General TopologyCourier Dover Publications, 7 Mar 2017 - 320 sayfa "The clarity of the author's thought and the carefulness of his exposition make reading this book a pleasure," noted the Bulletin of the American Mathematical Society upon the 1955 publication of John L. Kelley's General Topology. This comprehensive treatment for beginning graduate-level students immediately found a significant audience, and it remains a highly worthwhile and relevant book for students of topology and for professionals in many areas. A systematic exposition of the part of general topology that has proven useful in several branches of mathematics, this volume is especially intended as background for modern analysis. An extensive preliminary chapter presents mathematical foundations for the main text. Subsequent chapters explore topological spaces, the Moore-Smith convergence, product and quotient spaces, embedding and metrization, and compact, uniform, and function spaces. Each chapter concludes with an abundance of problems, which form integral parts of the discussion as well as reinforcements and counter examples that mark the boundaries of possible theorems. The book concludes with an extensive index that provides supplementary material on elementary set theory. |
İçindekiler
| 1 | |
| 10 | |
| 17 | |
countable sets | 25 |
HAUSDORFF MAXIMAL PRINCIPLE | 31 |
TOPOLOGIES AND NEIGHBORHOODS | 37 |
INTERIOR AND BOUNDARY | 44 |
RELATIVIZATION SEPARATION | 50 |
LOCALLY COMPACT SPACES | 146 |
LEBESGUEs coverING LEMMA | 154 |
PROBLEMS | 161 |
UNIFORM SPACES | 174 |
UNIFoRM continuITY PRODUCT UNIFORMITIEs | 180 |
completeNEss | 190 |
compact spaces | 197 |
PROBLEMs | 203 |
MOORESMITH CONVERGENCE | 62 |
SUBNETS AND CLUSTER POINTS | 69 |
PROBLEMS | 76 |
PRODUCT AND QUOTIENT SPACES | 84 |
QUOTIENT SPACES | 94 |
PROBLEMS | 100 |
EMBEDDING AND METRIZATION | 111 |
EMBEDDING IN CUBES e e e e e | 115 |
METRIZATION e e s e º º e º e e e | 124 |
PROBLEMS | 130 |
COMPACTNESS AND SEPARATION PROPERTIES e e | 140 |
FUNCTION SPACES | 217 |
UNIFORM CONVERGENCE | 225 |
COMPACTNESS AND EQUICONTINUITY | 231 |
PROBLEMS | 238 |
ELEMENTARY SET THEORY | 250 |
EXISTENCE OF SETS | 256 |
WELL ORDERING | 262 |
INTEGERS | 271 |
BIBLIOGRAPHY | 282 |
| 293 | |
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accumulation point axiom of countability belongs cardinal number cartesian product Cauchy Cauchy net closed sets closed subset closure cluster point compact set compact space compact subset compactification complement complete Consequently contains continuous functions coordinate space countable base defined definition disjoint domain f equicontinuous equivalent f is continuous family F finite intersection finite number follows function f Hausdorff space hence homeomorphic identical jointly continuous lemma Let f Let G linear locally compact locally finite member of G metric space n e w neighborhood system non-void open cover open set open subset ordinal pairs paracompact pointwise convergence product space product topology proposition pseudo-metric pseudo-metric space quotient space quotient topology real numbers real-valued function relative sequence subbase subcover subfamily subspace summable Suppose THEOREM Let tion topological group topological space Tychonoff space uniform space uniformly continuous union usual topology X X X