V2EX closed set

Closed Set

定义 Definition

(数学/拓扑学)闭集:在给定的拓扑空间中,其补集是开集的集合。直观上,闭集通常“包含自己的边界/极限点”。(在不同数学分支中表述略有差异,但核心性质相近。)

发音 Pronunciation (IPA)

/klozd st/

例句 Examples

The interval [0,1] is a closed set.
区间 [0,1] 是一个闭集。

In \(\mathbb{R}^n\) with the usual topology, a set is closed if it contains all of its limit points.
在带有通常拓扑的 \(\mathbb{R}^n\) 中,一个集合如果包含它的所有极限点,就称为闭集。

词源 Etymology

closed 来自“close(关闭、封闭)”的过去分词形式,强调“封住、包含在边界之内”的感觉;set 在数学中指“集合”。合起来 closed set 直观表达为“封闭的集合”,即在拓扑意义下对极限/边界行为“封住不漏”(例如极限点不会跑到集合外面)。

相关词 Related Words

文学与著作中的用例 Literary Works

  • 《Topology》(James R. Munkres):系统定义开集、闭集及其基本性质。
  • 《Principles of Mathematical Analysis》(Walter Rudin):在度量空间与欧氏空间语境中频繁使用“closed set”。
  • 《Counterexamples in Topology》(Lynn A. Steen & J. Arthur Seebach Jr.):通过大量反例展示闭集在不同拓扑下的行为差异。
关于     帮助文档     自助推广系统     博客     API     FAQ     Solana     3033 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 17ms UTC 13:48 PVG 21:48 LAX 06:48 JFK 09:48
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