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