Topology

כריכה קדמית
Courier Corporation, 23 במאי 2012 - 384 עמודים

"As textbook and reference work, this is a valuable addition to the topological literature." — Mathematical Reviews
Designed as a text for a one-year first course in topology, this authoritative volume offers an excellent general treatment of the main ideas of topology. It includes a large number and variety of topics from classical topology as well as newer areas of research activity.
There are four set-theoretic chapters, followed by four primarily algebraic chapters. Chapter I covers the fundamentals of topological and metrical spaces, mappings, compactness, product spaces, the Tychonoff theorem, function spaces, uniform continuity and uniform spaces. The next two chapters are devoted to topics in point-set topology: various separation axioms, continua in Hausdorff spaces, real-valued functions, and more Chapter IV is on homotopy theory. Chapter V covers basic material on geometric and abstract simplicial complexes and their subdivisions. Chapter VI is devoted to simplicial homology theory, Chapter VII covers various topics in algebraic topology, including relative homology, exact sequences, the Mayer-Vietoris sequence, and more. Finally, Chapter VIII discusses Cech homology.
There are a large number of illuminating examples, counter-examples and problems, both those which test the understanding and those which deepen it. The authors have also made a special effort to make this an "open-ended" book, i.e while many topics are covered, there is much beyond the confines of this book. In many instances they have attempted to show the direction in which further material may be found.
Topology is so fundamental, its influence is apparent in almost every other branch of mathematics, as well as such fields as symbolic logic, mechanics, geography, network theory, and even psychology. This well-written text offers a clear and careful exposition of this increasingly important discipline.

 

תוכן

TOPOLOGICAL SPACES AND FUNCTIONS
1
THE ELEMENTS 0F POINTSET TOPOLOGY
37
FURTHER TOPICS IN POINTSET TOPOLOGY
105
THE ELEMENTS or HOMOTOPY THEORY
149
POLYTOPES AND TRIANGULATED SPACES
193
SIMPLIOIAL HOMOLOGY THEORY
218
torsion coefficients
234
FURTHER DEVELOPMENTS IN ALGEBRAIC TOPOLOGY
282
GENERAL HOMOLOGY THEORIES
320
REFERENCES
365
INDEX
371
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