Similar sets

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A generalization of the elementary geometrical concept of a similarity. Two sets $A$ and $B$ that are totally ordered by relations $R$ and $S$ respectively are said to be similar if there exists a bijection $f : A \rightarrow B$ such that for any $x,y \in A$ it follows from $x\, R\, y$ that $f(x)\, S\, f(y)$.


An equivalence class of totally ordered sets under the relation of similarity is often called an order type.

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Similar sets. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article