Another generalization of the m-topology

Abstract

It is well known that the m I -topology is a generalization of the mtopology on C(X), see [1]. Given two subsets A, B ⊆ X such that A ∪ B = X, we are going to define a topology on C(X) namely the m (A,B) -topology, finer than the m-topology and C(X) with this topology becomes a topological ring. Connectedness in this space is studied and it is shown that if A, B are closed realcompact subsets of X, then the component of the zero function in C(X) with m (A,B) -topology is the ideal C K (X). Mathematics Subject Classification: 54C40