V2EX simply connected

Simply Connected

释义 Definition

(拓扑/复分析)单连通的:指一个空间(或平面区域)是“整体连成一片、并且没有‘洞’”的;更正式地说,在该空间内任意闭合曲线都可以在空间内连续收缩到一点。常见于“simply connected domain(单连通区域)”。

发音 Pronunciation (IPA)

/smpli knktd/

例句 Examples

A disk is simply connected.
圆盘是单连通的。

In complex analysis, many theorems are easier to apply on simply connected domains because closed loops can be continuously contracted to a point.
在复分析中,许多定理在单连通区域上更容易应用,因为闭合回路可以在区域内连续收缩到一点。

词源 Etymology

simply(简单地) + connected(连通的) 组成;这里的“简单”并非指结构“容易”,而是指连通性在拓扑意义上“没有额外的环路障碍(洞)”。该术语在19世纪末至20世纪初的拓扑学与复变函数理论发展中逐渐固定下来,用于刻画“无洞的连通区域”。

相关词 Related Words

文献与作品 Notable Works

  • Topology James R. Munkres(常用“simply connected”描述空间与区域)
  • Algebraic Topology Allen Hatcher(以基本群等工具刻画单连通性)
  • Complex Analysis Lars Ahlfors(频繁讨论“simply connected domain”)
  • Real and Complex Analysis Walter Rudin(在复分析章节涉及单连通区域相关结论)
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