Let M be either a topological manifold, a Hilbert cube manifold, or a Menger manifold and let D be an arbitrary countable dense subset of M . Consider the topological group H(M,D) which consists of all autohomeomorphisms of M that map D onto itself equipped with the compact-open topology. We present a complete solution to the topological classification problem for H(M,D) as follows. If M is a o...

Abstract. The purpose of the paper is to introduce and study the concepts of fuzzy generalized γ closed sets and study their basic properties in fuzzy topological spaces. Moreover, in this paper we define fuzzy γT1⁄2 spaces in which every fuzzy generalized γ continuous is fuzzy γ continuous. In addition, we have also introduced and studied fuzzy generalized γ connectedness and fuzzy generalized...

This paper investigates roughness of fuzzy soft sets. A pair of fuzzy soft rough approximations is proposed and their properties are given. Based on fuzzy soft rough approximations, the concept of fuzzy soft rough sets is introduced. New types of fuzzy soft sets such as full, intersection complete and union complete fuzzy soft sets are defined and supported by some illustrative examples. We obt...

‎in this paper, a new class of fuzzy sets called fuzzy strongly ${{g}^{*}}$-closed sets is introduced and its properties are investigated. moreover, we study some more properties of this type of closed spaces.

Recently, El-Naschie has shown that the notion of fuzzy topology may be relevant to quantum paretical physics in connection with string theory and E-infinity space time theory. In this paper, we study the concepts of r-fuzzy semi-I-open, r-fuzzy pre-I-open, r-fuzzy α-I-open and r-fuzzy β-I-open sets, which is properly placed between r-fuzzy openness and r-fuzzy α-I-openness (r-fuzzy pre-I-openn...

We show here some of our results on intuitionistic fuzzy topological spaces. In 1983, K.T. Atanassov proposed a generalization of the notion of fuzzy set: the concept of intuitionistic fuzzy set [1]. Some basic results on intuitionistic fuzzy sets were publised in [2,3], and the book [4] provides a comprehensive coverage of virtually all results until 1999 in the area of the theory and applicat...

This paper presents a general framework for the study of rough fuzzy sets in which fuzzy sets are approximated in a crisp approximation space. By the constructive approach, a pair of lower and upper generalized rough fuzzy approximation operators is first defined. The rough fuzzy approximation operators are represented by a class of generalized crisp approximation operators. Properties of rough...