Topology on Equality Algebras

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.