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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 fundamental groups, homotopy classes, and coverings in connected manifolds.
Explores the spectrum of hyperbolic surfaces, discussing thin C-principle, grad, normalized functions, minimum volume, and embedding properties.
Explores the Jordan Curve Theorem, illustrating the division of a plane by a simple closed curve into two regions.
Explores the Mayer-Vietoris sequence, exact homomorphisms, embedded spheres, and path-connected spaces.
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.
