V2EX product space

Product Space

定义 Definition

product space(乘积空间/积空间):把两个或多个空间按“坐标并列”组合成一个新空间的构造。新空间中的一个点通常写成有序组(如 \((x,y)\)),并配上自然的结构(常见的是积拓扑;在概率论中也指由多个概率空间构成的乘积概率空间)。

发音 Pronunciation (IPA)

/prdkt spes/

例句 Examples

A point in the product space is written as \((x, y)\).
乘积空间中的一个点写作 \((x, y)\)。

In topology, the product space \(X \times Y\) is usually equipped with the product topology, which is the coarsest topology making the projection maps continuous.
在拓扑学中,乘积空间 \(X \times Y\) 通常配备积拓扑,即使投影映射连续的最粗拓扑。

词源 Etymology

product 源自拉丁语 productus(“延伸、产生”之意,来自 producere “向前引出/产生”);space 源自拉丁语 spatium(“空间、距离”)。合在一起的 product space 是数学术语,字面意思是“用乘积方式构造出来的空间”。

相关词 Related Words/h2>

文学与经典著作 Literary Works

  • Topology James R. Munkres(常用“product space”讨论积拓扑与投影映射)
  • General Topology John L. Kelley(系统介绍乘积空间与相关性质)
  • Measure Theory Paul R. Halmos(在乘积测度/概率空间语境中出现)
  • A Course in Probability Theory Kai Lai Chung(讨论独立性时常用乘积概率空间)
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