Binary ?ech soft closure spaces

Abstract

In this paper the notion of binary ?ech soft closure space which is defined over two initial universe sets with fixed sets of parameters is introduced and studied. This space extends and generalizes ?ech soft closure space. The main and basic notions for this space such as closed (open) binary soft sets, binary soft interior, and dense binary soft sets are defined and studied. Relationships between binary ?ech soft closure space and ?ech soft closure space are deduced. Examples and counterexamples are presented to illustrate some of our results. Finally, some operations on binary ?ech soft closure operators are defined.