V2EX homeomorphic

Homeomorphic

Definition|释义

(数学/拓扑学)同胚的:如果两个空间之间存在一个连续、可逆且逆映射也连续的对应(同胚),则这两个空间(或它们的子集)称为 homeomorphic;直观上表示“在不撕裂、不粘合的连续变形下是同一种形状”。(该词主要用于拓扑学语境。)

Pronunciation|发音

/homimrfk/

Examples|例句

A coffee mug and a donut are homeomorphic in topology.
在拓扑学里,咖啡杯和甜甜圈是同胚的。

The theorem shows that these two surfaces are homeomorphic, so they share the same topological properties even if their geometry looks different.
该定理表明这两个曲面同胚,因此即使它们的几何外观不同,也共享相同的拓扑性质。

Etymology|词源

来自希腊语构词:**homo-**(相同)+ morphē(形状),通过近代数学术语体系形成 homeomorphism(同胚),形容词形式为 homeomorphic,用于描述“具有同胚关系的”。

Related Words|相关词

Notable Works|文学与名著用例

  • Topology James R. Munkres(系统使用 homeomorphic 讨论空间的同胚分类)
  • Algebraic Topology Allen Hatcher(在同伦与基本群等章节中频繁出现)
  • Counterexamples in Topology Lynn Arthur Steen & J. Arthur Seebach, Jr.(用大量反例说明哪些空间彼此同胚或不同胚)
  • General Topology John L. Kelley(在一般拓扑框架下讨论同胚与连续映射)
关于     帮助文档     自助推广系统     博客     API     FAQ     Solana     3026 人在线   最高记录 6679       Select Language
创意工作者们的社区
World is powered by solitude
VERSION: 3.9.8.5 7ms UTC 13:55 PVG 21:55 LAX 05:55 JFK 08:55
Do have faith in what you're doing.
ubao msn snddm index pchome yahoo rakuten mypaper meadowduck bidyahoo youbao zxmzxm asda bnvcg cvbfg dfscv mmhjk xxddc yybgb zznbn ccubao uaitu acv GXCV ET GDG YH FG BCVB FJFH CBRE CBC GDG ET54 WRWR RWER WREW WRWER RWER SDG EW SF DSFSF fbbs ubao fhd dfg ewr dg df ewwr ewwr et ruyut utut dfg fgd gdfgt etg dfgt dfgd ert4 gd fgg wr 235 wer3 we vsdf sdf gdf ert xcv sdf rwer hfd dfg cvb rwf afb dfh jgh bmn lgh rty gfds cxv xcv xcs vdas fdf fgd cv sdf tert sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf shasha9178 shasha9178 shasha9178 shasha9178 shasha9178 liflif2 liflif2 liflif2 liflif2 liflif2 liblib3 liblib3 liblib3 liblib3 liblib3 zhazha444 zhazha444 zhazha444 zhazha444 zhazha444 dende5 dende denden denden2 denden21 fenfen9 fenf619 fen619 fenfe9 fe619 sdf sdf sdf sdf sdf zhazh90 zhazh0 zhaa50 zha90 zh590 zho zhoz zhozh zhozho zhozho2 lislis lls95 lili95 lils5 liss9 sdf0ty987 sdft876 sdft9876 sdf09876 sd0t9876 sdf0ty98 sdf0976 sdf0ty986 sdf0ty96 sdf0t76 sdf0876 df0ty98 sf0t876 sd0ty76 sdy76 sdf76 sdf0t76 sdf0ty9 sdf0ty98 sdf0ty987 sdf0ty98 sdf6676 sdf876 sd876 sd876 sdf6 sdf6 sdf9876 sdf0t sdf06 sdf0ty9776 sdf0ty9776 sdf0ty76 sdf8876 sdf0t sd6 sdf06 s688876 sd688 sdf86