Talk:Alexander horned sphere

Origin of the name
What is the origin of the name of Alexander horned sphere? Could it be that it comes from Russian mathematician Pavel Sergeevich Alexandrov? --Romanm 11:09, 21 Jun 2004 (UTC)


 * No, says that it's James Waddell Alexander. ( (archied at archive.org May 19, 2002; approximate translation via Google Translate) --Romanm 11:11, 21 Jun 2004 (UTC)

Double
In what sense is 'double' being used in the last paragraph? --Hvc 07:45, Jan 12, 2005 (UTC)


 * The double of a manifold with boundary is obtained by taking the disjoint union of two copies of the manifold and using the "identity map" from the boundary of one copy to the other to get a quotient space. In other words, you glue two copies of a manifold along their boundaries making sure the map is not complicated.  There needs to be a page on that concept.  I'll do it sometime.  The symbol often used for the double of M is 2M. --C S 10:14, Jan 12, 2005 (UTC)


 * I added short explanatory text (stolen from the above explanation) so the reader can understand the "double" of the A.h.s. without cross-referencing. An article on this concept would also be valuable. Zaslav 22:30, 23 August 2007 (UTC)

Too specialised
The phrase "the need for distinction between the TOP, DIFF, and PL categories" is totally meaningless and much of the rest of the article need more explanation to a lay reader. --Henrygb 11:14, 5 Mar 2005 (UTC)


 * Perhaps it is totally meaningless to the lay reader, but certainly not for many mathematicians. Your point that this page is too specialized has some merit and more explanation would be better.  Unfortunately, while the picture may be intuitively appealing, many interesting aspects of this object (some of which are explained in the article) are really only interesting to mathematicians and the layperson would have trouble indeed understanding. --C S July 5, 2005 20:04 (UTC)
 * It needn't be so a lay reader has no hope. With the links added to relevant articles they can track back to the definitions given sufficient patience. I think my edit is a slight improvement. A Geek Tragedy 15:05, 1 February 2007 (UTC)

Image
Due to copyvio problems, the image previously in the article has been deleted. Since it's basically impossible to describe the Alexander horned sphere without an image, let's work on getting an image. Preferably one that can also be easily explained in the article to give a more precise description, e.g. not a picture that is too stylistic and obscures the mathematics. One possibility is to use images from Alexander's P.N.A.S. article; I think there is no copyvio problem there (check this!) but I think we can do better than that anyway. --C S (Talk) 05:06, 17 December 2005 (UTC)


 * Any feedback on the image I added? I think it is a bit on the stylish side, hopefully not too much. --Bernard 12:04, 22 October 2006 (UTC)


 * It's a nice image. It's better than no image.  There's a description of the object now in the article, so the situation is not so bad as before.  But it's difficult, even when looking at the enlarged image, to make out the details of the construction.  --C S (Talk) 18:01, 13 December 2006 (UTC)


 * "Better than no image"... I could bear more positive and constructive comments. --Bernard 21:36, 14 December 2006 (UTC)


 * Sorry, I didn't mean to be rude. But I did say what the difficulty with the image was.  Make the first three levels of the construction easy to see at a glance.  Right now the noninteresting part of the embedding dominates, making the interesting part too small to see.  --C S (Talk) 07:05, 15 December 2006 (UTC)

Hello, I made a drawing which perhaps can be used? Four (talk) 19:58, 21 April 2008 (UTC)


 * Does anyone remember where I can find what the old image (that had copyvio problems) actually was? (As in perhaps a website that had a thumbnail of a picture for purchase that was watermarked or something..) Jimw338 (talk) 19:32, 22 January 2019 (UTC)

What is embedded?
The Alexander "horned sphere" is,
 * the particular embedding of a sphere in 3-dimensional Euclidean space obtained by the following construction, starting with a standard torus:
 * By considering only the points of the tori that are not removed at some stage, an embedding results of the sphere with a Cantor set removed.
 * By considering only the points of the tori that are not removed at some stage, an embedding results of the sphere with a Cantor set removed.

But the construction only talks about tori; nowwhere does it mention a sphere being embedded. And where is the Cantor set that is removed? When you slice a torus or sphere, you are removing a continuum, whereas a Cantor set is disconnected. --91.115.54.195 (talk) 20:34, 19 July 2011 (UTC)