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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 manifolds and smooth maps. Many topological problems can be solved by using either of these two kinds of methods, combinatorial or differential. In such cases, both approaches are discussed. One of the main goals of this book is to advance as far as possible in the study of the properties of topological spaces (especially manifolds) without employing complicated techniques. This distinguishes it from the majority of other books on topology. The book contains many problems; almost all of them are supplied with hints or complete solutions.
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 manifolds and smooth maps. Many topological problems can be solved by using either of these two kinds of methods, combinatorial or differential. In such cases, both approaches are discussed. One of the main goals of this book is to advance as far as possible in the study of the properties of topological spaces (especially manifolds) without employing complicated techniques. This distinguishes it from the majority of other books on topology. The book contains many problems; almost all of them are supplied with hints or complete solutions.
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We consider graph theory in much more detail than it is usually done in topology courses. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
vector field without singular points, relative spheroids, deleted join, deleted product, rectilinear cells, pendant edge, barycentric subdivision, simplicial approximation, homotopy equivalent, maximal tree, double tangents, locally trivial fibration, degenerate critical points, disjoint neighborhoods, end vertices, polygonal curve, universal covering space, initial simplex, required assertion, solid torus, fewer edges, regular value, fundamental group, required partition, constant map Key Phrases - Capitalized Phrases (CAPs): (learn more)
Properties of Graphs, Borsuk Ulant, Topology of Subsets of Euclidean Space New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
We consider graph theory in much more detail than it is usually done in topology courses. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
vector field without singular points, relative spheroids, deleted join, deleted product, rectilinear cells, pendant edge, barycentric subdivision, simplicial approximation, homotopy equivalent, maximal tree, double tangents, locally trivial fibration, degenerate critical points, disjoint neighborhoods, end vertices, polygonal curve, universal covering space, initial simplex, required assertion, solid torus, fewer edges, regular value, fundamental group, required partition, constant map Key Phrases - Capitalized Phrases (CAPs): (learn more)
Properties of Graphs, Borsuk Ulant, Topology of Subsets of Euclidean Space New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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