If $\cal A$ is an abelian Banach algebra, then its maximal ideal space $\Omega$ is a compact Hausdorff space.
In the proof of this theorem, the author says, since $\Omega \subset ball \cal A^*$, it suffices to show that $\Omega$ is weak* closed.
My question: Why does Heine - Borel theorem hold in $\cal A^*$?
Please help me. Thanks in advance.
The right naming here would not be "Heine-Borel" but "Banach-Alaoglu".