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On soft topological spaces. (English) Zbl 1219.54016
Summary: We introduce soft topological spaces which are defined over an initial universe with a fixed set of parameters. The notions of soft open sets, soft closed sets, soft closure, soft interior points, soft neighborhood of a point and soft separation axioms are introduced and their basic properties are investigated. It is shown that a soft topological space gives a parametrized family of topological spaces. Furthermore, with the help of an example it is established that the converse does not hold. The soft subspaces of a soft topological space are defined and inherent concepts as well as the characterization of soft open and soft closed sets in soft subspaces are investigated. Finally, soft ${T}_{i}$-spaces and notions of soft normal and soft regular spaces are discussed in detail. A sufficient condition for a soft topological space to be a soft ${T}_{1}$-space is also presented.

##### MSC:
 54A40 Fuzzy topology 54D10 Lower separation axioms (${T}_{0}$–${T}_{3}$, etc.)