Kamal El-Saady

Modification of weak structures via hereditary classes

Abstract In this paper, we show that the construction arising from a generalized topology and a hereditary class introduced by A. Csaszar (2007) [9] remains valid, together with many applications, if the generalized topology is replaced by a weak structure.

The category of double fuzzy preproximity spaces

In this paper, we introduce the notions of double neighborhood systems and double fuzzy preproximity in double fuzzy topological spaces. We used double neighborhoods to study the initial structure of double fuzzy topological spaces, and the joins between them and the initial structures of double fuzzy preproximity spaces. Furthermore, we have proved that the category of double fuzzy preproximity spaces is a topological category, and hence a topological construct.

Double Fuzzy Preproximity Spaces

In this paper, we introduce the concept of double fuzzy preproximity spaces as a generalization of a fuzzy preproximity spaces and investigate some of their properties. Also we study the relationships between double fuzzy preproximity spaces, double fuzzy topological spaces and double fuzzy closure spaces. In addition to this was the introduction of the concept of double fuzzy neighborhood system and has been studying the connection with double fuzzy preproximity, which resulted in the definition of the concept double fuzzy preproximal neighborhood.

Fuzzy proximity ordered spaces

In 1976 Singal and Lal extended the study of nearness between sets to the Nachbins [1965] topological and order structures. Also, in 1978 Dimitrijevic developed such an idea, in the same manner, with more study of its properties. The aim of this paper is to introduce the idea of order in a fuzzy proximity space (Katsaras, 1979, 1980, 1980) and construct new spaces in the area of fuzzy topological and order structures, the so-called fuzzy proximity ordered spaces. Also, we study some properties of these spaces.

Bicompletion of Lowen fuzzy quasi-uniform spaces

This paper is devoted to the construction of a bicompletion of Lowen fuzzy quasi-uniform spaces (or just [0,1]-fuzzy quasi-uniform spaces in this paper) and the study of that bicompletion, which appears to have a number of properties that one could resonably expect in analogy to the situation in ordinary quasi-uniform spaces, i.e., denseness of the original spaces in its bicompletion, extension property of quasi-uniformly continuous maps.

A non-commutative approach to uniform structures

This paper presents a theory of uniform-type structures in the non-commutative sense. The theory comprises the theory of covering-uniformities for quantales as a generalization of the classical theory of covering-uniformities for frames. Also, by introducing quantale-valued covers of a set, we present a general framework for uniform structures on very general L-valued spaces (for L a quantale). The categories of (covering) uniform quantales and L-valued uniform spaces here introduced and the adjunction between them is studied.