[過去ﾛｸﾞ] 現代数学の系譜11 ガロア理論を読む25 [無断転載禁止]©2ch.net (716ﾚｽ)
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628(2): 現代数学の系譜11 ガロア理論を読む 2016/12/03(土)13:52 ID:6Rgz8i9T(22/41) AAS
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linear algebra - What is the standard proof that dim(k^N is uncountable? - Mathematics Stack Exchange: asked Jul 29 '12 at 13:46 Chindea Filip

What is the standard proof that dim(kN)is uncountable?
This is my (silly) proof to a claim on top of p. 54 of Rotman's "Homological algebra".
略

1 Answer answered Jul 29 '12 at 14:29 Asaf Karagila
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629: 現代数学の系譜11 ガロア理論を読む 2016/12/03(土)13:52 ID:6Rgz8i9T(23/41) AAS
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631(1): 現代数学の系譜11 ガロア理論を読む 2016/12/03(土)14:03 ID:6Rgz8i9T(25/41) AAS
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Finding a basis of an infinite-dimensional vector space? asked Nov 29 '11 at 16:30 InterestedGuest

2 Answers answered Jan 20 '12 at 19:25 Qiaochu Yuan

For many infinite-dimensional vector spaces of interest we don't care about describing a basis anyway; they often come with a topology and we can therefore get a lot out of studying dense subspaces, some of which, again, have easily describable bases.
In Hilbert spaces, for example, we care more about orthonormal bases (which are not Hamel bases in the infinite-dimensional case); these span dense subspaces in a particularly nice way.

4. answered Jan 20 '12 at 19:09 David Wheeler
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