Concept

Weak topology

Related lectures (32)

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

Topologie: Attachment Applications

Covers exercises on attaching 1-cells to intervals in topology.

Topology: Course Notes 2021

Covers course notes on topology, discussing Stasheff Mérida, cost-savings, and representative points.

Topological Groups

Covers the definition and examples of topological groups, focusing on actions of groups on spaces.

Topology: Disk Deprivation

Delves into disk deprivation in topology, showcasing how spaces emerge from this process.

Dual Space and Weak Convergence

Explores the dual space of a Hilbert space and weak convergence, focusing on orthonormal bases and separable Hilbert spaces.

Weak Convergence in Hilbert Spaces

Explores weak convergence in Hilbert spaces, discussing definitions, implications, and examples.

CW Complexes

Covers the construction and properties of CW complexes, including weak topology and characteristic maps.

Topology: Homeomorphisms

Covers the concept of homeomorphisms in topology, focusing on functions that preserve topological properties.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

Topology: Compactness and Continuity

Explores compactness, continuity, and quotient spaces in topology, emphasizing the topology of lines in R² and the properties of compact sets.

Topology: Lecture Notes 2021

Covers fundamental concepts of topology, group actions, and Galoisian properties.

Convolution and Fourier Transform

Explores convolution properties, heat equation application, and Fourier transform on tempered distributions.

Seifert van Kampen: proof and identification

Covers the proof and identification of isomorphisms in the Seifert van Kampen theorem.

Normed Spaces & Reflexivity

Covers normed spaces, Banach spaces, and Hilbert spaces, as well as dual spaces and weak convergence.

Metric Spaces: Topology and Continuity

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

Local structure of totally disconnected locally compact groups II

Explores the local structure of totally disconnected locally compact groups, covering commensurated subgroups, completions, local automorphisms, and the quasi-centre.

Sobolev Spaces and Continuous Embeddings

Covers Sobolev spaces, continuous embeddings, weak convergence, and Poincare inequalities.

Barycenter and Young Measures

Explains barycenter, weak convergence, uniqueness of limits, distances, and Young measures in LP spaces.

Space Identification: SO(3)

Explores the identification of the space SO(3) and the topology of SS-space of R₃(R).