Concept

Separable space

Related lectures (30)

Covers the Disintegration Theorem in the context of Optimal Transport.

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

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

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

Explores orthonormal bases in Hilbert spaces, discussing their properties and generation using the Gram-Schmidt method.

Explores Hilbert space, scalar product, geometry, bases, complex functions, and quantum mechanics applications.

Covers the Perceptron model, SGD, and Fisher's Linear Discriminant in binary classification.

Explores DFS, Topological Sort, SCC in graphs, and introduces Flow Networks with practical examples.

Explores topological sort, acyclic graphs, Strongly Connected Components, magic algorithm, component graph, flow networks, and their applications.

Explores redescription SVM and Hilbert spaces for solving nonlinear problems using inner product spaces and separable Hilbert spaces.

Covers homomorphisms, algebraic extensions, cutting, splitting, and separable elements in Fok [x].

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

Covers topics like DFS output, edge classification, acyclic graphs, correctness, time analysis, SCCs, and the Topological Sort algorithm.

Covers the spectral theorem, focusing on the second part and orthonormal sequences in a separable Hilbert space.

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Covers normed vector spaces, including definitions, properties, examples, and sets in normed spaces.

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

Covers Breadth-First Search, Depth-First Search, and topological sort in graphs.

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