Timeline for Why is definable compact equivalent to bounded and closed for sets with o-minimal structures?
Current License: CC BY-SA 3.0
13 events
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| Dec 25, 2011 at 16:54 | history | edited | Goldstern |
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| Sep 6, 2011 at 21:46 | history | edited | j.c. | CC BY-SA 3.0 |
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| May 31, 2011 at 14:51 | comment | added | ACL | @Thierry: Why not? :-) Well, google pointed at it,this paper is the one where the definable compactness is introduced and shown to be equivalent to bounded & closed, and the proof is exactly as indicated by `unknown (google)'. | |
| May 31, 2011 at 13:43 | comment | added | Thierry Zell | @ACL: I'm just curious: why this paper in particular? | |
| May 31, 2011 at 13:34 | comment | added | ACL | Anyway, you need to prove that a subset of $M$ is definably compact if and only if it is bounded and closed. But this follows from the fact that definable functions $(a,b)\to M$ are piecewise monotonic. | |
| May 31, 2011 at 13:25 | comment | added | ACL | I presume the paper is Definable Compactness and Definable Subgroups of o-minimal groups, by Ya'acv Peterzil and Charles Steinhorn. Journal of the London Mathematical Society (1999), 59: 769-786 | |
| May 31, 2011 at 13:03 | comment | added | Thierry Zell | It would help if you actually referenced which article you are reading; this proof appears in many places. Your suggested proof appears to work, but your question does not really tell us what the "complicated" proof in the original paper is. | |
| May 31, 2011 at 12:54 | history | edited | Thierry Zell | CC BY-SA 3.0 |
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| May 31, 2011 at 12:15 | comment | added | Emil Jeřábek | This argument sounds OK to me. In fact, I think you don’t even need induction: just project $X$ on each coordinate individually. | |
| May 31, 2011 at 12:15 | comment | added | David Roberts♦ | I also added a tag. | |
| May 31, 2011 at 12:14 | history | edited | David Roberts♦ |
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| May 31, 2011 at 12:14 | comment | added | David Roberts♦ | This is a decent question, but can I suggest editing it and changing the title? With the title as is (and with no capital), it may not generate the interest it deserves. | |
| May 31, 2011 at 11:57 | history | asked | user15496 | CC BY-SA 3.0 |