A Quasi-Uniformity on BCC-algebras

Abstract

We introduce a quasi uniformity U on a BCC-algebra X by a family of ideals of X. If T(U) is the topology induced by U, we study some conditions under which (X,T(U)) becomes a (semi) topological BCC-algebra. Also, we show that bicompletion of the quasi uniformity U can be considered a T(U*)-topological BCC-algebra which contains X as a sub-dense space.