Topology on Equality Algebras

Mona Aaly Kologani; Sogol Niazian; Rajab Ali Borzooei

doi:10.18778/0138-0680.2026.07

Authors

Mona Aaly Kologani Hatef Higher Education Institute, Zahedan, Iran Author https://orcid.org/0000-0002-5234-2876
Sogol Niazian TeMS. C, Islamic Azad University, Faculty of Medicine, Tehran, Iran Author https://orcid.org/0000-0002-1064-4139
Rajab Ali Borzooei Shahid Beheshti University, Faculty of Mathematical Sciences, Department of Mathematics, Tehran, Iran Author https://orcid.org/0000-0001-7538-7885

DOI:

https://doi.org/10.18778/0138-0680.2026.07

Keywords:

equality algebra, upset, topology, product topology, quotient topology

Abstract

In this paper, by special upsets on equality algebras, we construct a topology on bounded equality algebras and investigate some of their topological properties, such as Hausdorff, T₀-space, T₁-space and disconnected. In addition, we express the relation between closed and compact sets in this topology. Moreover, by considering the binary operation ↠ and constructing a topology on the bounded equality algebra E, we introduce the notion of semi-topological algebra and prove that any involutive equality algebra is a right semi-topological algebra and by some conditions it can be a semi-⋏-topological algebra. Also, we show that it is not necessarily a left semi-topological algebra. Finally, we investigate converse image, product and quotient topology on equality algebra and show that under what condition we can make finer topology.

Author Biography

Rajab Ali Borzooei, Shahid Beheshti University, Faculty of Mathematical Sciences, Department of Mathematics, Tehran, Iran

Additional Affiliations

Istinye University, Faculty of Engineering and Natural Sciences, Department of Mathematics, Istanbul, Turkiye

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