Lp Cone and Approximate Embeddings

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

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

Delves into preimages of closed sets in a disjoint union.

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

Explores optimal transport in heat equations and metric spaces.

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

Covers Lipschitz maps, compact domains, changing variables, counting problems, and probability of ideals.

Explores compression schemes, texture recognition, range patches, evolution, and variants on persistence in applied topology.

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

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