General TopologyCourier Corporation, 1 Oca 2004 - 369 sayfa Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Its treatment encompasses two broad areas of topology: "continuous topology," represented by sections on convergence, compactness, metrization and complete metric spaces, uniform spaces, and function spaces; and "geometric topology," covered by nine sections on connectivity properties, topological characterization theorems, and homotopy theory. Many standard spaces are introduced in the related problems that accompany each section (340 exercises in all). The text's value as a reference work is enhanced by a collection of historical notes, a bibliography, and index. 1970 edition. 27 figures. |
İçindekiler
Set theory 2 Metric spaces | 1 |
Topological Spaces | 23 |
Fundamental concepts | 27 |
Neighborhoods | 32 |
Bases and subbases | 37 |
New Spaces from | 41 |
Subspaces | 43 |
Continuous functions | 50 |
Metrizable Spaces | 161 |
23 | 162 |
Connectedness | 191 |
31 | 197 |
36 | 225 |
Uniform Spaces | 238 |
41 | 264 |
Function Spaces | 278 |
Product spaces weak topologies | 55 |
Quotient spaces | 60 |
Convergence 10 Inadequacy of sequences | 70 |
Nets | 73 |
Filters | 82 |
Separation and Countability | 85 |
The separation axioms | 89 |
Regularity and complete regularity | 97 |
Normal spaces | 105 |
Countability properties | 114 |
Compactness | 116 |
Compact spaces Contents 1 | 125 |
15 | 126 |
44 | 290 |
Historical Notes | 297 |
Bibliography | 323 |
52 | 326 |
77 | 329 |
99 | 330 |
108 | 331 |
| 335 | |
| 345 | |
| 357 | |
| 364 | |
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Sık kullanılan terimler ve kelime öbekleri
A₁ Alexandroff algebraic Amer B₁ Banach basic nhood Cauchy closed sets closed subset cluster point collection compact Hausdorff space compact spaces compact subset compact-open topology compactification completely regular connected space connectedness containing continuous functions continuous map continuum convergence countable defined Definition denote dense diagonal uniformity elements equivalent example f₁ filter follows function f function spaces Hausdorff space hence homeomorphic homotopy intersection isomorphic k-space Lemma Lindelöf linear locally compact locally connected locally finite map ƒ Math metrization theorem nhood base noncut points nonempty normal space one-one open cover open set open-closed paracompact space pathwise connected product space Proof proved proximity space pseudometric quotient result retract Section separable sequence ẞX subalgebra subbase subspace Suppose topological space totally bounded totally disconnected Tychonoff space U₁ uniform convergence uniform cover uniform space uniformizable uniformly continuous Urysohn x₁