Timeline for Can a vector space over an infinite field be a finite union of proper subspaces?
Current License: CC BY-SA 3.0
5 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jul 1, 2011 at 17:25 | history | edited | Pierre-Yves Gaillard | CC BY-SA 3.0 |
Edit clearly indicated.
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| Jul 1, 2011 at 16:29 | comment | added | Pierre-Yves Gaillard | @Anton Geraschenko - Thanks for your vote and your comment, so much clearer than my answer! | |
| Jul 1, 2011 at 16:21 | comment | added | Anton Geraschenko | Ahhh +1. It took me a while to understand what's going on here. The confusing statement was "the product of the $f_i$ is nonzero". Here's my expansion of that statement. (1) The set of functions which are polynomial on each finite-dimensional subspace is clearly a ring. (2) Given two non-zero functions of this form, there is a finite-dimensional subspace on which they are both non-zero (a 2-dimensional subspace spanned by two points witnessing the non-zero-ness of the two functions will do). (3) By (2) and the finite-dimensional case, the ring is an integral domain. | |
| Jul 1, 2011 at 3:44 | history | answered | Pierre-Yves Gaillard | CC BY-SA 3.0 |