Lectures related to Complete metric space

Metric Spaces: Topology and Continuity

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

Riemannian distance, geodesically convex sets

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

Hyperbolic Geometry

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

Metric Spaces and Isometric Embeddings

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

Probability Theory: Laws and Convergence

Covers Borel-Cantelli lemmas, laws of random variables, and convergence in probability.

Functional Analysis I: Consequences of Baire Theorem

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

Metric Spaces: Norms and Distances

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

Preliminaries in Measure Theory

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

Lp Cone and Approximate Embeddings

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

Preimages in a Gluing Construction

Delves into preimages of closed sets in a disjoint union.

Properties of Complete Spaces

Covers the properties of complete spaces, including completeness, expectations, embeddings, subsets, norms, Holder's inequality, and uniform integrability.

Convergence and Completeness

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

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.

Applied Topology: Compression Schemes and Range Patches

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

Lipschitz Maps and Compact Domains

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

Optimal Transport: Disintegration Theorem

Covers the Disintegration Theorem in the context of Optimal Transport.

Absolute Value and Intervals

Introduces absolute value, intervals, triangle inequality, and complete numbers in the complex plane.

Probability Convergence

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

Linear Operators: Boundedness and Convergence

Explores linear operators, boundedness, and convergence in Banach spaces, focusing on Cauchy sequences and operator identification.

Stereographic Projection and Metric Tensors

Explores stereographic projection and metric tensors on hyperbolic planes, emphasizing isometry and conforming models.