Some Local Properties of Soft Semi-Open Sets

Soft set theory [1] was firstly introduced byMolodtsov in 1999 as a general mathematical tool for dealing with uncertain, fuzzy, not clearly defined objects. He has shown several applications of this theory in solvingmany practical problems in economics, engineering, social science, medical science, and so forth, in [1]. In the recent years, papers about soft sets theory and their applications in various fields have been writing increasingly [2–6]. Shabir and Naz [7] introduced the notion of soft topological spaces which are defined over an initial universe with a fixed set of parameters. The authors introduced the definitions of soft open sets, soft closed sets, soft interior, soft closure, and soft separation axioms. And the authors got some important results for soft separation axioms.The results are valuable for research in this field. Tanay and Kandemir [8] introduced the definition of fuzzy soft topology over a subset of the initial universe set while Jun et al. [9] studied the ideal theory in BCK/BCI-Algebras based on soft sets. Along the line of Shabir and Naz, Chen introduced the notations of soft semi-open sets in soft topological spaces in [10]. In the present study, we introduce some local properties by soft semi-open sets. For example, soft semi-neighborhoods of the soft point, soft semi-first-countable spaces, and soft semi-pu-continuous at the softpoint are given.And some of their properties are studied.