A study on metrizability in M-topology

Résumé

Metrization is one of the most vital topological property as every metric space induces a topology on it but the converse may not be true always. So its natural to raise the question that when a topological space is metrizable in the multiset context. This paper primarily aims to give the answer for the query along with relavent notions. Also, the version of Nagata-Smirnov Metrization Theorem which gives an equivalent condition to metrizability of a topological space in general topology is studied in this environment by introducing some metrics in $\mathbb R_M^m$.