英语词汇“metric space”的英英意思、用法、释义、翻译、读音、例句、短语、词组-英语词典

metric space n. [after German metrischer Raum (F. Hausdorff Grundzüge der Mengenlehre (1914) vii. 211)] Mathematics a topological space together with a metric (sense A. 3) defined for all pairs of points of the space.

ΚΠ

1900 Amer. Jrnl. Math. 22 336 One speaks of the geometries of metric space, of unilateral and of bilateral projective space.]

1919 Trans. Amer. Math. Soc. 20 213 We develop the general theory in terms of five completely independent properties of a development Δ which together suffice to make the developed class  a compact metric space.

1927 Bull. Amer. Math. Soc. 33 14 The following illustrations convey some notion of the scope of the concept metric space. If the aggregate P denotes the linear continuum of all real numbers and (p, q) = |p − q |, the resulting space is metric. Similarly euclidean space is also metric.

1968 E. T. Copson Metric Spaces ii. 21 Different choices of metric on a given set E give rise to different metric spaces.

1983 T. W. Gamelin & R. E. Greene Introd. Topol. i. 4 The union of a family of open subsets of a metric space X is an open subset of X.

单词	metric space
释义	> as lemmas metric space metric space n. [after German metrischer Raum (F. Hausdorff Grundzüge der Mengenlehre (1914) vii. 211)] Mathematics a topological space together with a metric (sense A. 3) defined for all pairs of points of the space. ΚΠ 1900 Amer. Jrnl. Math. 22 336 One speaks of the geometries of metric space, of unilateral and of bilateral projective space.] 1919 Trans. Amer. Math. Soc. 20 213 We develop the general theory in terms of five completely independent properties of a development Δ which together suffice to make the developed class  a compact metric space. 1927 Bull. Amer. Math. Soc. 33 14 The following illustrations convey some notion of the scope of the concept metric space. If the aggregate P denotes the linear continuum of all real numbers and (p, q) = \|p − q \|, the resulting space is metric. Similarly euclidean space is also metric. 1968 E. T. Copson Metric Spaces ii. 21 Different choices of metric on a given set E give rise to different metric spaces. 1983 T. W. Gamelin & R. E. Greene Introd. Topol. i. 4 The union of a family of open subsets of a metric space X is an open subset of X. extracted from metricn.¹adj.¹ < as lemmas
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