CW Complexes: Normal and Hausdorff

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Introduction to Topology

Covers fundamental concepts of space, topology, groups, and homology theory.

Serre model structure: Left and right homotopy

Explores the Serre model structure, focusing on left and right homotopy equivalences.

Separation Conditions: Graph and Saturations

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

Surfaces: The Torus

Explores the definition of surfaces, focusing on the torus and its construction through various examples and morphic images.

Separation Criterion in Recollement

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

Local structure of totally disconnected locally compact groups I

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

Metric Spaces: Topology and Continuity

Introduces metric spaces, topology, and continuity, emphasizing the importance of open sets and the Hausdorff property.

Homology Theorem

Covers the proof of Theorem A, discussing homology, quotients, and isomorphisms.

Group Actions: Quotients and Homomorphisms

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

Modular curves: Riemann surfaces and transition maps

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