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completely metrizable (Definition)

Let $ X$ be a topological space. $ X$ is said to be completely metrizable if there is a metric $ d$ on $ X$ under which $ X$ is complete.

In particular, a completely metrizable space is metrizable.



"completely metrizable" is owned by Evandar.
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Other names:  complete metrizability, topologically complete, topological completeness
Keywords:  topology
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Cross-references: metrizable, complete, metric, topological space
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This is version 1 of completely metrizable, born on 2002-01-24.
Object id is 1609, canonical name is CompletelyMetrizable.
Accessed 4386 times total.

Classification:
AMS MSC: 54E35 (General topology :: Spaces with richer structures :: Metric spaces, metrizability)
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