Lectures related to Closure Finiteness of CW Complexes

Explores the construction and properties of CW complexes, focusing on characteristic maps, closed subsets, products, quotients, and cell formation.

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Focuses on a criterion for separability in recollement, demonstrating iron properties and applications in various cases.

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Explores the exponential law for mapping spaces and the role of compactness in topological theory.

Covers the definitions and basic results of endomorphisms and automorphisms of totally disconnected locally compact groups.

Explores compact subsets of R^n, convergence theorems, and set properties.

Explains setting up experiments with compactness, isometries, and quasi-isometry.

Explores compact sets, extreme values, and function theorems on bounded sets.

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

Covers extreme values of continuous functions on compact sets and differentiability.

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

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Covers the compact-open topology, defining maps between spaces and discussing continuous maps and preimages in topology.

Explores adhesion, convergence, closed sets, compact subsets, and examples of subsets in R^n.

Covers the decomposition of a CW complex based on characteristic maps and cell containment.

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