Timeline for The generalization of Brouwer's fixed point theorem?
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
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| Mar 30, 2011 at 7:19 | comment | added | Daniel Litt | Alex, as for the Bing paper, if you email me, I'd be happy to send it to you. My email is on my user page. | |
| Mar 30, 2011 at 7:18 | history | edited | Daniel Litt | CC BY-SA 2.5 |
Added another reference.; deleted 1 characters in body; added 1 characters in body
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| Mar 30, 2011 at 7:14 | comment | added | Daniel Litt | Alex, don't worry about it; the change was understandable. I am unaware of an answer to the revised question, and have done some searching; as far as I can tell it is open. If you replace "contractible" with "acyclic," however, there are counterexamples, i.e. locally connected acyclic compact spaces without the fixed point property. I've edited my answer to remark on this. | |
| Mar 30, 2011 at 6:57 | comment | added | Alex Gavrilov | Daniel, Let me explain myself. Suppose for a moment that the question was "A continuous map of a good contractible compact topological space into itself has a fixed point" (Which is what I mean, actually). You gave an example, I did not accept it for the space is not good enough for me. Would you like this? I failed to foresee all the possible pathology: the fault is mine. But is it a good reason to create a new question? I doubt it. P.S. By the way, could anyone give me Bing's article? For now, I cannot get it from where I am. | |
| Mar 28, 2011 at 22:46 | comment | added | Alex Gavrilov | Explanation: The statement should be of kind "Let $X$ looks like a ball. Then...". Definitely, Kinoshita's example does not look like a ball, for it is not locally connected. So, I added this condition to rule it out. | |
| Mar 28, 2011 at 20:16 | comment | added | Thierry Zell | @Alex: adding details to your questions is perfectly fine and should be encouraged. If you feel like you need to point out that a detail was not there before, you can always write it like: Let X be a contractible compact [edit: locally connected] topological space | |
| Mar 28, 2011 at 12:28 | comment | added | Alex Gavrilov | I do not know if it is a right policy, but i added the local connectedness condition. Surely I missed it initially. | |
| Mar 28, 2011 at 12:14 | comment | added | Alex Gavrilov | Oops! I know why he call it this. What I do not know is how to delete my own foolish remark:( | |
| Mar 28, 2011 at 11:29 | comment | added | Alex Gavrilov | Thank you. The example is nice! (By the way, why he call a compactum a continuum?) | |
| Mar 28, 2011 at 11:24 | vote | accept | Alex Gavrilov | ||
| Mar 28, 2011 at 5:35 | comment | added | Michael Greinecker | The original article can be found at: matwbn.icm.edu.pl/ksiazki/fm/fm40/fm4019.pdf | |
| Mar 28, 2011 at 4:34 | history | answered | Daniel Litt | CC BY-SA 2.5 |