V2EX pseudometric

Pseudometric

定义 Definition

pseudometric(伪度量/拟度量):数学中一种“像度量(metric)一样”的距离函数,满足非负性、对称性、三角不等式,但允许不同的点之间距离为 0(即不要求“d(x,y)=0 必须推出 x=y”)。

发音 Pronunciation (IPA)

/sudomtrk/

例句 Examples

A pseudometric can assign distance 0 to different points.
伪度量可以把不同的点之间的距离定义为 0。

In functional analysis, one often uses a family of pseudometrics to describe a topology that distinguishes points only up to an equivalence relation.
在泛函分析中,人们常用一族伪度量来刻画某种拓扑,它只在某个等价关系的意义下区分点。

词源 Etymology

由 **pseudo-**(“假的、拟似的”,源自希腊语 pseudes,意为“虚假的”)+ metric(“度量的/距离的”,与“measure/ meter”同源)构成,字面意思是“看起来像度量但不完全是度量”。

相关词 Related Words

文学与典籍 Literary Works

  • James R. Munkres, Topology(在讨论由距离函数诱导拓扑、以及相关推广概念时常出现)
  • John L. Kelley, General Topology(一般拓扑学语境中涉及伪度量/度量化相关内容)
  • Nicolas Bourbaki, General Topology(以较抽象的方式处理度量化与相关结构,常见“pseudometric”用法)
  • Walter Rudin, Functional Analysis(在拓扑向量空间与半范数/伪度量相关表述中常可见)
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