Some stronger forms of fuzzy continuous mapping on fuzzy topological spaces

Completely continuous functions in intuitionistic fuzzy topological spaces

Abstract: In this paper, after giving the basic results related to the product of functions and the graph of functions in intuitionistic fuzzy topological spaces, we introduce and study the concept of fuzzy completely continuous functions between intuitionistic fuzzy topological spaces.

On fuzzy t-continuous mappings

Abstract: The concepts of fuzzy almost continuous, fuzzy θ-continuous and fuzzy weakly continuous mappings have been introduced by Yalvac and by Mukherjee and Sinha. The aim of this paper is mainly to study and to find the mutual interrelations among these concepts.

Fuzzy semi-preopen sets and fuzzy semi-precontinuous mappings

Abstract: The aim of this paper is to introduce and discuss the concepts of fuzzy semi-preopen sets and fuzzy semi-precontinuous mappings.

Fuzzy semiregularization topologies and fuzzy submaximal spaces

Abstract: The aim of the paper is to investigate the fuzzy semiregularization spaces associated with fuzzy topological spaces. The concept of fuzzy submaximal spaces is introduced and it is proved that corresponding to every fuzzy topological space, there always exists a fuzzy submaximal space which is an expansion of the given space. Fuzzy submaximal and semiregular spaces are shown to be closely associated with those spaces which are minimal or maximal with respect to certain types of properties which we call fuzzy semiregular properties. This has induced us to take up different properties for investigation whether these are fuzzy semiregular ones. Lastly we consider certain mappings between fuzzy topological spaces and study their behaviour when either or both the domain and codomain spaces are replaced by their semiregulatization spaces.

Fuzzy weakly completely continuous functions

Abstract: A new class of functions, called fuzzy weakly completely continuous functions, is introduced as generalization of fuzzy completely continuous functions. The concepts of fuzzy R-map and fuzzy faintly continuous function are also introduced and their relationships with fuzzy weakly completely continuous functions are investigated. The composition of fuzzy weakly completely continuous functions and its properties are studied. The concept of fuzzy extremally disconnected space is also introduced.

Fuzzy topology. II. Product and quotient spaces

Abstract: In [6], after introducing the fundamental concepts of fuzzy points which take crisp singletons or ordinary points as special cases, q-relations and Q-neighborhoods of fuzzy points, we built up a satisfactory theory of neighborhood structures and generalized many fundamental notions and theorems, especially those theorems in the theory of Moore-Smith’s convergence such as those contained in [5, Chaps. I, II]. The purpose of the present paper is to generalize all the ehtorems concerning product spaces and quotient spaces contained in [5, Chap. III]..Our treatment will sharpen the related results contained in the literature [l-4] so that these problems in fuzzy topology will be solved to the same degree as the corresponding ones in general topology. The present work is the continuation of [6] and hence all the conventions in [6] still hold good in the present paper, especially that (X, r) and (Y, %) d enote fuzzy topological spaces.