Prove or disprove: If $M$ is complete and $f:(M, d )\to (N, p)$ is continuous, then $f(M)$ is complete.
If $M$ is complete and $f : (M,d)\to(N,p)$ is continuous, then $f(M)$ is complete?
2
$\begingroup$
real-analysis
general-topology
metric-spaces
-
2Asymptotes and such things kill this: consider the function $x\mapsto e^{-x^2}$, for example. – 2012-05-20