Where can I find a reference for the general Arzela Ascoli theorem for the space $C(X,Y)$. $X$ anything, but a $Y$ Banach space?
2026-04-03 09:09:21.1775207361
Reference for general Arzela Ascoli theorem
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For compact metric $X$ and complete metric $Y$ you can find it as Theorem 1.5.11 in
Also have a look at Theorem 3.4.20 in
This variant is valid for arbitrary $k$-spaces $X$ and regular spaces $Y$. However, the topology on the set $C(X,Y)$ of continuous functions $X \to Y$ is the compact-open topology. For compact $X$ and metric $Y$ this topology agrees with usual metric topology induced by the $\sup$-metric.