The Short map reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Short map

In mathematics, a short map is a function f from a metric space X to another metric space Y such that for any we have

.

Here and denote metrics on and , respectively. In other words, f is short iff it is 1-Lipschitz.

One can say that f is strictly short if the inequality is always strict. Then a contraction mapping is strictly short, but not conversely (even with X = Y).

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