Fundamentals of Topology

Author: Lin Jinkun
Publisher:
Publish Date: 2004-08-01
Features: After introducing metric spaces, this book introduces topological spaces, then discusses continuous mappings and homeomorphisms, compactness, connectedness, product spaces, and quotient spaces of topological spaces. Starting with simplices, it explains the concepts and properties of simplicial complexes and polyhedra, centroids, subdivision, and the existence theorem of simplicial approximation. It defines the fundamental group and its homotopy equivalence invariance, computational methods, and applications of some computational results. After simplicial homology groups, it introduces singular homology groups, their homotopy equivalence invariance, exact sequences of homology groups, and excision theorems. The second edition, based on the first edition, has refined some content, supplemented some extended material originally intended as exercises to the main text, and added some targeted exercises.