Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
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.
Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.
Explores the Jordan Curve Theorem, illustrating the division of a plane by a simple closed curve into two regions.
Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.
Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.
Covers the fundamentals of group theory in physics, focusing on symmetries and transformations leaving physical equations unchanged.
Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.
