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Topological spaces and soft sets. (English) Zbl 1218.54018

Summary: We establish some relations between topology and soft set theory. Our work is to give some characterizations of trivial (resp., discrete, \(T_0\), \(T_1\)-, \(T_D\)- and \(R_0\)-) topological spaces by the null soft set, the absolute soft set, the identical soft set and so on. Our results may be useful in the application research of classical topology.

MSC:

54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
54A05 Topological spaces and generalizations (closure spaces, etc.)
54H99 Connections of general topology with other structures, applications
03E47 Other notions of set-theoretic definability
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