The notion of SQV-map and IQV-map in a BM-algebra are introduced and the relation between them are studied. Using these notions, the binary oper-ation in BM-algebra is found to be uniformly continuous by constructing (pseudo) metric spaces. A quotient BM-algebra is constructed using the congruence relation induced by the IQV-map on it. The relation between the induced congruence relation and an ideal obtained from an IQV-map are studied. The condition under which two BM-algebras become homeomorphic is also derived by defining suitable IQV-maps on them. © 2020, Research Publication. All rights reserved.