Weierstrass extreme value theorem

Theorem

Let $f : \Omega \to \mathbb{R}$ be a continuous function defined on a nonempty and compact set $\Omega$. Then, there exists a minimizer $x^* \in \Omega$ of $f$ on $\Omega$, that is

References

1. https://www.mit.edu/~gfarina/2025/67220s25_L01_introduction/