Teichmüller–Tukey lemma
THEOREM
Teichmueller-Tukey lemma; Tukey's lemma; Teichmüller-Tukey lemma; Teichmuller–Tukey lemma; Teichmuller-Tukey lemma; Tukey lemma
In mathematics, the Teichmüller–Tukey lemma (sometimes named just Tukey's lemma), named after John Tukey and Oswald Teichmüller, is a lemma that 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.