Embedding in Metric Spaces

Related lectures (32)

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Introduces metric spaces, topology, and continuity, emphasizing the importance of open sets and the Hausdorff property.

Covers convergence, completeness, and properties of metric spaces and Banach spaces.

Covers stability in optimal transport and provides examples of discontinuous optimal solutions.

Explores probability convergence, discussing conditions for random variable sequences to converge and the uniqueness of convergence.

Explores optimal transport in heat equations and metric spaces.

Explores the implications of Baire Theorem in functional analysis and metric spaces.

Explores norms, distances, scalar products, and norm convergence in metric spaces.

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

Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.

Covers metric spaces, isometric embeddings, and equilateral spaces with examples and proofs.