Metrizable space

In topology and related areas of mathematics, a metrizable space is a topological space that is homeomorphic to a metric space. That is, a topological space ${\displaystyle (X,\tau )}$ is said to be metrizable if there is a metric ${\displaystyle d:X\times X\to [0,\infty )}$ such that the topology induced by ${\displaystyle d}$ is ${\displaystyle \tau .}$ Metrization theorems are theorems that give sufficient conditions for a topological space to be metrizable.