A Study on Soft Set Topological Spaces

Abstract

ABSTRACT newlineThe aim of the thesis is to extend the study of the properties of soft sets in soft topological spaces via soft open set and soft closed set. It was established that every (F_A,and#964; and#771;)is a soft topological space [Çaand#287;man et al (2011)]. A soft topology on F_A, denoted by and#964; and#771;, is a collection of soft subsets of F_A which satisfy (i) F_A, F_and#8709;and#8712;and#964; and#771;, (ii) {F_(A_i ) and#9508; and#61645; and#771;F_A : iand#8712;I and#61645; and#771;and#9500; N} and#61645; and#771;and#964; and#771;and#8658;U and#771;_(iand#8712;I) F_(A_i )and#8712;and#964; and#771; and (iii) {F_(A_i ) and#9508; and#61645; and#771;F_A :1and#8804;iand#8804; n, nand#8712;and#9500; N} and#61645; and#771;and#964; and#771;and#8658;and#8745; and#771;_(i=1)^n F_(A_i )and#8712;and#964; and#771;. newlineIn this dissertation, we study soft set, union of two soft sets, intersection of two soft sets, soft subset, soft equal set, null soft set, relative complement soft set, absolute soft set, soft topology, soft topological space, soft open set, soft closed set, soft interior and soft closure, etc.,. in a soft topological space (F_A,and#964; and#771;)and give various decompositions of soft open sets. In the first chapter, we give all the definitions and results which are essential for the development of the dissertation. newlineSoft subsets play an important role in Soft topological spaces. We derive some properties of the soft and#945;and#8722;open sets and soft and#945;and#8722;closed sets in a soft topological space (F_A,and#964; and#771;). Various kinds of soft semi-open sets, soft semi-closed sets were defined and discuss the relation between these soft sets. Next, we define the extension of soft pre-open sets and soft pre-closed sets in a STS. Next, we define the extension of soft b open sets and soft b closed setsin a STS. We then define soft and#946;-open sets, soft and#946;-closed sets, in terms of (F_A,and#964; and#771;). newlineUsing soft generalized closed sets, we extend the study of soft g closed sets and soft g open sets, a decomposition of soft g closed sets and soft g open sets in a soft topological spaces (F_A,and#964; and#771;). Next, we define soft g* closed sets and soft g* closure, soft g* interior and a decomposition in terms of (F_A,and#964; and#771;). newlineFinally, we define the soft swg closed sets, soft swg open sets, characterization were given and a decomposition in STS of (F_A,and#964; and#771;). newline