Advanced Analysis I: Continuous Functions on Compact Sets

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Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Explores dense sets, Cauchy sequences, periodic solutions, and unique solutions in differential equations.

Explores the Darboux theorem for continuous functions on closed intervals, emphasizing uniform continuity and function behavior implications.

Covers the Cantor-Heine theorem, discussing uniform continuity and compactness.

Covers the concept of uniform continuity and a theorem on continuous functions.

Covers the description of problem solutions and the concept of compactness and uniform continuity.

Delves into advanced analysis topics, emphasizing continuity, limits, and uniform continuity.

Covers continuous functions with compact support, density, and approximation, focusing on the heat equation.

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

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