Difference between revisions of "Similar sets"
From Encyclopedia of Mathematics
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| − | A generalization of the elementary geometrical concept of a [[ | + | A generalization of the elementary geometrical concept of a [[similarity]]. Two sets $A$ and $B$ that are [[totally ordered set|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 $f(x)\, S\, f(y)$. |
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| − | An equivalence class of totally ordered sets under the relation of similarity is often called an | + | An equivalence class of totally ordered sets under the relation of similarity is often called an ''[[order type]]''. |
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Latest revision as of 18:37, 6 October 2016
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 $f(x)\, S\, f(y)$.
Comments
An equivalence class of totally ordered sets under the relation of similarity is often called an order type.
How to Cite This Entry:
Similar sets. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Similar_sets&oldid=14379
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