@article{Elostath_Mahdi_2020, title={Somewhere dense on upper bounded \(T_{0}\)-Alexandroff spaces}, volume={11}, url={https://m-sciences.com/?journal=jast&page=article&op=view&path[]=1636}, abstractNote={<p>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.</p>}, number={1-2}, journal={Journal of Advanced Studies in Topology}, author={Elostath, Lubna and Mahdi, Hisham}, year={2020}, month={Sep.}, pages={6–15} }