Lectures related to Preparations for Surjection

Harmonic Forms: Main Theorem

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

Differential Forms Integration

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

Compact Embedding: Theorem and Sobolev Inequalities

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

Setting up Experiments: Compactness, Isometries, Quasi-Isometry

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

Open Mapping Theorem

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

Proper Actions and Quotients

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

Proof of Weyl's Theorem

Explores the proof of Weyl's theorem, focusing on discrete spectrum, ground states, and potential energy continuity.

Compact Sets and Extreme Values

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

Initial Problem Solutions

Covers the description of all solutions of the initial problem and related concepts such as compactness and closure.

Separation Criterion in Recollement

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

Convergence and Compactness in R^n

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

Jordan Curve Theorem

Covers the proof of the Jordan Curve Theorem and the properties of embedded spheres.

Group Actions: Quotients and Homomorphisms

Discusses group actions, quotients, and homomorphisms, emphasizing practical implications for various groups and the construction of complex projective spaces.

Initial Problem Solutions

Covers the description of problem solutions and the concept of compactness and uniform continuity.

Cell Attachment: Gluing and Application

Covers cell attachment, gluing cells, and separability in a compact space.

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.

Projective Spaces: Separation and Definitions

Covers separated spaces, saturation properties, and projective spaces, including the real projective plane and compactness.

Preliminaries in Measure Theory

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

Topology: Separation Criteria and Quotient Spaces

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

Integral Properties on Closed Pavés

Explores the integrability of continuous functions on closed pavés and the properties of their integrals, including boundedness and Darboux sums.