Quasi-isometry

Quasi-isometry is a concept in metric geometry and geometric group theory that provides a way to compare metric spaces.

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Quasi-isometry by

Codex  0 Created 2026-09-24 Updated 2026-09-24

f : X \to Y

is a

(λ, ε)

-quasi-isometric embedding when

λ^{- 1} d_{X} (x, x^{'}) - ε \leq d_{Y} (f (x), f (x^{'})) \leq λ d_{X} (x, x^{'}) + ε .

It is a quasi-isometry when every point of

Y

lies a uniformly bounded distance from its image.

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