Covers the concept of intervals in Rn using geometric balls and defines open and closed sets, interior points, boundaries, closures, bounded domains, and compact sets.
Explores the Jordan Curve Theorem, illustrating the division of a plane by a simple closed curve into two regions.
Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.
Covers the compact-open topology, defining maps between spaces and discussing continuous maps and preimages in topology.
Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.
