### Hausdorff Topological BE-algebras

#### Abstract

In this paper, we introduce the notion of (semi) topological BE-algebras and derive here conditions that imply a BE-algebra to be a (semi) topological BE-algebra. We prove that for each cardinal number $\alpha$ there is at least a (semi) topological BE-algebra of order $\alpha.$ Also we study separation axioms on (semi) topological BE-algebras and show that for any infinite cardinal number $\alpha$ there is a Hausdorff (semi) topological BE-algebra of order $\alpha$ with nontrivial topology.