Short feature

In mathematics, one short function It's a function. f of a metric space X in another metric space And such as for all x,and한 한 X{displaystyle x,yin X}We've got

dAnd(f(x),f(and))≤ ≤ dX(x,and){displaystyle d_{Y}(f(x),f(y))leq d_{X}(x,y)}.

Here. dX{displaystyle d_{X}} and dAnd{displaystyle d_{Y} denote metrics in X{displaystyle X} and And{displaystyle Y}respectively. In other words, f is short ssi is 1-Lipschitz.

We can say that f That's it. strictly short if inequality, except in case x=and{displaystyle x=y}It's always strict. Then a contraction is strictly short, but not reciprocal (even with X = And).