This is a book of elementary geometric topology, in which geometry, frequently illustrated, guides calculation. The book starts with a wealth of examples, often subtle, of how to be mathematically certain whether two objects are the same from the point of view of topology. After introducing surfaces, such as the Klein bottle, the book explores the properties of polyhedra drawn on these surfaces. Even in the simplest case, of spherical polyhedra, there are good questions to be asked. There are many examples and exercises making this a useful textbook for a first undergraduate course in topology. For much of the book the prerequisites are slight, though, so anyone with curiosity and tenacity will be able to enjoy the book. As well as arousing curiosity, the book gives a firm geometrical foundation for further study. Takes a new approach to the subject by choosing a geometrical rather than an algebraic or combinatorial approach Contains many examples to develop the student's grasp of the subject and their ability to produce rigorous arguments Includes a foreword written by Roger Penrose INDICE: 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.
- ISBN: 978-1-84800-912-7
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 185
- Fecha Publicación: 01/01/2009
- Nº Volúmenes: 1
- Idioma: Inglés