Metric Spaces and Isometric Embeddings

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Related lectures (30)

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Generalization Error

Explores generalization error in machine learning, focusing on data distribution and hypothesis impact.

Functional Analysis I: Consequences of Baire Theorem

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

Lp Cone and Approximate Embeddings

Covers the concept of Lp cone and approximate embeddings in metric spaces.

Riemannian distance, geodesically convex sets

Covers the structure of Riemannian manifolds, geodesic convexity, and the Riemannian distance function.

Preimages in a Gluing Construction

Delves into preimages of closed sets in a disjoint union.

Hyperbolic Geometry

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

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Compression: Kraft Inequality

Explains compression and Kraft inequality in codes and sequences.

Joint Equidistribution of CM Points

Covers the joint equidistribution of CM points and the ergodic decomposition theorem in compact abelian groups.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.