Soft N-Topological Spaces

TL;DR

This paper introduces Soft N-Topological Spaces, a new framework combining soft topologies and N-topologies, and explores their properties, subspaces, and separation axioms.

Contribution

It generalizes existing soft and N-topological concepts, providing new structures and separation axioms in the field of soft topology.

Findings

Defined Soft N-Topological Spaces and their basic properties

Analyzed subspaces and parameterized families of crisp topologies

Introduced and studied new separation axioms N-wise soft T0, T1, T2

Abstract

Very recently, the idea of studying structures equipped with two or more soft topologies has been considered by several researchers. Soft bitopological spaces were introduced and studied, in 2014, by Ittanagi as a soft counterpart of the notion of bitopological space and, independently, in 2015, by Naz, Shabir and Ali. In 2017, Hassan too introduced the concept of soft tritopological spaces and gave some first results. The notion of N-topological space related to ordinary topological spaces was instead introduced and studied, in 2011, by Tawfiq and Majeed. In this paper we introduce the concept of Soft N-Topological Space as generalization both of the concepts of Soft Topological Space and N-Topological Space and we investigate such class of spaces and their basic properties with particular regard to their subspaces, the parameterized families of crisp topologies generated by them and some new separation axioms called N-wise soft T0, N-wise soft T1, and N-wise soft T2.