Lectures related to Path Lifting: Unique Path Lifting

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

Group Actions: Quotients and Homomorphisms

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

Setting up Experiments: Compactness, Isometries, Quasi-Isometry

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

Compact Sets and Extreme Values

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

Compact Embedding: Theorem and Sobolev Inequalities

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

Preparations for Surjection

Covers the fundamental group of a reattachment and surjection proofs with neighborhoods and cover overlays.

Open Subsets and Compact Sets

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

Proof of Weyl's Theorem

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

Initial Problem Solutions

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

Cell Attachment: Gluing and Application

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

Proper Actions and Quotients

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

Separation Criterion in Recollement

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

Separation Conditions: Graph and Saturations

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

Projective Spaces: Separation and Definitions

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

Research Methods: Setting Up Experiments and Interview Guides

Explores setting up experiments, interview guides, and self-experimentation in research methods.

Properties of X/G

Explores the properties of the quotient space X/G when X is compact and sometimes separated.

Interior Points and Compact Sets

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

Functional Analysis: Compactness and Uniqueness

Explores compactness and uniqueness in functional analysis, emphasizing equicontinuity and boundedness.

Topology: Separation Criteria and Quotient Spaces

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

Extreme Values of Continuous Functions

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