# compact set

a set is compact iff it is both closed and bounded, i.e of finite size.

for a function \(f: \Gamma \to \mathbb{R}\) where \(\Gamma\) is a compact set, \(f\) is bounded above and has a maximum within \(\Gamma\).

a set is compact iff it is both closed and bounded, i.e of finite size.

for a function \(f: \Gamma \to \mathbb{R}\) where \(\Gamma\) is a compact set, \(f\) is bounded above and has a maximum within \(\Gamma\).