# Similar sets

From Encyclopedia of Mathematics

A generalization of the elementary geometrical concept of a similarity. Two sets and that are totally ordered by relations and are said to be similar if there exists a bijection such that for any it follows from that .

#### Comments

An equivalence class of totally ordered sets under the relation of similarity is often called an order type (cf. also Totally ordered set; Order type).

**How to Cite This Entry:**

Similar sets.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Similar_sets&oldid=14379

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