On The Topological Structure Of Soft Sets And Related Results

Soft set theory is a new mathematical tool to deal with uncertain problems, whichis successfully applied to many fields and has made great achievements. In this paper,we give the concept of soft points and discuss their properties. We introduce softapproximation spaces. We study topological structure of soft set such as the internalstructure of soft topological spaces and the topological structure of soft approximatespaces.This paper is parted into four chapters.In the first chapter, we introduce background knowledge and the basic concepts ofsoft sets.In the second chapter, we give the concept of soft points, discuss their propertiesand prove the fact that soft sets can be translated into soft point sets and may beconveniently deal with soft sets as same as ordinary sets.In the third chapter, we reveal the internal structure of soft topological spaces anddiscuss soft continuousness.In the fourth chapter, we introduce soft approximate spaces, give two soft approx-imation operators and study the topological structure of soft approximate spaces.