Overview

Introduction In the present essay, we attempt to convey some idea of the skeleton of topology, and of various topological concepts. It must be said at once that, apart from the necessary minimum, the subject-matter of this survey does not indude that subdiscipline known as ""general topology"" - the theory of general spaces and maps considered in the context of set theory and general category theory. (Doubtless this subject will be surveyed in detail by others. ) With this qualification, it may be daimed that the ""topology"" dealt with in the present survey is that mathematieal subject whieh in the late 19th century was called Analysis Situs, and at various later periods separated out into various subdisciplines: ""Combinatorial topology"", ""Algebraic topology"", ""Differential (or smooth) topology"", ""Homotopy theory"", ""Geometrie topology"". With the growth, over a long period of time, in applications of topology to other areas of mathematics, the following further subdisciplines crystallizedout: the global calculus of variations, global geometry, the topology of Lie groups and homogeneous spaces, the topology of complex manifolds and alge­ braic varieties, the qualitative (topologieal) theory of dynamical systems and foliations, the topology of elliptic and hyperbolic partial differential equations. Finally, in the 1970s and 80s, a whole complex of applications of topologie al methods was made to problems of modern physiesj in fact in several instances it would have been impossible to understand the essence of the real physical phenomena in question without the aid of concepts from topology.

Full Product Details

Author:   S.P. Novikov ,  S.P. Novikov ,  B. Botvinnik ,  R. Burns
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of hardcover 1st ed. 1996
Volume:   12
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   0.510kg
ISBN:  

9783642057359

ISBN 10:   3642057357
Pages:   322
Publication Date:   05 December 2010
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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