Take the 2-minute tour ×  Someone I know is trying to figure out
if the following concepts already have an established name in
the literature, and MO is a great place to ask around.  1)
Suppose $X$ is a metric space equipped with an associative
product and a unit element. Let $m: X \times X \to X$ be the
product. Suppose also that $m$ is nonexpansive, i.e. $$ d\big(
m(x,x'),m(y,y') \big) \le d\big((x,x'),(y,y')\big) $$ say when
$X\times X$ is given the Euclidean metric with respect to the
given metric of $X$. Is there a standard name for this type of
structure?  2) Let $f : X \to Y$ be a map between metric spaces
with the property that for all $x,y \in X$ $$ d(f(x), f(y)) \geq
d(x,y). $$ So in a way this is the opposite of a nonexpansive
map. Is there a name for such maps?   share|improve this
question 2) Expansive. –  Bill Johnson Sep 27 '10 at 18:01 2)
noncontracting map –  Anton Petrunin Sep 28 '10 at 0:06  Your
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