A Topological Aperitif
Seiten
2009
|
2nd ed. 2009
Springer London Ltd (Verlag)
978-1-84800-912-7 (ISBN)
Springer London Ltd (Verlag)
978-1-84800-912-7 (ISBN)
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.
Foreword (written by Roger Penrose).- Homeomorphic Sets.- Topological Properties.- Equivalent Subsets.- Surfaces and Spaces.- Polyhedra.- Winding Number.- Appendix A: Continuity.- Appendix B: Knots.- Appendix C: History.- Appendix D: Solutions.- Bibliography.- Index.
| Erscheint lt. Verlag | 26.3.2009 |
|---|---|
| Zusatzinfo | 135 Illustrations, black and white; IX, 152 p. 135 illus. |
| Verlagsort | England |
| Sprache | englisch |
| Maße | 178 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 1-84800-912-7 / 1848009127 |
| ISBN-13 | 978-1-84800-912-7 / 9781848009127 |
| Zustand | Neuware |
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