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=39364
Similar sets. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Similar_sets&oldid=39364
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article