##  [Urysohn Metrization Theorem](/urysohn-metrization-theorem) 

  ##  [Urysohn Metrization Theorem](https://puremath.quantumdictionary.io/urysohn-metrization-theorem-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A sufficient criterion for a topological space to admit a compatible metric: a second-countable, regular Hausdorff space (equivalently regular T1 with a countable base) is metrizable — there exists a metric that induces the given topology.