Topology Without Tears
| Автор(ы): | Sidney A. Morris
06.10.2007
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| Год изд.: | 2003 |
| Описание: | Topology is an important and interesting area of mathematics, the study of which will not only introduce you to new concepts and theorems but also put into context old ones like continuous functions. However, to say just this is to understate the significance of topology. It is so fundamental that its influence is evident in almost every other branch of mathematics. This makes the study of topology relevant to all who aspire to be mathematicians whether their first love is (or will be) algebra, analysis, category theory, chaos, continuum mechanics, dynamics, geometry, industrial mathematics, mathematical biology, mathematical economics, mathematical finance, mathematical modelling, mathematical physics, mathematics of communication, number theory, numerical mathematics, operations research or statistics. |
| Оглавление: |
Обложка книги.
1.1 Topology [2] 1.2 Open Sets [9] 1.3 Finite-Closed Topology [14] 1.4 Postscript [21] 2 The Euclidean Topology [23] 2.1 Euclidean Topolology [24] 2.2 Basis for a Topology [29] 2.3 Basis for a Given Topology [36] 2.4 Postscript [43] 3 Limit Points [44] 3.1 Limit Points and Closure [45] 3.2 Neighbourhoods [50] 3.3 Connectedness [54] 3.4 Postscript [57] 4 Homeomorphisms [58] 4.1 Subspaces [58] 4.2 Homeomorphisms [63] 4.3 Non-Homeomorphic Spaces [69] 4.4 Postscript [76] 5 Continuous Mappings [77] 5.1 Continuous Mappings [77] 5.2 Intermediate Value Theorem [84] 5.3 Postscript [90] 6 Metric Spaces [91] 6.1 Metric Spaces [91] 6.2 Convergence of Sequences [105] 6.3 Completeness [109] 6.4 Contraction Mappings [120] 6.5 Baire Spaces [123] 6.6 Postscript [128] 7 Compactness [130] 7.1 Compact Spaces [131] 7.2 The Heine-Borel Theorem [135] 7.3 Postscript [142] 8 Finite Products [143] 8.1 The Product Topology [144] 8.2 Projections onto Factors of a Product [148] 8.3 TychonofF's Theorem for Finite Products [153] 8.4 Products and Connectedness [156] 8.5 Fundamental Theorem of Algebra [160] 8.6 Postscript [162] Appendix 1: Infinite Sets [163] Bibliography [186] Index [200] |
| Формат: | djvu |
| Размер: | 1958280 байт |
| Язык: | ENG |
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| Открыть: | Ссылка (RU) |