Abstract
In this paper, we define soft ω -open sets and strongly soft ω -open sets as two new classes of soft sets. We study the natural properties of these types of soft sets and we study the validity of the exact versions of some known results in ordinary topological spaces regarding ω -open sets in soft topological spaces. Also, we study the relationships between the ω -open sets of a given indexed family of topological spaces and the soft ω -open sets (resp. strongly soft ω -open sets) of their generated soft topological space. These relationships form a biconditional logical connective which is a symmetry. As an application of strongly soft ω -open sets, we characterize soft Lindelof (resp. soft weakly Lindelof) soft topological spaces.
Highlights
The soft set introduced by Molodtsov [1] is applied in many fields such as economics, engineering, social science, medical science, etc
A is called an ω-closed subset of X if it contains all its condensation points, A is called an ω-open subset of X if X − A is ω-closed
It is well known that =ω forms a topology on X finer than
Summary
The soft set introduced by Molodtsov [1] is applied in many fields such as economics, engineering, social science, medical science, etc. When we define a reasonable generalization of soft open sets in topological spaces, we hope that this will open the door for a number of future related research. Symmetry 2020, 12, 265 soft open sets in soft topological spaces, soft semiopen sets were defined in [44], many related research articles have appeared, for instance, [45,46,47,48,49,50]. We will study the relationships between the ω-open sets of a given indexed family of topological spaces and the soft ω-open sets of their generated soft topological space These relationships form a biconditional logical connective which is a symmetry. We characterize soft weakly Lindelof sets STS’s which are strongly soft anti-locally countable via sω-open sets
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