| Summary: | In this paper, we define soft <inline-formula> <math display="inline"> <semantics> <mi>ω</mi> </semantics> </math> </inline-formula>-open sets and strongly soft <inline-formula> <math display="inline"> <semantics> <mi>ω</mi> </semantics> </math> </inline-formula>-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 <inline-formula> <math display="inline"> <semantics> <mi>ω</mi> </semantics> </math> </inline-formula>-open sets in soft topological spaces. Also, we study the relationships between the <inline-formula> <math display="inline"> <semantics> <mi>ω</mi> </semantics> </math> </inline-formula>-open sets of a given indexed family of topological spaces and the soft <inline-formula> <math display="inline"> <semantics> <mi>ω</mi> </semantics> </math> </inline-formula>-open sets (resp. strongly soft <inline-formula> <math display="inline"> <semantics> <mi>ω</mi> </semantics> </math> </inline-formula>-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 <inline-formula> <math display="inline"> <semantics> <mi>ω</mi> </semantics> </math> </inline-formula>-open sets, we characterize soft Lindelof (resp. soft weakly Lindelof) soft topological spaces.
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