ON TOPOLOGICAL EQ-ALGEBRAS

In this paper, by using a special family of lters F on an EQ- algebra E, we construct a topology TF on E and show that (E; TF) 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; TF) 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.