Isometry
Posted: Sun May 29, 2016 10:34 pm
Let \( (X, \rho) \) be a compact space and let \( f \) be a function defined on \( X \) such that:
$$\rho(f(x), f(y)) \geq \rho(x, y) $$
Prove that all functions that obey the above equation are all isometries.
$$\rho(f(x), f(y)) \geq \rho(x, y) $$
Prove that all functions that obey the above equation are all isometries.