Smirnov metrization theorem

The Smirnov metrization theorem establishes necessary and sufficient conditions for a topological space to be metrizable. The theorem reduces questions of metrizability to paracompactness and a local metrizability condition.

Definition: A space $X$ is locally metrizable if every point $x\\in X$ has a neighborhood that is metrizable in the subspace topology.

Theorem (Smirnov metrization theorem): A space is metrizable if and only if it is paracompact and locally metrizable.

单词	SmirnovMetrizationTheorem
释义	Smirnov metrization theorem The Smirnov metrization theorem establishes necessary and sufficient conditions for a topological space to be metrizable. The theorem reduces questions of metrizability to paracompactness and a local metrizability condition. Definition: A space $X$ is locally metrizable if every point $x\\in X$ has a neighborhood that is metrizable in the subspace topology. Theorem (Smirnov metrization theorem): A space is metrizable if and only if it is paracompact and locally metrizable.
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