General Topology

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Courier 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.
 

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There are two introductions to general topology which are classics. Thsi book, Kelley, is the lighter one of them, while Engelking is the heavier one. Tam incelemeyi okuyun

İçindekiler

PRELIMINARIES
1
FUNCTIONS
10
ALGEBRAIC conce PTs
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
INDEX
293
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John L. Kelley (1916–99) taught at Notre Dame, the University of Chicago, and other universities, including Berkeley, from which he retired in 1985.

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