ON TOPOLOGICAL EQ-ALGEBRAS

In this paper, by using a special family of filters $mathcal{F}$ on an EQ-algebra $E$, we construct a topology $mathcal{T}_{mathcal{mathcal{F}}}$ on $E$ and show that $(E,mathcal{T}_{mathcal{F}})$ is a topological EQ-algebra. First of all, we give some properties of topological EQ-algebras and investigate the interaction of topological EQ-algebras and quotient topological EQ-algebras. Then we obtain the form of closure of each subset and show that $(E,mathcal{T}_{mathcal{F}})$ is a zero-dimensional space. Finally, we introduce the concept of convergence of sequences on topological EQ-algebras and give a condition under which the limit of a sequence is unique.