الفهرس | يوجد فقط 14 صفحة متاحة للعرض العام |
المستخلص A large part of mathematics is based on the notions of a set and mappings. Mappings on topological spaces are important tools for studying topological properties and for constructing new spaces from previously existing ones. More types of continuous, open and closed mappings arise as one goes further in mathematics. In 1980, Bandler and Kohout [3] introduced several new compositions of relations, the triangular compositions, with interesting applications. De Bates and Kerre in [6] have improved their definitions and applied similar ideas on the concept of the direct image of a set under a relation, leading to new ones: the subdirect and superdirect images. In [7] they have extended the improved compositions to fuzzy relations. A new and weaker form of continuity called “subcontinuity”, based on the subinverse images of a set under a mapping, is introduced and studied. In similar way the subinverse image of a fuzzy set under a mapping leads to the definition of fuzzy subcontinuity. As a continuation to study a framework of continuous mappings, our purpose here is to investigate some further types of continuous mappings. This thesis breaks into: a preface, three chapters, and a list of references. In chapter 1, we attempt to cover fundamental concepts; definitions and known results concerning our object to make this study more completed and clear. In chapter 2, we establish the concepts of subcontinuity and supercontinuity and study their properties in general topology and fuzzy topology. The compositions laws for continuous and subcontinuous mappings are discussed. By the end of this chapter, some weaker forms of subcontinuity are introduced . Chapter 3, is devoted to introduce the concepts of subcontinuity and supercontinuity and study some of their properties in fuzzifying topology. Finally, the compositions laws for continuous and subcontinuous mappings are also discussed. |