Nucleus topology in equality algebras

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. Finally, the relations between the two topologies in quotient equality algebras are revealed.

کلیدواژه ها:

Equality algebra ، nucleus map ، topology ، compactness ، connectedness ، quotient topology