On Pairwise λ-Open Soft Sets and Pairwise Locally Closed Soft Sets

  • Kandil Kandil Department of Mathematics, Faculty of Science, Helwan University, Helwan, Egypt
  • O. A. E. Tantawy Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
  • S. A. El-Sheikh Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt
  • Shawqi. A. Hazza Department of Mathematics, Faculty of Education, Taiz University, Taiz, Yemen
Keywords: Soft set, Soft topology, Soft bitopology, Soft bitopological spaces, Pairwise soft separation axioms, - closed soft sets, Pairwise -open soft sets, and - locally closed soft sets.

Abstract

Kandil and his colleagues [10], introduced the notion of -closed soft set by involving -soft set and -closed soft set. In this paper, we give some additional properties of -closed soft sets. We also introduce and study a related new class of -spaces which lies between  and  . Moreover, we show that there exists a very important relation between the notion of -closed soft sets and the  property, ,  , . In addition, we offer the notion of -locally closed soft sets and we investigate a related new pairwise soft separation axiom  which is independent from . The relationships between the -closed soft sets and the -locally closed soft sets are obtained. Furthermore, we introduce the notion of -open soft sets and we construct supra soft topology associated with the class of -open soft sets and we present pairwise soft separation axioms related to such soft sets, namely . We provide some illustrative examples to support the results.

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Published
2017-03-01
Section
Articles