Studies on soft topological spaces

Abstract

Soft set is a completely generic mathematical tool for modeling uncertainties. Topology is a branch of mathematics, whose concepts exist not only in almost all branches of mathematics, but also in many real life applications. This paper mainly focuses on soft continuous functions and soft product topology. The concept soft homeomorphism and soft subbasis is also introduced and results based on these concepts are also obtained. It is also introduced the concept of soft connectedness and soft compactness. Moreover separation axioms on soft topological space are also studied and derived some relationship among these concepts.

On Soft Lebesgue Measure

“…Min [32] gave some results on soft topological spaces. There are several literature available on the structure of soft topological spaces [8], [10], [17], [18], [22], [39], [41], [43] and extended the idea of soft topology according to the definition of soft topology by Shabir, Naz and Cagman et al…”

On elementary soft compact topological spaces

“…Shabir and Naz [8] introduced the notion of soft topological space. Many authors studied on soft topological spaces and considered the concept of soft point [9][10][11][12][13][14][15]. Then, Das and Samanta introduced notions of soft element, soft reel set and number [16] and soft complex set and number [19] over soft sets.…”

A new approach for soft topology and soft function via soft element

“…The topological structures on the soft sets began to be studied after Shabir and Naz 4 . Many authors 5–21 studied on the soft topology and its properties, which are based on the notion of soft point. Later, Das and Samanta 22,23 brought forward the concepts of soft elements, soft real sets, soft real numbers and the elementary union ( ‐union), intersection ( ‐intersection), and complement ( ‐complement) operations over the soft sets.…”