Some new properties on soft topological spaces
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In this paper, we introduce and study some new soft properties namely, soft $R_0$ and soft $R_1$($SR_i$, for short $i=0,1$) by using the concept of distinct soft points and we obtain some of their properties. We show how they relate to some soft separation axioms in [21]. Also we, show that the properties $SR_0 , {SR}_1$ are special cases of soft regularity. We further, show that in the case of soft compact spaces, ${SR}_1$ is equivalent to soft regularity. Finally, the relations between these properties in soft topologies and that in crisp topologies are studied. Moreover, some counterexamples are given.
Abstract
In this paper, we introduce and study some new soft properties namely, soft $R_0$ and soft $R_1$($SR_i$, for short $i=0,1$) by using the concept of distinct soft points and we obtain some of their properties. We show how they relate to some soft separation axioms in [21]. Also we, show that the properties $SR_0 , {SR}_1$ are special cases of soft regularity. We further, show that in the case of soft compact spaces, ${SR}_1$ is equivalent to soft regularity. Finally, the relations between these properties in soft topologies and that in crisp topologies are studied. Moreover, some counterexamples are given.
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