現代数学の系譜11 ガロア理論を読む13

現代数学の系譜11 ガロア理論を読む13at MATH

現代数学の系譜11 ガロア理論を読む13 - 暇つぶし2ch380:ｽことがない「上界がF内に存在することを F has the chain property で保証している。」・・か・・わからんかったが、検索でヒットしたものを貼っておきます http://math.stackexchange.com/questions/1266621/zorns-lemmas-chain-condition Zorn's Lemma's chain condition https://gowers.wordpress.com/2008/08/12/how-to-use-zorns-lemma/ How to use Zorn’s lemma This entry was posted on August 12, 2008 Terence Tao Says: August 13, 2008 at 3:31 am | Reply I like to think of Zorn’s lemma as a guarantee that greedy algorithms can go on as long as necessary, before being stopped by some sort of obstruction (either a chain without an upper bound, or a maximal element). So any finitary construction that is built via the greedy algorithm (e.g. selecting a basis for a finite-dimensional vector space greedily) has a decent chance of extending to the infinitary setting as well by a Zorn’s lemma argument. Which is of course essentially what you are saying above :-)

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