Fundamental GroupsExplores fundamental groups, homotopy classes, and coverings in connected manifolds.
Surfaces: The TorusExplores the definition of surfaces, focusing on the torus and its construction through various examples and morphic images.
Open Mapping TheoremExplains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.
Hyperbolic GeometryIntroduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.
Lifting CriterionExplores the lifting criterion for maps between path-connected and locally path-connected spaces.
Connected ComponentsExplores connected components in a decked space and the well-defined application of functions.
