Lectures related to Implicit Functions Theorem

Explores compact sets, extreme values, and function theorems on bounded sets.

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

Explores linear operations, convergence, sequences, and compact sets in mathematical analysis.

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

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

Explores the Stone-Weierstrass theorem, proving uniform density of specific function families on compact sets.

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

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

Explores Lagrange multipliers for finding extrema under constraints and implicit functions theorem.

Covers the conditions for finding absolute extrema in multivariable functions.

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

Covers the Prokhorov Theorem in Optimal Transport, emphasizing support sets and optimality conditions.

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

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

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

Explores optimal transport, emphasizing convexity properties and inequalities in compact sets.

Explains setting up experiments with compactness, isometries, and quasi-isometry.

Discusses optimization techniques, focusing on local and global extrema in functions.

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

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