Jiang Yang - School of Mathematics, Northwest University, Xi&#۰۳۹;an,۷۱۰۱۲۷, China
Xiao Long Xin - School of Mathematics, Northwest University, Xi&#۰۳۹;an,۷۱۰۱۲۷, China
Peng Fei He - School of Mathematics and Information Science, Shaanxi Normal University, Xi&#۰۳۹;an, ۷۱۰۱۱۹, China

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.

Topological EQ-algebra, System of filters, Cauchy sequence