Two Classes of Infrasoft Separation Axioms

Abstract

One of the considerable topics in the soft setting is the study of soft topology which has enticed the attention of many researchers. To contribute to this scope, we devote this work to investigate two classes of separation axioms with respect to the distinct ordinary elements through one of the generalizations of soft topology called infrasoft topology. We first formulate the concepts of infra-tp-soft Tj using total belong and partial nonbelong relations and then introduce the concepts of infra-tt-soft Tj-spaces using total belong and partial nonbelong relations. To illustrate the relationships between them, we provide some examples. We discuss their fundamental properties and study their behaviors under some special types of infrasoft topologies. An extensive discussion is given for the transmission of these two classes between infrasoft topology and its parametric infratopologies. In the end, we demonstrate which ones have topological and hereditary properties, and we show their behaviors under the finite product of soft spaces.