cs-模糊赋范空间的模糊拓扑结构-基础数学专业毕业论文.docx

Abstract
Abstract
In【3l( (2)(2006)255-265),Chelvam and Singadurai intro— duced a new definition of fuzzy normed space and studied some of its fuzzy topo— logical order tO distinguish other definitions of fuzzy normed spaces,in this paper,we call the fuzzy normed space defined by Chelvam and Singaduraj be the CS—fuzzy normed this paper the work on launch the structure of
normcd space.
(1)In Chapter 1,as preliminaries,we will first review some basic definitions
on fuzzy topology,/-topological vector space and normed also introduce some preliminary then,several lemmas are ,
with our study,we know that the/-topology鼠on the fuzzy normcd space(X,N,木)
constructed by Chelvam and Singadurai【3]patible with the linear structure on
X,that is,(X,N,牢)is not an/-topological vector space with respect to the/-topology
磊.
(2)In Chapter 2,we prove that(X,。‰)constructed by Chelvam and Singadurai
【3】is not patible with the linear structure on X,that is,(X,N,半)is not an,. topological vector space with respect tO the/-topology。‰.Therefore,a main result in Chelvam and Singadurai’S article,.,Theorem is the analysis of the reasons for such errors will be show in this papeL
(3)In Chapter 3,through the defimtion of&.open sphere on CS—fuzzy normed
space in[3】,we construct a new/- prove the new/-topology tO be
.a locally convex/-topological vector addition,we also study some natures of the new/-topological vector space on(X,N,rain).
Keywords:CS—fuzzy normed space;/-topology; base;I. topological vector space;Locally convex/-topological vector space.
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