UID:
almahu_9947366682102882
Umfang:
1 online resource (333 pages)
ISBN:
1-281-76634-8
,
9786611766344
,
0-08-087328-6
Serie:
Pure and applied mathematics; a series of monographs and textbooks ; 16
Inhalt:
Point set topology
Anmerkung:
Front Cover; Point Set Topology; Copyright Page; Contents; Preface; Notation; Introduction to Set Theory; 1. Elementary Operations on Sets; 2. Set Theoretical Equivalence and Denumerability; 3. The Axiom of Choice and Its Equivalents; References; Chapter I. Topological Spaces; 1. Open Sets and Closed Sets; 2. Interior, Exterior, Boundary, and Closure; 3. Closure Operators; 4. Bases and Subbases; 5. Topologies on Linearly Ordered Sets; 6. Metric Spaces; 7. Neighborhood Filters; 8. Uniform Structures; 9. Simple Results on Uniform Structures and Uniform Spaces; 10. Subspaces; 11. Product Spaces
,
12. Products of Uniformizable Spaces; 13. Inverse and Direct Images of Topologies; 14. Quotient Spaces; Notes; References; Chapter II. Separation Properties; 1. (T0) and (T1) Axioms, Hausdorff Spaces; 2. (T3) Spaces, Regular and Semiregular Spaces; 3. (T,) Spaces and Normal Spaces; 4. Point-Finite and Star-Finite Open Coverings; 5. (T5) Spaces and Completely Normal Spaces; 6. Separated Sets; 7. Connected Spaces and Sets; 8. Maximal Connected Subsets; 9. (T) Axiom and Complete Regularity; 10. Uniformization and Axiom (T); 11. Axioms of Separation in Product Spaces
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12. Separable Spaces and Countability Axioms; Notes; References; Chapter III. Compactness and Uniformization; 1. Compactness; 2. Compact Metric Spaces; 3. Subspaces and Separation Properties of Compact Spaces; 4. The Product of Compact Topological Spaces; 5. Locally Compact Spaces; 6. Paracompactness and Full-Normality; 7. The Equivalence of Paracompactness and Full-Normality; 8. Metrizable Uniform Structures and Structure Gages; 9. Metrizability Conditions; Notes; References; Chapter IV. Continuity; 1. Functional Relations and Functions; 2. Local Continuity; 3. Continuous Functions
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4. Homeomorphisms, Open and Closed Maps; 5. Real-Valued Functions; 6. Continuity and Axioms of Separation; 7. Continuity and Compactness; 8. Continuity and connectedness; 9. Continuity in Product Spaces; 10. Uniform Continuity and Equicontinuity; 11. The Topology of Uniform Convergence; 12. The Algebra of Continuous Functions; Notes; References; Chapter V. Theory of Convergence; 1. Filters and Nets; 2. Convergence of Filters, Nets, and Sequences; 3. Ultrafllters and Universal Nets; 4. Bounds, Traces, and Products of Filters; 5. Applications of Filters and Nets to Compactness
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6. Cauchy Filters and Complete Spaces; 7. Completion of Metric Structures; 8. Baire's Category Theorem, the Principles ofUniform Boundedness and of the Condensation of Singularities; 9. Completions and Compactifications; Notes; References; Author Index; Subject Index
,
English
Weitere Ausg.:
ISBN 0-12-374566-7
Sprache:
Englisch
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