Somewhere dense on upper bounded \(T_{0}\)-Alexandroff spaces

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Lubna Elostath
Hisham Mahdi


Studying different types of generalized open sets is a major area of research in topology during the last few decades. In this paper, we study somewhere dense sets and\( swd\)-continuity on upper-bounded \(T_{0}\)-Alexandroff spaces. We introduce and investigate various types of generalized somewhere dense; namely \(^{*}sw\)-dense, \(sw^{*}\)-dense, and \(sw^{**}\)-dense. We prove that a subset \(A\) of a topological space is preclosed if and only if it is \(p^{*}gp\)-closed sets. We give a characterization for a set \(A\) to be pre\(^{*}\)-closed.


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Elostath, L. ., & Mahdi, H. . (2022). Somewhere dense on upper bounded \(T_{0}\)-Alexandroff spaces. Journal of Advanced Studies in Topology, 11(1-2), 6–15. Retrieved from
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