Connectedness, local connectedness, and components on bipolar soft generalized topological spaces

Volume 30, Issue 4, pp 302--321 http://dx.doi.org/10.22436/jmcs.030.04.01

Publication Date: February 09, 2023 Submission Date: December 02, 2022 Revision Date: December 27, 2022 Accteptance Date: January 18, 2023

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Authors

H. Y. Saleh - Department of Mathematics, College of Basic Education, University of Duhok, Duhok, 42001, Iraq. B. A. Asaad - Department of Computer Science, College of Science, Cihan University, Duhok, Iraq. - Department of Mathematics, Faculty of Science, University of Zakho, Zakho, 42002, Iraq. R. A. Mohammed - Department of Mathematics, College of Basic Education, University of Duhok, Duhok, 42001, Iraq.

Abstract

Connectedness represents the most significant and fundamental topological property. It highlights the main characteristics of topological spaces and distinguishes one topology from another. There is a constant study of bipolar soft generalized topological spaces (\( \mathcal{BSGTS}s \)) by presenting \(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}} \)-connected set and \(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}} \)-connected space in \(\mathcal{BSGTS}s\) as well as it is discussing some properties and results for these topics. Additionally, the notion of bipolar soft disjoint sets is put forward, \(\mathcal{BS} \) \(\widetilde{\widetilde{\mathfrak{g}}}\)-separation set, \(\widetilde{\widetilde{\mathfrak{g}}}\)-separated \(\mathcal{BSS}s\) and \(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}} \)-hereditary property. Moreover, there is an extensive study of \(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}} \)-locally connected space and \(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}} \)-component with some related properties and theorems following them, such as the concepts of \( \mathcal{BS} \) \(\widetilde{\widetilde{\mathfrak{g}}}\)-locally connected spaces and \( \mathcal{BS} \) \(\widetilde{\widetilde{\mathfrak{g}}}\)-connected are independent of each other; also determined the conditions under which the \( \mathcal{BS} \) \(\widetilde{\widetilde{\mathfrak{g}}}\)-connected subsets are \( \mathcal{BS} \) \(\widetilde{\widetilde{\mathfrak{g}}}\)-components.

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Keywords

• \(\mathcal{BSGTS}\)
• \( \widetilde{\widetilde{\mathfrak{g}}}\)-separated \(\mathcal{BSS}s\)
• \(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}}\)-connected set
• \( \mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}} \)-connected space
• \(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}}\)-locally connected space
• \(\mathcal{BS}\) \( \widetilde{\widetilde{\mathfrak{g}}}\)-component

MSC

•  03E75
•  54D05

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