# Continuous Function on Compact Subspace of Euclidean Space is Bounded

## Theorem

Let $\R^n$ be the $n$-dimensional Euclidean space.

Let $S \subseteq \R^n$ be a compact subspace of $\R^n$.

Let $f: S \to \R$ be a continuous function.

Then $f$ is bounded in $\R$.

## Proof

An application of Continuous Function on Compact Space is Bounded.