Adjective
measurable, quantifiable
(topology) Of a topological space: for which a metric exists that will induce the original topology.
Source: en.wiktionary.orgA 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