Interior and Closure in Topology

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Sub-Varieties and Topological Concepts

Covers sub-varieties in different dimensions and topological concepts with examples and applications of theorems.

Homotopy Extension Property

Introduces the homotopy extension property, exploring conditions for extending continuous maps.

Modular curves: Riemann surfaces and transition maps

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

CW Complexes

Covers the construction and properties of CW complexes, including weak topology and characteristic maps.

Dimension theory of rings

Covers the dimension theory of rings, including additivity of dimension and height, Krull's Hauptidealsatz, and the height of general complete intersections.

Sheaves: Hartshorne I.1

Covers the concept of sheaves, emphasizing the unique determination of functions by local data and the importance of direct limits.

Homology of Riemann Surfaces

Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.

Advanced Analysis 2: Isolated Points and Continuity

Covers advanced topics in analysis, focusing on isolated points, continuity, and level sets.

Closed Curves and Topological Spaces

Explores closed curves in topological spaces, emphasizing their properties and significance in mathematics.

Topology of Riemann Surfaces

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