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Khalaf, Alias B.; Ahmed, Nehmat K.; Hamko, Qumri H.

Soft separation axioms and functions with soft closed graphs. (English) Zbl 1485.54003

Proyecciones 41, No. 1, 177-195 (2022).
Summary: Several notions on soft topology are studied and their basic properties are investigated by using the concept of soft open sets and soft closure operators which are derived from the basics of soft set theory established by D. Molodtsov [Comput. Math. Appl. 37, No. 4–5, 19–31 (1999; Zbl 0936.03049)]. In this paper we introduce some soft separation axioms called Soft \(R_0\) and soft \(R_1\) in soft topological spaces which are defined over an initial universe with a fixed set of parameters. Many characterizations and properties of these spaces are found. Necessary and sufficient conditions for a soft topological space to be a soft \(R_i\) for \(i = 0, 1\) space are also presented. Furthermore, the concept of functions with soft closed graph and soft cluster sets are defined. Many results on theses two concepts are proved also it is proved that a function has a soft closed graph if and only if its soft cluster set is degenerate.

Cited in 1 Document

MSC:

54A05 Topological spaces and generalizations (closure spaces, etc.)
54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
54C05 Continuous maps
54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)

Keywords:

soft open set; soft \(T_1\) space; soft \(R_i\) space \(i = 0,1\); soft graph; soft cluster set; soft kernel

Citations:

Zbl 0936.03049
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Full Text: DOI

References:

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