Projective Spaces: Separation and Definitions

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Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Compact Sets and Extreme Values

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

The Jordan Curve Theorem

Explores the Jordan Curve Theorem, illustrating the division of a plane by a simple closed curve into two regions.

Properties of X/G

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

Preparations for Surjection

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

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.

Modular curves: Riemann surfaces and transition maps

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

Proof of Weyl's Theorem

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

Topology: Compactness and Continuity

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