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What (who) is Švarc–Milnor lemma - definition
Švarc–Milnor lemma
LEMMA IN GEOMETRIC GROUP THEORY, GIVING SUFFICIENT CONDITIONS FOR WHEN A GROUP EQUIPPED WITH AN ISOMETRIC ACTION ON A METRIC SPACE IS QUASI-ISOMETRIC TO THE METRIC SPACE
Švarc-Milnor lemma; Schwarz-Milnor lemma
In the mathematical subject of geometric group theory, the Švarc–Milnor lemma (sometimes also called Milnor–Švarc lemma, with both variants also sometimes spelling Švarc as Schwarz) is a statement which says that a group G, equipped with a "nice" discrete isometric action on a metric space X, is quasi-isometric to X.
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.
Nine lemma
CATEGORY THEORY LEMMA ABOUT COMMUTATIVE DIAGRAMS
9-lemma
[mathematics], the nine lemma (or 3×3 lemma) is a statement about [[commutative diagrams and exact sequences valid in the category of groups and any abelian category. It states: if the diagram to the right is a commutative diagram and all columns as well as the two bottom rows are exact, then the top row is exact as well.
