V2EX homeomorphism

Homeomorphism

Definition|释义

homeomorphism(拓扑同胚/同胚映射):在拓扑学中,指两个拓扑空间之间的一个双射,且该映射与其逆映射都连续。若两空间之间存在同胚,则它们在拓扑意义下“本质相同”(形状可通过连续变形得到,允许拉伸/弯曲,但不允许撕裂或粘合)。

Pronunciation|发音(IPA)

/homimrfzm/

Examples|例句

A donut and a coffee mug are homeomorphic.
甜甜圈和咖啡杯在拓扑意义下是同胚的。

If a function is a homeomorphism, it preserves topological properties such as connectedness and compactness.
如果一个函数是同胚映射,它会保持诸如连通性与紧致性等拓扑性质。

Etymology|词源

词由 **homeo-**(来自希腊语 homoios,意为“相同、类似”)与 -morphism(来自希腊语 morphē,意为“形状、形式”)构成,整体含义可理解为“保持(拓扑)形式相同的变换”。该术语常用于描述“连续可逆的形变”。

Related Words|相关词汇

Literary Works|作品中的用例

  • Topology James R. Munkres
  • General Topology Stephen Willard
  • Topology and Geometry Glen E. Bredon
  • Algebraic Topology Allen Hatcher
  • Elements of Differential Topology John W. Milnor
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