PlanetMath: metrizable

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metrizable

(Definition)

A topological space $(X,\mathcal{T})$ is said to be metrizable if there is a metric $d\colon X\to [0,\infty)$ such that the topology induced by is $\mathcal{T}$ .

"metrizable" is owned by mathcam. [ full author list (2) | owner history (1) ]

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See Also: metric, Urysohn metrization theorem

Other names:

metrization, metrizable space

Keywords:

topology

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Cross-references: induced, metric, topological space
There are 22 references to this entry.

This is version 2 of metrizable, born on 2002-01-22, modified 2004-11-13.
Object id is 1538, canonical name is Metrizable.
Accessed 6388 times total.

Classification:

AMS MSC:	54-00 (General topology :: General reference works )
	55-00 (Algebraic topology :: General reference works )
	22-00 (Topological groups, Lie groups :: General reference works )

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