Axioms (Apr 2022)

Soft <i>Rω</i>-Open Sets and the Soft Topology of Soft <i>δ</i><sub>ω</sub>-Open Sets

  • Samer Al Ghour

DOI
https://doi.org/10.3390/axioms11040177
Journal volume & issue
Vol. 11, no. 4
p. 177

Abstract

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The author devotes this paper to defining a new class of soft open sets, namely soft Rω-open sets, and investigating their main features. With the help of examples, we show that the class of soft Rω-open sets lies strictly between the classes of soft regular open sets and soft open sets. We show that soft Rω-open subsets of a soft locally countable soft topological space coincide with the soft open sets. Moreover, we show that soft Rω-open subsets of a soft anti-locally countable coincide with the soft regular open sets. Moreover, we show that the class of soft Rω-open sets is closed under finite soft intersection, and as a conclusion, we show that this class forms a soft base for some soft topology. In addition, we define the soft δω-closure operator as a new operator in soft topological spaces. Moreover, via the soft δω-closure operator, we introduce soft δω-open sets as a new class of soft open sets which form a soft topology. Moreover, we study the correspondence between soft δω-open in soft topological spaces and δω-open in topological spaces.

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