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More notions and mappings via somewhere dense sets

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Abstract

In this paper, the authors continue studying more properties of somewhere dense sets. They derive some interesting results related to them such as the collection of all somewhere dense subsets of a strongly hyperconnected space \((X,\tau )\) forms a filter on X, and a topological space which contains at least two disjoint somewhere dense sets is an \(ST_1\)-space. Then they introduce and study a concept of S-limit points of a soft set. Depending on somewhere dense and cs-dense sets, they also define and investigate various maps between topological spaces, namely SD-continuous, SD-irresolute, SD-open, SD-closed and SD-homeomorphism maps.

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Acknowledgements

The authors are grateful to the anonymous referees for their useful comments on the paper.

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Authors and Affiliations

  1. Department of Mathematics, Sana’a University, Sanaa, Yemen

    T. M. Al-shami

  2. 2949-1 Shiokita-cho, Hinagu, Yatsushiro, Kumamoto, 869-5142, Japan

    T. Noiri

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  1. T. M. Al-shami
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  2. T. Noiri
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Correspondence to T. M. Al-shami.

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Al-shami, T.M., Noiri, T. More notions and mappings via somewhere dense sets. Afr. Mat. 30, 1011–1024 (2019). https://doi.org/10.1007/s13370-019-00700-4

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