Lectures related to Axiomatic foundations of topological spaces

Miniaturized Microwave Systems: Topological Wave Control

Explores miniaturized microwave systems, wave control challenges, and topological filters for miniaturized applications.

CW Complexes

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

Topological Waves for Robust Signal Processing Applications

Explores topological waves for robust signal processing applications, focusing on resistance to perturbations and the design paradigm of topological systems.

Induced Homomorphisms on Relative Homology Groups

Covers induced homomorphisms on relative homology groups and their properties.

Homotopy: Fundamentals and Examples

Covers the fundamentals of homotopy and its applications in topology.

Spatial Topological Queries

Explores topology, test functions, and space operators for spatial queries.

Homotopy Extension Property

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

Group Actions and Fundamental Groups

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

Inverse Limits and Topologies

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

Topology: Separation Criteria and Quotient Spaces

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

Homotopy Extension Property

Introduces the homotopy extension property, exploring conditions for extending continuous maps.

Topology: Homotopy and Projective Spaces

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

Knot Theory: The Quadratic Linking Degree

Covers the quadratic linking degree in knot theory, exploring its definitions, properties, and significance in algebraic geometry.

Functional Analysis I: Foundations and Applications

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

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: Homotopy and Cone Attachments

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

Topology: Open Sets, Compactness, and Connectivity

Explores open sets, compactness, and connectivity in topology, covering topological spaces and compact sets.

Pushouts in Group Theory: Universal Properties Explained

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

Introduction to Model Categories

Explores lifting properties and model categories in topological spaces.

Limits and colimits in Top

Covers the concepts of limits and colimits in the category of Topological Spaces, emphasizing the relationship between colimit and limit constructions and adjunctions.