Let $f : (M, d) \to (N, p)$ be one-to-one and onto. Then the following are equivalent:
$f$ is a homeomorphism.
$d_1(x , y) = p(f(x), f(y))$ defines a metric on $M$ equivalent to $d$.
↧
f is a homeomorphism thrn show that the following statement are equivalent [closed]
↧