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.

Soft N-Topological Spaces

This paper defines the base of soft topology, studies the properties of base. We give the definition of the product over the soft topological space, and discuss the relative properties of soft topological product space, and finally generate these results to the soft rough topological space.

Soft topological product space

Characterizations of several soft covering properties

In this article, we introduce the concept of soft intervals, soft ordering and sequences of soft real numbers and study their properties and some interesting results. Also the notion of soft Lebesgue measure on the soft real numbers has been introduced. A correspondence relationship between the soft Lebesgue measure and the Lebesgue measure has been established.

/pdf/on-soft-lebesgue-measure-3hdh6ba230.pdf

On Soft Lebesgue Measure

In this paper, we further discuss soft compactness and soft separation axioms in the soft topological space over the rough soft formal context T = (G;M;R; F). We define the compact soft topological space , give soft separation axioms of soft rough topological space and study their relationship in the soft topological space over the rough soft formal context.

Soft Compactness and Soft Topological Separate axioms

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Soft Compactness and Soft Topological Separate axioms