V2EX path-connected

Path-connected

释义 Definition

path-connected(路径连通的):一个集合(常指拓扑空间)中任意两点,都能用一条连续路径连接起来。
(在数学里常与 connected(连通) 区分:路径连通通常更强;有些空间“连通”但不“路径连通”。)

发音 Pronunciation

/pθ knktd/

例句 Examples

A disk is path-connected.
圆盘是路径连通的。

In a path-connected space, any two points can be joined by a continuous map from the interval \([0,1]\).
在路径连通的空间中,任意两点都可以通过从区间 \([0,1]\) 出发的连续映射连接起来。

词源 Etymology

path(路径) + connected(连通的) 组合而成。这里的 path 指数学意义上的“连续曲线/连续映射”,强调“通过一条连续路径把点连起来”。

相关词 Related Words

文学与名著出处 Literary Works

  • Topology James R. Munkres(常用“path-connected”定义与比较连通性概念)
  • Algebraic Topology Allen Hatcher(在基本群与覆盖空间等章节频繁出现)
  • Topology George F. Simmons(入门拓扑教材中讨论路径连通与连通的差异)
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