Geodesic
Soft maps via soft somewhere dense sets
Filomat, Tome 34 (2020) no. 10, p. 3429

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DOI

The concept of soft sets was proposed as an effective tool to deal with uncertainty and vagueness. Topologists employed this concept to define and study soft topological spaces. In this paper, we introduce the concepts of soft SD-continuous, soft SD-open, soft SD-closed and soft SD-homeomorphism maps by using soft somewhere dense and soft cs-dense sets. We characterize them and discuss their main properties with the help of examples. In particular, we investigate under what conditions the restriction of soft SD-continuous, soft SD-open and soft SD-closed maps are respectively soft SD-continuous, soft SD-open and soft SD-closed maps. We logically explain the reasons of adding the null and absolute soft sets to the definitions of soft SD-continuous and soft SD-closed maps, respectively, and removing the null soft set from the definition of a soft SD-open map.
DOI : 10.2298/FIL2010429A
Classification : 54C08, 54C10, 54B10
Keywords: Soft somewhere dense set, soft cs-dense set, soft SD-continuous map, soft SD-open map, soft SD-closed map, soft SD-homeomorphism map, restricted soft map 
Tareq M Al-Shami; Ibtesam Alshammari; Baravan A Asaad. Soft maps via soft somewhere dense sets. Filomat, Tome 34 (2020) no. 10, p. 3429 . doi: 10.2298/FIL2010429A
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     title = {Soft maps via soft somewhere dense sets},
     journal = {Filomat},
     pages = {3429 },
     year = {2020},
     volume = {34},
     number = {10},
     doi = {10.2298/FIL2010429A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2010429A/}
}
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