ИСТИНА

For a mapping $f:(X,\rho_1)\to(Y,\rho_2)$ between bounded metric spaces the following statements are equivalent: 1) the mapping $f$ has the property of lipschitz; 2) the mapping $M_\tau(f):(M_\tau(X),M_\tau(\rho_1))\to(M_\tau(Y),M_\tau(\rho_2))$ has the property of lipschitz; 3) the mapping $M_\tau(f)$ is uniformly continuous.