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Urysohn's Metrization Theorem

Urysohn's metrization theorem states that for every topological T1-space X, the following conditions are equivalent.

1. X is regular and second countable,

2. X is separable and metrizable.

3. X is homeomorphic to a subspace of the Hilbert cube.

This entry contributed by Margherita Barile

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References

Willard, S. General Topology. Reading, MA: Addison-Wesley, p. 166, 1970.

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Urysohn's Metrization Theorem

Cite this as:

Weisstein, Eric W., with contributions by Margherita Barile. "Urysohn's Metrization Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/UrysohnsMetrizationTheorem.html

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