Lectures related to Optimal Transport: Stability and Monotonicity

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

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

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

Covers the fundamental group of a reattachment and surjection proofs with neighborhoods and cover overlays.

Explores the proof of Weyl's theorem, focusing on discrete spectrum, ground states, and potential energy continuity.

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

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

Covers cell attachment, gluing cells, and separability in a compact space.

Covers separated spaces, saturation properties, and projective spaces, including the real projective plane and compactness.

Explores the properties of the quotient space X/G when X is compact and sometimes separated.

Focuses on a criterion for separability in recollement, demonstrating iron properties and applications in various cases.

Covers the description of all solutions of the initial problem and related concepts such as compactness and closure.

Discusses separation conditions, graph, and saturations in equivalence relations on a space.

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

Discusses separation criteria and quotient spaces in topology, emphasizing their applications and theoretical foundations.

Explores the construction and properties of CW complexes, focusing on characteristic maps, closed subsets, products, quotients, and cell formation.

Explores setting up experiments, interview guides, and self-experimentation in research methods.

Explores compactness and uniqueness in functional analysis, emphasizing equicontinuity and boundedness.

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

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