Metric Spaces: Topology and Continuity

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Manifolds: Charts and Compatibility

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Functional Analysis I: Foundations and Applications

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Euclidean Spaces: Properties and Concepts

Covers the properties of Euclidean spaces, focusing on R^n and its applications in analysis.

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.

Normed Spaces

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Metric spaces: topology

Covers metric spaces and topology, exploring properties of metrics, open/closed sets, and boundaries.

Local structure of totally disconnected locally compact groups I

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

Topology of Riemann Surfaces

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

Topology: Open Sets, Compactness, and Connectivity

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