Fuzzy orbit topological spaces

Abstract

The concept of fuzzy orbit open sets under the mapping f:X → X in a fuzzy topological space (X,τ) was introduced by Malathi and Uma (2017). In this paper, we introduce some conditions on the mapping f, to obtain some properties of these sets. Then we employ these properties to show that the family of all fuzzy orbit open sets construct a new fuzzy topology, which we denoted by τF0 coarser than τ. As a result, a new fuzzy topological space (X, τF0) is obtained. We refer to this topological space as a fuzzy orbit topological space. In addition, we define the notion of fuzzy orbit interior (closure) and study some of their properties. Finally, the category of fuzzy orbit topological spaces is defined, and we prove it can be embedded in the category of fuzzy topological spaces .