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Quasi-isometric spaces

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Metric spaces (cf. Metric space) and , for which there exist two mappings and and two constants and such that for all and in and for all and in , the following four inequalities hold:

This definition appears in [a1], where it is attributed to G.A. Margulis. The relation "X is quasi-isometric to Y" is an equivalence relation between metric spaces.

See also Quasi-isometry.

References

[a1] E. Ghys, "Les groupes hyperboliques" Astérisque , 189–190 (1990) pp. 203–238 (Sém. Bourbaki Exp. 722)
How to Cite This Entry:
Quasi-isometric spaces. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quasi-isometric_spaces&oldid=14441
This article was adapted from an original article by A. Papadopoulos (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article