Concept

Topology

Related lectures (29)

Topology of Riemann Surfaces

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

Topologie: Attachment Applications

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

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Local structure of totally disconnected locally compact groups I

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

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: Homeomorphisms

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

Cell Attachment and Homotopy

Covers cell attachment, homotopy, mappings, and universal properties in topology.

Topology in Complex Networks: Insights from Topological Data Analysis

Explores the role of higher-order topological properties in complex networks using topological data analysis for structural break and price anomaly detection.

Topology: Open and Faded Subspace

Covers open and faded subspaces in topology with examples and exercises.

Homotopy and Quotient Spaces

Covers homotopy, quotient spaces, and the universal property in topology.

Topology: Course Notes

Covers the definition of edges, vertices, and cells in geometric shapes.

Metric Spaces: Topology and Continuity

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

Topologie: Exercice 4

Covers Exercise 4 in Topology, focusing on continuous functions and constructing functions.

Topology: Lecture Notes 2021

Covers polygonal performance, homomorphisms, and the Klein bottle in topology.

Space Identification: SO(3)

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

Spatial Relations and Topology

Covers spatial relations, topology, adjacency, connectivity, and intersections in geographic information systems.

Group Cohomology

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

The Topological Künneth Theorem

Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.

Acyclic Models: Cup Product and Cohomology

Covers the cup product on cohomology, acyclic models, and the universal coefficient theorem.

Algebraic Kunneth Theorem

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.