Complete metric space

Related lectures (32)

Page 3 of 4

Explores distance, geodesics, and complete manifolds, emphasizing the existence of minimizing geodesics and the concept of metric completeness.

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

Covers the foundations of modern analysis, introductory functional analysis, and applications in MAB111.

Explores optimal transport, gradient flows, the implicit Euler scheme, and the heat equation in the context of Dirichlet energy functional.

Explores the Banach Fixed Point Theorem, showing the uniqueness of fixed points in contraction mappings.

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

Explores embedding in metric spaces, discussing mappings, distances, and convergence.

Covers the Class Number Formula and a counting problem related to the lattice and Lipschitz principle.

Covers the construction of Qp, norms, valuations, and Ostrovski's theorem.

Covers metric spaces and topology, exploring properties of metrics, open/closed sets, and boundaries.