Teichmüller–Tukey lemma について

Words near each other

Dictionary Lists

mini英和辞書

翻訳と辞書　辞書検索 [ 開発暫定版 ]

スポンサードリンク

Tukey's lemma ：ウィキペディア英語版

Teichmüller–Tukey lemma
In mathematics, the Teichmüller–Tukey lemma (sometimes named just Tukey's lemma), named after John Tukey and Oswald Teichmüller, states that every nonempty collection of finite character has a maximal element with respect to inclusion. Over Zermelo–Fraenkel set theory, the Teichmüller–Tukey lemma is equivalent to the axiom of choice, and therefore to the well-ordering theorem, Zorn's lemma, and the Hausdorff maximal principle.
==Definitions==
A family of sets is of finite character provided it has the following properties:
#For each

A\in \mathcal

, every finite subset of

A

belongs to

\mathcal

.
#If every finite subset of a given set

A

belongs to

\mathcal

, then

A

belongs to

\mathcal

翻訳と辞書 : 翻訳のためのインターネットリソース