F. H. Khedr

On pairwise super continuous mappings in bitopological spaces

The aim of this paper is to define and study super-continuous mappings and some other forms of continuity such as strong continuity, perfect continuity and complete continuity in bitopological spaces and investigate the relations between these kinds of continuity and their effects

On seperation axioms in fuzzifying topology

Abstract In the present paper we introduce R 0 - and R 1 -separation axioms in fuzzifying topology and study their relations with T 1 - and T 2 -separation axioms, respectively. Furthermore, we introduce and study semi- T 0 -, semi- R 0 -, semi- T 1 -, semi- R 1 -, semi- T 2 (semi-Hausdorff)-, semi- T 3 (semi-regularity)- and semi- T 4 (semi-normality)-separation axioms in fuzzifying topology and give some of their characterizations as well as the relations of these axioms and other separation axioms in fuzzifying topology introduced by Shen, Fuzzy Sets and Systems 57 (1993) 111–123.

a -continuity and ca -continuity in fuzzifying topology

The concepts of α-continuity and cα-continuity are considered and studied in fuzzifying topology and by making use of these concepts, some decompositions of fuzzy continuity are introduced. It is proved that the family of all α-sets in fuzzifying topology may not be a fuzzifying topology.

Fuzzy s-continuous functions and semilocally connected fuzzy topological spaces

Abstract The concept of s-continuous functions (Kohli, 1978) is translated in fuzzy setting into two concepts, fuzzy s-continuous functions and fuzzy os-continuous functions. The concepts of semiconnected functions (Kohli, 1978) and semilocally connected spaces (Kohli, 1978) do the same. Interactions between those concepts in fuzzy setting and fuzzy continuity (Chang, 1968) are discussed. Also, characterizations of semilocally connected and semilocally o-connected fuzzy topological spaces in terms of fuzzy s-continuous functions and fuzzy os-continuous functions, respectively, are obtained.

A classification of types of extensions from TOP to QFTOP

Abstract By making use of the concept of the introduced quasi-fuzzy topological space [C.-Y. Zheng, Fuzzy Sets and Systems 14 (1984) 273–280], we introduce the concept of s-extensions. Mainly, we generalize and characterize the concepts of good extensions [R. Lowen, J. Math. Anal. Appl. 56 (1976) 621–633], weak inducement [H.W. Martin, J. Math. Anal. Appl. 78 (1980) 634–639] and s-extensions by introducing some relations between the category of topological spaces and the category of quasi-topological spaces.