Solution
= Solution
The map is $K$-<Lipschitz continuous> when
$$
\boxed{d_Y(f(x),f(x'))\leq Kd_X(x,x')\quad\text{for every }x,x'\in X.}
$$
The same finite <Lipschitz constant> $K$ must work for all pairs of points.
= Solution
The map is $K$-<Lipschitz continuous> when
$$
\boxed{d_Y(f(x),f(x'))\leq Kd_X(x,x')\quad\text{for every }x,x'\in X.}
$$
The same finite <Lipschitz constant> $K$ must work for all pairs of points.