Lectures related to Spatial Topological Queries

Delves into group actions, coverings, fundamental groups, and homomorphisms in topological spaces.

Covers the fundamentals of homotopy and its applications in topology.

Explores closed curves in topological spaces, emphasizing their properties and significance in mathematics.

Topology: Separation Criteria and Quotient Spaces

Discusses separation criteria and quotient spaces in topology, emphasizing their applications and theoretical foundations.

Topology: Homotopy and Projective Spaces

Discusses homotopy, projective spaces, and the universal property of quotient spaces in topology.

Topology: Homotopy and Cone Attachments

Discusses homotopy and cone attachments in topology, emphasizing their significance in understanding connected components and fundamental groups.

Introduction to Model Categories

Explores lifting properties and model categories in topological spaces.

Topology: Exploring Cohomology and Quotient Spaces

Covers the basics of topology, focusing on cohomology and quotient spaces, emphasizing their definitions and properties through examples and exercises.

Topology: Fundamental Groups and Surfaces

Discusses fundamental groups, surfaces, and their topological properties in detail.

Topology: Fundamental Groups and Applications

Provides an overview of fundamental groups in topology and their applications, focusing on the Seifert-van Kampen theorem and its implications for computing fundamental groups.

Group Actions: Examples

Showcases examples of group actions on vector spaces and topological spaces.

Topology: Classification of Surfaces and Fundamental Groups

Discusses the classification of surfaces and their fundamental groups using the Seifert-van Kampen theorem and polygonal presentations.

Pushouts in Group Theory: Universal Properties Explained

Covers the construction and universal properties of pushouts in group theory.

Functional Analysis and Distribution Theory

Introduces functional analysis, distribution theory, topological vector spaces, and linear operators, emphasizing their importance in engineering applications.

Base B for X: Connected Sets and Open Bases

Explores the concept of a base B for a topological space X and the properties of connected sets and open bases.

Functional Analysis I: Foundations and Applications Log in to Mediaspace to watch this video

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

CW Complexes Log in to Mediaspace to watch this video

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

Homotopy Extension Property Log in to Mediaspace to watch this video

Demonstrates how to obtain homotopy equivalences between different spaces using the homotopy extension property.

Induced Homomorphisms on Relative Homology Groups Log in to Mediaspace to watch this video

Covers induced homomorphisms on relative homology groups and their properties.

Inverse Limits and Topologies Log in to Mediaspace to watch this video

Explores inverse limits, profinite completions, and Hausdorff topologies in group theory and topology.