Advanced Analysis I: Continuous Functions on Compact Sets

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Convergence and Compactness in R^n

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

Bolzano-Bastra-Sterl: Applications and Uniform Continuity

Explores the Bolzano-Bastra-Sterl theorem and uniform continuity in sequences.

Uniqueness of Solutions: Cauchy-Lipschitz Theorem

Covers the uniqueness of solutions in differential equations, focusing on the Cauchy-Lipschitz theorem and its implications for local and global solutions.

Integral Properties on Closed Pavés

Explores the integrability of continuous functions on closed pavés and the properties of their integrals, including boundedness and Darboux sums.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Compact Subsets of R^n

Explores compact subsets of R^n, convergence theorems, and set properties.

Compact Embedding: Theorem and Sobolev Inequalities

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Continuous Functions on Closed Interval

Explores continuous functions on closed intervals, emphasizing the importance of understanding definitions for continuity.

The Intermediate Value Theorem

Explains the Intermediate Value Theorem for continuous functions on closed intervals.

Endomorphisms and automorphisms of totally disconnected locally compact groups I

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