Advanced Topics of Topology

Book excerpt: Topology is an area of mathematics that establishes relations and transformations between spaces with a certain structure depending on their position and considering the structure of the ambient space where these relations exist. This book discusses various concepts and theories of topology, including diffeomorphisms, immersions, Hausdorff spaces, cobordisms, homotopy theory, symplectic manifolds, topology of quantum field theory, algebraic varieties, dimension theory, Koszul complexes, continuum theory, and metrizability, among others.