Wikipedia:Articles for deletion/Alexander's Trick

The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result of the debate was keep. -R. fiend 04:24, 15 October 2005 (UTC)

[edit] Alexander's Trick

Original research. Delete. utcursch | talk 13:33, 6 October 2005 (UTC)

• Keep, not convinced its original research. Kappa 14:01, 6 October 2005 (UTC)
  • Google is slightly muddled by the inconvenient name, but [1], [2], [3], [4], [5] and [6] show that it's something real in advanced topology (note - except the last, all the links are to Adobe Postscript files). Keep. DS 14:19, 6 October 2005 (UTC)
• Comment not convinced it's accurate--where's the center of the disk supposed to go? Certainly needs to be explained better, but even once it is, I think it'll be kind of a trivial observation that ought to be merged somewhere (but I don't know where) --Trovatore 16:27, 6 October 2005 (UTC)
• Keep. Not original research: not only is this well-known in topology, a Google search for 'Alexanders trick topology' gives 46500 hits. Result is more general than stated: any homeomorphism of the boundary of the n-ball extends to a homeomorphism of the ball. The map as stated has a removable discontinuity at the center (the center maps to the center).--JahJah 17:23, 6 October 2005 (UTC)

That was my guess, but it's not what the article currently says. It still strikes me as kind of borderline for a whole article; isn't there somewhere to merge it? BTW perhaps you'd like to rephrase it so it's correct, and throw in the n-dim case as well. --Trovatore 18:08, 6 October 2005 (UTC)

• Keep per JahJah. Xoloz 09:54, 7 October 2005 (UTC)
• Keep. This will be J. W. Alexander, and as Alexander trick is well-known to Google. Move, clean-up, all those good things. Not a delete in a million years. Charles Matthews 20:28, 7 October 2005 (UTC)
• This is obviously some bullshit because F(0) is undefined.  Grue  12:53, 8 October 2005 (UTC)
  • Huh? Lots of functions have F(0) undefined. Xoloz 14:51, 8 October 2005 (UTC)
    • Yet the article claims that F is defined on D² and it is homeomorphism. Now F(x)=f(x/|x|)/|x| looks more like the desired function. Grue  15:37, 8 October 2005 (UTC)
• Keep and move to Alexander trick (or perhaps Alexander's trick). I expanded the article a bit based on some papers I found via Google. -- Jitse Niesen (talk) 21:48, 8 October 2005 (UTC)
• Comment. There are related results which are referred to as Alexander's Trick, for example: A homeomorphism of a disk that fixes the boudary sphere is isotopic to the identity, relative to the sphere. This type of result is also important because it works in PL as well as Top. --JahJah 07:08, 9 October 2005 (UTC)
  • Did you read the article after I've expanded it (which I did just before my vote here)? I think this is now included in the article. Anyway, I'd be very grateful if you could have a look and check what I wrote, because I don't know that much topology. Jitse Niesen (talk) 11:19, 9 October 2005 (UTC)
    • Jitse: I did not see your edit: looks good. I have made a minor correction to the second Alexander's trick. --JahJah 17:26, 9 October 2005 (UTC)
      • Jitse and JahJah: it looks much better now than it did at the time of nomination. My only quibble is that it's tacitly assumed that Sⁿ and Dⁿ⁺¹ are embedded in Rⁿ⁺¹ with center at the origin and the usual scalar multiplication on Rⁿ⁺¹. But perhaps that's easy enough to figure out (assume the author meant something obvious, try it, see it that works), and explaining it might just add verbiage and make the page harder to follow. --Trovatore 05:48, 10 October 2005 (UTC)
• Keep. Original research claim not established.--Nicodemus75 17:59, 9 October 2005 (UTC)
• I am glad that I woke up such many commentaries and I want to say that originally I did must write ||x||f(x/||x||) for the true formula for the extended homeomorphism. My best wishes are that discussions continue in a constructive fashion. Of course I vote Keep. Juan Marquez 14:05, 13 October 2005 (UTC)
• Keep though I fair to have a surface understanding of this article, it seems harmless enough. Klonimus 00:58, 14 October 2005 (UTC)
• Keep. This is taught in beginning topology courses. I have some further comments (and references) that I will put on the talk page. --Chan-Ho 03:40, 14 October 2005 (UTC)

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.