ISBN-10:
1848009127
ISBN-13:
9781848009127
Pub. Date:
02/27/2009
Publisher:
Springer London
A Topological Aperitif / Edition 2

A Topological Aperitif / Edition 2

by Stephen Huggett, David Jordan

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Overview

Topologyhasbeenreferredtoas“rubber-sheetgeometry”.Thenameisapt,for the subject is concerned with properties of an object that would be preserved, no matter how much it is stretched, squashed, or distorted, so long as it is not in any way torn apart or glued together. One’s ?rst reaction might be that such animprecise-soundingsubjectcouldhardlybepartofseriousmathematics,and wouldbeunlikelytohaveapplicationsbeyondtheamusementofsimpleparlour games. This reaction could hardly be further from the truth. Topology is one of the most important and broad-ranging disciplines of modern mathematics. It is a subject of great precision and of breadth of development. It has vastly many applications, some of great importance, ranging from particle physics to cosmology, and from hydrodynamics to algebra and number theory. It is also a subject of great beauty and depth. To appreciate something of this, it is not necessary to delve into the more obscure aspects of mathematical formalism. For topology is, at least initially, a very visual subject. Some of its concepts apply to spaces of large numbers of dimensions, and therefore do not easily submit to reasoning that depends upon direct pictorial representation. But even in such cases, important insights can be obtained from the visual - rusal of a simple geometrical con?guration. Although much modern topology depends upon ?nely tuned abstract algebraic machinery of great mathematical sophistication, the underlying ideas are often very simple and can be appre- ated by the examination of properties of elementary-looking drawings.

Product Details

ISBN-13: 9781848009127
Publisher: Springer London
Publication date: 02/27/2009
Edition description: 2nd ed. 2009
Pages: 152
Product dimensions: 6.80(w) x 9.10(h) x 0.40(d)

Table of Contents

Homeomorphic Sets.- Topological Properties.- Equivalent Subsets.- Surfaces and Spaces.- Polyhedra.- Winding Number.

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