V2EX injective hull

Injective Hull

释义 Definition

injective hull(内射包/注入包):在数学中(尤其是度量空间与范畴论相关语境),指一个对象(如度量空间)最小的“注入/内射”扩张,使得它嵌入到一个内射对象(injective object)中,并且该扩张在某种意义下是最小或最紧的。
度量空间里,injective hull 常指Isbell 的 injective hull,也常与 tight span(紧张跨度)联系在一起。

发音 Pronunciation (IPA)

/ndktv hl/

例句 Examples

The injective hull of this metric space adds the missing “between” points.
这个度量空间的 injective hull 会补上缺失的“介于其间”的点。

In geometric group theory, the injective hull (tight span) can help study the large-scale shape of a space via a minimal injective extension.
在几何群论中,injective hull(tight span)可以通过一种最小的内射扩张来帮助研究空间的宏观几何形状。

词源 Etymology

injective 来自拉丁语词根 iacere(“投掷”)的生含义,在现代数学中固定为“内射/可注入”的术语,用来描述某种“延拓性质很好”的对象(能把映射延伸出去)。hull 原义是“船壳、外壳”,引申为“包壳、包、最外层结构”。合起来 injective hull 就是“把对象包进一个内射结构里”的“最小外壳/包”。

相关词 Related Words

文献与著作 Literary / Notable Works

  • Isbell, J. R. (1964), Six theorems about injective metric spaces(提出并系统研究度量空间的 injective hull 概念的经典论文之一)
  • Burago, Burago & Ivanov, A Course in Metric Geometry(度量几何教材中讨论 tight span / injective hull 相关内容)
  • Bridson & Haefliger, Metric Spaces of Non-Positive Curvature(涉及度量空间与几何群论背景下的相关结构与工具,常与 injective hull 主题相邻出现)
About     Help     Advertise     Blog     API     FAQ     Solana     3339 Online   Highest 6679       Select Language
创意工作者们的社区
World is powered by solitude
VERSION: 3.9.8.5 74ms UTC 12:54 PVG 20:54 LAX 05:54 JFK 08:54
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