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Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.
Explores the spectrum of hyperbolic surfaces, discussing thin C-principle, grad, normalized functions, minimum volume, and embedding properties.
Explores the Mayer-Vietoris sequence, exact homomorphisms, embedded spheres, and path-connected spaces.
Explores the Jordan Curve Theorem, illustrating the division of a plane by a simple closed curve into two regions.
Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
Explores the definition of surfaces, focusing on the torus and its construction through various examples and morphic images.
Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.
Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.
Explores the lifting criterion for maps between path-connected and locally path-connected spaces.
Explores connected components in a decked space and the well-defined application of functions.
