الفهرس يوجد فقط 14 صفحة متاحة للعرض العام
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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.