Fuzzy Homogeneous Bitopological Spaces

Abstract

We continue the study of the concepts of minimality and homogeneity in the fuzzy context. Concretely, we introduce two new notions of minimality in fuzzy bitopological spaces which are called minimal fuzzy open set and pairwise minimal fuzzy open set. Several relationships between such notions and a known one are given. Also, we provide results about the transformation of minimal, and pairwise minimal fuzzy open sets of a fuzzy bitopological space, via fuzzy continuous and fuzzy open mappings, and pairwise continuous and pairwise open mappings, respectively. Moreover, we present two new notions of homogeneity in the fuzzy framework. We introduce the notions of homogeneous and pairwise homogeneous fuzzy bitopological spaces. Several relationships between such notions and a known one are given. And, some connections between minimality and homogeneity are given. Finally, we show that cut bitopological spaces of a homogeneous (resp. pairwise homogeneous) fuzzy bitopological space are homogeneous (resp. pairwise homogeneous) but not conversely.