Fμ-strongly semiopen sets, Fμ-strong semicontinuity and Fμ-strongly semiretracts

摘要

Throughout the literature, if (X,δ) is an F-ts, and Y⊂X, the induced F-topological subspace (Y,δY) is defined so that . Macho Stadler and de Prada Vicente [Fuzzy Sets and Systems 58 (1993) 365] introduced a new concept of F-topological subspaces, which coincides with the usual definition in the case that . Also, they introduced the concepts of Fμ-open sets and Fμ-continuity. In this paper, using the previous concepts, we introduce weaker forms of Fμ-open sets and Fμ-continuity. The notion of an F-retract was introduced by Rodabough [J. Math. Anal. Appl. 79 (1981) 273]. Here, we introduce the notion of a Fμ-retract and weaker forms of it. The basic properties of these notions are given. Many results are obtained.