metricizability
Metricizability refers to the property of a topological space that allows it to be equipped with a metric that induces the same topology. A topological space is called metricizable if there exists a metric d on its underlying set X such that the open sets generated by d are precisely the open sets of the topology of X.
The existence of a metric for a topological space is a significant structural property. Spaces that admit
There are several important characterizations of metricizable spaces. One of the most well-known is the Urysohn
The study of metricizability is important because many mathematical constructions and theorems are naturally defined for