V2EX t1 space

T1 Space

释义 Definition

T1 空间:拓扑学中的一种拓扑空间,满足 T1 分离公理直观地说,空间中任意两个不同的点都“可以用开集区分开来”:对任意两点 \(x \neq y\),存在一个包含 \(x\) 但不包含 \(y\) 的开集;等价地,每个单点集 \(\{x\}\) 都是闭集。(该术语还有更高阶相关概念,如 T2/Hausdorff 空间等。)

发音 Pronunciation (IPA)

/ti wn spes/

例句 Examples

A T1 space has all singletons closed.
T1 空间的每个单点集都是闭集。

In a T1 space, limit points and closures behave more like they do in familiar metric spaces, which makes many proofs easier to organize.
在 T1 空间中,极限点与闭包的性质更接近我们熟悉的度量空间,因此许多证明更容易整理与推进。

词源 Etymology

“T1” 来自拓扑学分离公理(separation axioms)的编号体系(T0、T1、T2…),用于标记空间满足的“可分离程度”。“space” 在此指“拓扑空间”。这一编号体系在 20 世纪早期的拓扑学发展中逐渐固定下来,用以系统化比较不同空间的分离性质。

相关词 Related Words

文学与著作 Literary Works

  • James R. Munkres, Topology(常见教材中在分离公理章节讨论 T1 space)
  • Stephen Willard, General Topology(系统讲解 T0/T1/T2 等分离公理)
  • John L. Kelley, General Topology(经典参考书,包含 T1 空间的定义与性质)
关于     帮助文档     自助推广系统     博客     API     FAQ     Solana     2707 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 35ms UTC 03:56 PVG 11:56 LAX 20:56 JFK 23:56
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