[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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148: 現代数学の系譜11 ガロア理論を読む 2016/11/05(土)19:59:07.06 ID:DzICE8Th(38/47) AAS
外部ﾘﾝｸ:en.wikipedia.org
Simplicial set
From Wikipedia, the free encyclopedia

In mathematics, a simplicial set is a construction in categorical homotopy theory that is a pure algebraic model of the notion of a "well-behaved" topological space.
Historically, this model arose from earlier work in combinatorial topology and in particular from the notion of simplicial complexes. Simplicial sets are used to define quasi-categories, a basic notion of higher category theory.

History and uses of simplicial sets

Simplicial sets were originally used to give precise and convenient descriptions of classifying spaces of groups. This idea was vastly extended by Grothendieck's idea of considering classifying spaces of categories, and in particular by Quillen's work of algebraic K-theory.
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528(1): 2016/11/27(日)08:23:34.06 ID:Saxg5SCY(1) AAS
「科学的には」と前置きを付ける人は科学者ではない、みたいな話だな。

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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)14:03:09.06 ID:6Rgz8i9T(25/41) AAS
>>628 ついで

外部ﾘﾝｸ:math.stackexchange.com
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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