Urysohn Metrization Theorem
If a topological space $X$ satisfies a certain countability axiom (the second) and a certain separation axiom (the regularity axiom), then $X$ can be imbedded in a metric space and is thus metrizable.
- nLab - Urysohn Metrization Theorem
- Urysohn's Metrization Theorem - University of Toronto Mathematics (pdf)
- University of Arizona Mathematics (pdf)
- Munkres, James R. Topology, 2015. pg. 187.