Show that the set $\mathcalF = \le 1, $ is compact.
(subspace of product): Let $X$ be compact Hausdorff. Show $X$ is homeomorphic to a subspace of $[0,1]^J$ for some $J$ (this is a step toward Urysohn metrization).
Prove that $[0,1]^\mathbbR$ is compact in product topology.
Let $X$ be compact metric, $Y$ complete metric. Show $C(X,Y)$ is complete in uniform metric.
Show that the set $\mathcalF = \le 1, $ is compact.
(subspace of product): Let $X$ be compact Hausdorff. Show $X$ is homeomorphic to a subspace of $[0,1]^J$ for some $J$ (this is a step toward Urysohn metrization). munkres topology solutions chapter 5
Prove that $[0,1]^\mathbbR$ is compact in product topology. Show that the set $\mathcalF = \le 1, $ is compact
Let $X$ be compact metric, $Y$ complete metric. Show $C(X,Y)$ is complete in uniform metric. $Y$ complete metric. Show $C(X