Advanced Analysis II: Eigenvalues and Compact Sets

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Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Covers matrix diagonalization, compact sets, continuity of functions, and the Mandelbrot set.

Explores interior points, boundaries, adherence, and compact sets, including definitions and examples.

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Explores adhesion, convergence, closed sets, compact subsets, and examples of subsets in R^n.

Discusses open subsets, compact sets, and methods for demonstrating openness in a space.

Covers open balls in Euclidean spaces, their properties, and their significance in topology.

Explores continuous functions on compact sets, discussing boundedness and extremum values.

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Covers the definitions and basic results of endomorphisms and automorphisms of totally disconnected locally compact groups.