metrizable

Adjective

Meaning

measurable, quantifiable

(topology) Of a topological space: for which a metric exists that will induce the original topology.

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Phrases with the word

Examples

A Hausdorff uniform space is metrizable if its uniformity can be defined by a countable family of pseudometrics. Source: Internet

Although the weak topology of the unit ball is not metrizable in general, one can characterize weak compactness using sequences. Source: Internet

A topological space which can arise in this way from a metric space is called a metrizable space; see the article on metrization theorems for further details. Source: Internet

Examples The group of unitary operators on a separable Hilbert space endowed with the strong operator topology is metrizable (see Proposition II.1 in Neeb, Karl-Hermann, On a theorem of S. Banach. Source: Internet

Completely metrizable spaces can be characterized as those spaces that can be written as an intersection of countably many open subsets of some complete metric space. Source: Internet

Every metrizable space is Hausdorff and paracompact (and hence normal and Tychonoff). Source: Internet

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