General topology
Metrizability theory

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 (X, τ) {\displaystyle (X,\tau)} is said to be metrizable if there is a metric

such that the topology induced by d is τ {\displaystyle \tau }. Metrization theorems are theorems that give sufficient conditions for a topological space to be metrizable.
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