Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.
Explores the properties of the quotient space X/G when X is compact and sometimes separated.
Explores the construction and properties of CW complexes, focusing on characteristic maps, closed subsets, products, quotients, and cell formation.
Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.
Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.
