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Many topological problems can be solved by using either combinatorial or differential methods. The main goal of this text is to advance as far as possible in the study of the properties of topological spaces (especially manifolds) without employing complicated techniques.
"Modern topology uses very diverse methods. This book is devoted largely to methods of combinatorial topology, which reduce the study of topological spaces to investigations of their partitions into elementary sets, and to methods of differential topology, which deal with smooth…