Let $X$ be compact metric, $Y$ complete metric. Show $C(X,Y)$ is complete in uniform metric.
Show that the set $\mathcalF = f(x)$ is compact.
Prove that $[0,1]^\mathbbR$ is compact in product topology.
Show that the set $\mathcalF = f(x)$ is compact. munkres topology solutions chapter 5
Prove that $[0,1]^\mathbbR$ is compact in product topology. Let $X$ be compact metric, $Y$ complete metric