General topology

Preface......Page f005.djvu
Acknowledgments......Page f007.djvu
Contents......Page f008.djvu
Sets......Page p001.djvu
Subsets and Complements; Union and Intersection......Page p002.djvu
Relations......Page p006.djvu
Functions......Page p010.djvu
Orderings......Page p013.djvu
Algebraic Concepts......Page p017.djvu
The Real Numbers......Page p019.djvu
Countable Sets......Page p025.djvu
Cardinal Numbers......Page p027.djvu
Ordinal Numbers......Page p029.djvu
Cartesian Products......Page p030.djvu
Hausdorff Maximal Principle......Page p031.djvu
Topologies and Neighborhoods......Page p037.djvu
Accumulation Points......Page p040.djvu
Closure......Page p042.djvu
Interior and Boundary......Page p044.djvu
Bases and Subbases......Page p046.djvu
Relativization; Separation......Page p050.djvu
Connected Sets......Page p053.djvu
Problems......Page p055.djvu
Introduction......Page p062.djvu
Directed Sets and Nets......Page p065.djvu
Subnets and Cluster Points......Page p069.djvu
Sequences and Subsequences......Page p072.djvu
*Convergence Classes......Page p073.djvu
Problems......Page p076.djvu
Continuous Functions......Page p084.djvu
Product Spaces......Page p088.djvu
Quotient Spaces......Page p094.djvu
Problems......Page p100.djvu
4 Embedding and Metrization......Page p111.djvu
Existence of Continuous Functions......Page p112.djvu
Embedding in Cubes......Page p115.djvu
Metric and Pseudo-Metric Spaces......Page p118.djvu
Metrization......Page p124.djvu
Problems......Page p130.djvu
Equivalences......Page p135.djvu
Compactness and Separation Properties......Page p140.djvu
Products of Compact Spaces......Page p143.djvu
Locally Compact Spaces......Page p146.djvu
Quotient Spaces......Page p147.djvu
Compactification......Page p149.djvu
Lebesgue\'s Covering Lemma......Page p154.djvu
*Paracompactness......Page p156.djvu
Problems......Page p161.djvu
6 Uniform Spaces......Page p174.djvu
Uniformities and the Uniform Topology......Page p175.djvu
Uniform Continuity; Product Uniformities......Page p180.djvu
Metrization......Page p184.djvu
Completeness......Page p190.djvu
Completion......Page p195.djvu
Compact Spaces......Page p197.djvu
For Metric Spaces Only......Page p200.djvu
Problems......Page p203.djvu
Pointwise Convergence......Page p217.djvu
Compact Open Topology and Joint Continuity......Page p221.djvu
Uniform Convergence......Page p225.djvu
Uniform Convergence On Compacta......Page p229.djvu
Compactness and Equicontinutty......Page p231.djvu
*Even Continuity......Page p234.djvu
Problems......Page p238.djvu
Appendix: Elementary Set Theory......Page p250.djvu
Classification Axiom Scheme......Page p251.djvu
Elementary Algebra of Classes......Page p253.djvu
Existence of Sets......Page p256.djvu
Ordered Pairs; Relations......Page p259.djvu
Functions......Page p260.djvu
Well Ordering......Page p262.djvu
Ordinals......Page p266.djvu
Integers......Page p271.djvu
The Choice Axiom......Page p272.djvu
Cardinal Numbers......Page p274.djvu
Bibliography......Page p282.djvu
Index......Page p293.djvu