Lectures related to CW Complexes

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

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.

Metric Spaces: Topology and Continuity

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

Topology: Open Sets, Compactness, and Connectivity

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

Functional Analysis I: Foundations and Applications

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

Normed Spaces

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

Topology: Fundamental Groups and Surfaces

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

Topology: Homotopy and Projective Spaces

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

Modular curves: Riemann surfaces and transition maps

Covers modular curves as compact Riemann surfaces, explaining their topology, construction of holomorphic charts, and properties.

Dimension Theory: Topological Space and Closed Subsets

Explores dimension theory in topological spaces and closed subsets, including height interpretation and additivity.

Homotopy Extension Property

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

Homotopy Extension Property

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

Topology: Separation Criteria and Quotient Spaces

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

Vector Spaces and Topology

Covers vector spaces, topology, and proof methods like the pigeonhole principle in R^n.

Vector Spaces and Topology

Covers normed vector spaces, topology in R^n, and the principle of drawers as a demonstration method.

Inverse Limits and Topologies

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

Topology: Homotopy and Cone Attachments

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

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.

Induced Homomorphisms on Relative Homology Groups

Covers induced homomorphisms on relative homology groups and their properties.

Closed Curves and Topological Spaces

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