Metrizability of multiset topological spaces

Abstract

In this paper, we have investigated one of the basic topological properties, called Metrizability in multiset topological space. Metrizable spaces are those topological spaces that are homeomorphic to a metric space. So, we first, give the notion of metric between two multi-points in a nite multiset and studied some significant properties of a multiset metric space. The notion of metrizability is then studied by using this metric. Besides, Urysohn's lemma which is considered to be one of the important tools in studying some metrization theorems in topology is also discussed in context with multisets.