Combinatorial Topology (Dover Books on Mathematics)

Readers seeking knowledge of topology through a systematic study of its essentials need look no further than this excellent text for graduate students specializing in topology or any other related branch of mathematics. Originally published in three volumes, this comprehensive introduction to modern homology theory is geared toward those familiar with general set-theoretic and algebraic concepts.Fundamental topological facts, together with detailed explanations of the necessary technical apparatus, make this three-art volume an invaluable tool for achieving a thorough background in topology. Part one deals with certain classic problems such as the Jordan curve theorem and the classification of closed surfaces without using the formal techniques of homology theory; parts two and three focus on the central concept of combinatorial topology, the Betti groups.This clearly written, well-organized text offers a remarkably coherent introduction to combinatorial topology. Its concise definitions and numerous detailed examples assure readers of a confident grasp of this complex subject, an area of vital importance in modern mathematics.