Subject: QA Mathematics
Year: 2022
Type: Article
Type: NonPeerReviewed
Title: CHARACTERIZATION OF ISOLATED POINTS IN T1 SPACES USING CHAINS
Author: DURMISHI, Emin
Author: MISAJLESKI, Zoran
Author: RUSHITI, Agim
Author: SADIKI, Flamure
Author: IBRAIMI, Alit
Abstract: By the standard definition, a point x is an isolated point in a topological space if its corresponding one-element set is open. Here it is characterized the notion of isolated point using chains and open covers of the space. Namely, x is an isolated point in a T1 topological space if there exists an open covering of the space such that for any point of the space different from x, there is no chain in the covering joining it with the point x. Equivalently, it is provided a characterization of isolated point using the notion of pair of chain separated sets relatively a T1 space, while when using the notion of pair of weakly chain separated sets relatively a T1 space it is shown that only the sufficiency of the claim holds. Using these results, it is provided a characterization of discrete topological spaces and it is reproved that every compact Hausdorff space without isolated points is uncountable.
Publisher: Faculty of Natural Sciences and Mathematics
Relation: https://eprints.unite.edu.mk/1065/
Identifier: oai:eprints.unite.edu.mk:1065
Identifier: https://eprints.unite.edu.mk/1065/1/JNSM%2013-14%20e%20formatuar-108-113.pdfIdentifier: DURMISHI, Emin and MISAJLESKI, Zoran and RUSHITI, Agim and SADIKI, Flamure and IBRAIMI, Alit (2022) CHARACTERIZATION OF ISOLATED POINTS IN T1 SPACES USING CHAINS. Journal of Natural Sciences and Mathematics of UT, 7 (13-14). pp. 108-113. ISSN 2671-3039
