On soft topological spaces

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• 作者：Muhammad Shabir ; ^a ; ^{mshabirbhatti@yahoo.co.uk} ; Munazza Naz^a ; ^{munazzanaz@yahoo.com}
• 关键词：Soft sets ; Soft topology ; Open sets ; Closed sets ; Topological spaces ; Separation axioms
• 刊名：Computers and Mathematics with Applications
• 出版年：2011
• 出版时间：April 2011
• 年：2011
• 卷：61
• 期：7
• 页码：1786-1799
• 全文大小：267 K

文摘

In the present paper we introduce soft topological spaces which are defined over an initial universe with a fixed set of parameters. The notions of soft open sets, soft closed sets, soft closure, soft interior points, soft neighborhood of a point and soft separation axioms are introduced and their basic properties are investigated. It is shown that a soft topological space gives a parametrized family of topological spaces. Furthermore, with the help of an example it is established that the converse does not hold. The soft subspaces of a soft topological space are defined and inherent concepts as well as the characterization of soft open and soft closed sets in soft subspaces are investigated. Finally, soft T_i-spaces and notions of soft normal and soft regular spaces are discussed in detail. A sufficient condition for a soft topological space to be a soft T₁-space is also presented.