The Connected Sum: Surfaces and Gluing

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

Covers the concept of homeomorphisms in topology, focusing on functions that preserve topological properties.

Covers open and faded subspaces in topology with examples and exercises.

Covers the definition of edges, vertices, and cells in geometric shapes.

Explores the identification of the space SO(3) and the topology of SS-space of R₃(R).

Covers Riemann surfaces as complex manifolds of dimension 1, including transition maps and holomorphic functions.

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

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

Covers spatial relations, topology, adjacency, connectivity, and intersections in geographic information systems.

Delves into disk deprivation in topology, showcasing how spaces emerge from this process.