Soft expandable spaces

Abstract

In this study, we first introduce a new class of spaces, namely soft expandable spaces, which is a generalization of soft paracompact and countably soft compact spaces. Some properties of these spaces that are discussed in this paper the soft expandable space is equivalent to every Aσ-soft cover has soft-LF soft open refinement. Also, we discuss under what conditions that countably soft expandable space is soft paracompact. With the help of interesting examples, we elucidate there is no relationship between soft topology and its parametric topologies with respect to possession the property of being a soft expandable space. In this regards, we discuss the role of extended soft topology to inherited this property to classical topology. Second, we define the concept of s-expandable spaces which is stronger than soft expandable spaces. We give some characterizations of this concept, and investigate some equivalent concepts to s-expandable spaces. In the end, we study the behaviours of soft s-expandable spaces under some types of soft mappings.