Novel types of soft compact and connected spaces inspired by soft Q-sets

Abstract

In this work, we make use of soft Q-sets to introduce the concepts of soft Q-compact, soft Q-Lindelof and soft Q-connected spaces. We explore the essential properties of these concepts and elucidate the relationships between them with the assist of examples and counterexamples. We also give each one of these concepts a complete description and investigate how they behave under specific kinds of soft mappings. Moreover, we demonstrate the unique characterizations of these concepts which are not satisfied for their counterpart notions existing in the published literature; for example, we prove that every soft Q-subset of soft Q-compact and soft Q-Lindelof spaces is respectively soft Q-compact and soft Q-Lindelof as well as we discover the conditions under which the concepts of soft connected and soft Q-connected spaces are equivalent. The role of extended and full soft topologiesto obtain some relationships between these concepts and their counterparts via parametric topologies is also discussed.