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单词 UniformStructureOfAMetricSpace
释义

uniform structure of a metric space


Let (X,d) be a metric space. There is a natural uniform structure on X, which induces the same topologyMathworldPlanetmath as the metric. We define a subset V of the Cartesian product X×X to be an entourage if and only if it contains a subset of the form

Vε={(x,y)X×X:d(x,y)<ε}

for some ε.

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更新时间:2025/5/4 15:33:55