Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 25 1 2026 07 01 Nucleus topology in equality algebras 106967 10.48308/cgasa.2026.243407.1601 EN Sogol Niazian Faculty of Medicine, Tehran Medical Sciences, Islamic Azad University, Tehran, Iran Rajab Ali Borzooei Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran Mona Aaly Kologani Hatef Higher Education Institute, Zahedan, Iran 0000-0002-5234-2876 Journal Article 2026 02 03 In this paper, we define the concept of nucleus map on equality algebras and study related results. Then, using this concept and upsets, a topology on equality algebras is constructed and it is shown that the equality algebra with this topology becomes a topological space. In addition, some properties of topological space such as compactness and connectedness are investigated. Moreover, we study the continuity of all operations with respect to the topology on equality algebras. <br>Finally, the relations between the two topologies in quotient equality algebras are revealed. Equality algebra nucleus map topology compactness connectedness quotient topology https://cgasa.sbu.ac.ir/article_106967_b43aadb7a6768920486ff2a7302d7901.pdf