, we generalize the concepts of soft compact and soft Lindel¨of spaces.  We define the concepts of soft α-compact, soft α-Lindel¨of, almost (approximately, mildly) soft α-compact and almost (approximately, mildly) soft α-Lindel¨of spaces.  We present two new kinds of the finite intersection property and utilize them to characterize almost soft α-compact and approximately soft α-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 α-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 α-connectedness, soft α-T₂-spaces, soft α-partition and soft subspaces.