Lectures related to Compact Sets and Extreme Values

Covers extreme values of continuous functions on compact sets and differentiability.

Explores limits, minimum and maximum values of functions, and continuity criteria in a compact set.

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

Covers the conditions for finding absolute extrema in multivariable functions.

Covers weak derivatives, their properties, and applications in functional analysis.

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

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

Explores limits, convergence, and boundedness of functions and sequences.

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Covers the construction of measures in RN, focusing on separation and partition of compact sets.

Covers the optimization of functions, focusing on finding the maximum and minimum values over a given domain.

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

Covers the optimization of functions, focusing on finding the maximum and minimum values.

Explains convergence, limits, bounded sequences, and the Bolzano-Weierstrass theorem in real numbers.

Explores limits of functions in several real variables, including the two gendarmes theorem and the minimum and maximum theorem on compact sets.

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

Covers the concepts of sequences, convergence, and boundedness in mathematics.

Explores optimal transport analysis and proofs, emphasizing weak convergence and compactness.

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

Explores mild dissipative surface dynamics, including conservative behavior and ergodic functions.