Timeline for Homotopy injection between the unit ball in the Euclidean n space and an n-dimensional metric AR
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 2, 2015 at 0:38 | comment | added | Włodzimierz Holsztyński | It's been a while ago (I don't have the paper around me available). Disk is treated as any other 2-dim metric compact AR. Borsuk constructed a continuum of 2-dim metric compact ARs such that none of them contains a subset homeomorphic to any open subset of any other. *** *** Later, a still harder example was provided (if my memory serves me well enough) jointly by Bing and Borsuk--they constructed a 3-dim metric compact AR which doesn't contain any subspace homeomorphic to a disk (i.e. $\ \mathbb I^2$). | |
| Apr 1, 2015 at 20:31 | comment | added | Pedro Perez | @Włodzimierz Holsztyński The paper contains counterexamples? Could you give more details about the paper of Borsuk? Thanks! | |
| Apr 1, 2015 at 19:38 | comment | added | Włodzimierz Holsztyński | There are plenty of the requested examples. Karol Borsuk had a paper in dimension $\ 2\ $ with a more advanced goal. The paper was presented during the first topological conference in Prague, during the summer of 1961. And it was published in the conference proceedings. | |
| Apr 1, 2015 at 19:35 | comment | added | Włodzimierz Holsztyński | My mistake, sorry (I assumed--wrongly--that $\ X\subseteq\mathbb R^n$). | |
| Apr 1, 2015 at 14:44 | comment | added | Pedro Perez | @Włodzimierz Holsztyński I do not understand your comment, in general $X$ does not embeds in $\mathbf{R}^n$. Could you explain what do you mean? | |
| Apr 1, 2015 at 8:43 | comment | added | Włodzimierz Holsztyński | ?? -- make your ball big enough. | |
| Apr 1, 2015 at 5:42 | review | First posts | |||
| Apr 1, 2015 at 7:10 | |||||
| Apr 1, 2015 at 5:40 | history | asked | Pedro Perez | CC BY-SA 3.0 |