Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.
Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.
Explores the proof of Weyl's theorem, focusing on discrete spectrum, ground states, and potential energy continuity.
Explores the integrability of continuous functions on closed pavés and the properties of their integrals, including boundedness and Darboux sums.
Covers the compact-open topology, defining maps between spaces and discussing continuous maps and preimages in topology.
