metrizableadj.

Brit.

/mᵻˈtrʌɪzəbl/, U.S.

/məˈtraɪzəb(ə)l/

Forms: 1900s– metrisable, 1900s– metrizable.

Origin: Formed within English, by derivation; modelled on a German lexical item. Etymons: metrization n., -able suffix.

Etymology: < metriz- (in metrization n.) + -able suffix, after German metrisierbar (P. Urysohn 1924, in Math. Ann. 92 275). Compare later metrize v.²

Mathematics.

Of a topological space: capable of being assigned a metric which makes it a metric space with the same topology as the original space.

ΘΚΠ

the world > relative properties > number > geometry > geometric space > [adjective] > of topological space

monoidal1894

metrizable1927

complete1934

triangulable1940

monoidal1943

1927 Bull. Amer. Math. Soc. 33 25 It is therefore of interest to formulate the conditions that a space be metrizable in terms of continuous functions.

1935 Bull. Amer. Math. Soc. 41 644 In a metrizable space the Borel theorem holds without the restriction of denumerability of the original family.

1964 A. P. Robertson & W. Robertson Topol. Vector Spaces i. 16 The convex space E is metrisable if and only if it is separated and there is a countable base of neighbourhoods (of the origin).

1968 E. T. Copson Metric Spaces ix. 142 General topology is a generalization of the theory of metric spaces since there are topological spaces which are not metrizable.

1990 Proc. London Math. Soc. 61 481 The term ‘compact group’ will always denote a compact metrizable group.

This entry has been updated (OED Third Edition, December 2001; most recently modified version published online March 2022).

单词	metrizable
释义	metrizableadj. Brit. /mᵻˈtrʌɪzəbl/, U.S. /məˈtraɪzəb(ə)l/ Forms: 1900s– metrisable, 1900s– metrizable. Origin: Formed within English, by derivation; modelled on a German lexical item. Etymons: metrization n., -able suffix. Etymology: < metriz- (in metrization n.) + -able suffix, after German metrisierbar (P. Urysohn 1924, in Math. Ann. 92 275). Compare later metrize v.² Mathematics. Of a topological space: capable of being assigned a metric which makes it a metric space with the same topology as the original space. ΘΚΠ the world > relative properties > number > geometry > geometric space > [adjective] > of topological space monoidal1894 metrizable1927 complete1934 triangulable1940 monoidal1943 1927 Bull. Amer. Math. Soc. 33 25 It is therefore of interest to formulate the conditions that a space be metrizable in terms of continuous functions. 1935 Bull. Amer. Math. Soc. 41 644 In a metrizable space the Borel theorem holds without the restriction of denumerability of the original family. 1964 A. P. Robertson & W. Robertson Topol. Vector Spaces i. 16 The convex space E is metrisable if and only if it is separated and there is a countable base of neighbourhoods (of the origin). 1968 E. T. Copson Metric Spaces ix. 142 General topology is a generalization of the theory of metric spaces since there are topological spaces which are not metrizable. 1990 Proc. London Math. Soc. 61 481 The term ‘compact group’ will always denote a compact metrizable group. This entry has been updated (OED Third Edition, December 2001; most recently modified version published online March 2022). < adj.1927
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