Lectures related to CW Complexes: Products and Quotients

Closure Finiteness of CW Complexes

Explores closure finiteness in CW complexes, proving compact subspaces are contained in finite subcomplexes through induction and characteristic maps.

Open Mapping Theorem

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

Interior Points and Compact Sets

Explores interior points, boundaries, adherence, and compact sets, including definitions and examples.

Convergence and Compactness in R^n

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

Open Subsets and Compact Sets

Discusses open subsets, compact sets, and methods for demonstrating openness in a space.

Differential Forms Integration

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

Separation Conditions: Graph and Saturations

Discusses separation conditions, graph, and saturations in equivalence relations on a space.

Open Balls and Topology in Euclidean Spaces

Covers open balls in Euclidean spaces, their properties, and their significance in topology.

Analysis IV: Measurable Sets and Functions

Introduces measurable sets, functions, and the Cantor set properties, including ternary development of numbers.

Proper Actions and Quotients

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

Properties of Convergence: Sequences and Topology

Discusses the properties of sequences, convergence, and their relationship with topology and compactness.

Compact Subsets of R^n

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

Properties of Closed Sets

Covers the properties of closed sets and their convergence within subsequences.

Harmonic Forms: Main Theorem

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

Demonstration of Theorem on Compact Functions

Explores the demonstration of a theorem on compact functions and non-regular boundaries.

Topology: Open Sets, Compactness, and Connectivity

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

Endomorphisms and automorphisms of totally disconnected locally compact groups I

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

Distribution & Interpolation Spaces

Covers the concept of distributions with compact support and their interpolation spaces.

Compact Embedding: Theorem and Sobolev Inequalities

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