Topology On BCK-Modules

Abstract

In this paper, we introduce the notion of a BCK-topological module in a natural way and establish that every decreasing sequence of submodules on a BCK-module M over bounded commutative BCK-algebra X is indeed a BCK- topological module. We have defined the notion of compatible and strict BCK- module homomorphisms, and establish that a strict BCK-module homomorphism is an open as well as a continuous mapping. Also, we establish the necessary and sufficient condition for a compatible mapping to be strict.