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.

Keywords:

Topological EQ-algebra , System of filters , Cauchy sequence