Metric map

I don’t know about this concept. In fact the metric map is the nonexpansive map.

A continuous function between two metric spaces that does not increase distance, i.e.

d(f(x),f(y) \le d(x,y) with f: X \to Y.

There are many names for this concept: metric map, nonexpansive map, Lipschitz map with constant K=1, short map, weak contraction, nonexpanding map.

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