Compact Subsets of R^n

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Convergence and Limits in Real Numbers

Explains convergence, limits, bounded sequences, and the Bolzano-Weierstrass theorem in real numbers.

The Jordan Curve Theorem

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

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.

Modular curves: Riemann surfaces and transition maps

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

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.

Convergent Sequences: Definitions and Illustrations

Explains convergent sequences, bounded sequences, subsequences, and compact sets with illustrations and proofs.

Compact-open topology

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

Topology of Adeles

Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.

Compact Sets and Extreme Values

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

Topology: Separation Criteria and Quotient Spaces

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