Continuous Functions on a Compact Set are Banach

Last updated Nov 1, 2022

Let $K$ be a Compact Topological Space and suppose $(Y, |\cdot|)$ is a Banach Space over $\mathbb{K}$. Then $C(K, Y)$, the space of Continuous Functions, is a Banach Space over $\mathbb{K}$ when equipped with the Supremum Norm.

Observe that for $f,g \in C(K, Y)$ and $c \in \mathbb{K}$, we have that $cf + g \in C(K, Y)$ because TODO