# ON TOPOLOGICAL EQ-ALGEBRAS

Document Type: Research Paper

Authors

1 School of Mathematics, Northwest University, Xi'an,710127, China

2 School of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710119, China

Abstract

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.

Keywords

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