Author | Howes, Norman R. author |
---|---|
Title | Modern Analysis and Topology [electronic resource] / by Norman R. Howes |
Imprint | New York, NY : Springer New York, 1995 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0833-4 |
Descript | XXVIII, 444 p. online resource |
1: Metric Spaces -- 1.1 Metric and Pseudo-Metric Spaces -- 1.2 Stoneโs Theorem -- 1.3 The Metrization Problem -- 1.4 Topology of Metric Spaces -- 1.5 Uniform Continuity and Uniform Convergence -- 1.6 Completeness -- 1.7 Completions -- 2: Uniformities -- 2.1 Covering Uniformities -- 2.2 Uniform Continuity -- 2.3 Uniformizability and Complete Regularity -- 2.4 Normal Coverings -- 3: Transfinite Sequences -- 3.1 Background -- 3.2 Transfinite Sequences in Uniform Spaces -- 3.3 Transfinite Sequences and Topologies -- 4: Completeness, Cofinal Completeness And Uniform Paracompactness -- 4.1 Introduction -- 4.2 Nets -- 4.3 Completeness, Cofinal Completeness and Uniform Paracompactness -- 4.4 The Completion of a Uniform Space -- 4.5 The Cofinal Completion or Uniform Paracompactification -- 5: Fundamental Constructions -- 5.1 Introduction -- 5.2 Limit Uniformities -- 5.3 Subspaces, Sums, Products and Quotients -- 5.4 Hyperspaces -- 5.5 Inverse Limits and Spectra -- 5.6 The Locally Fine Coreflection -- 5.7 Categories and Functors -- 6: Paracompactifications -- 6.1 Introduction -- 6.2 Compactifications -- 6.3 Tamanoโs Completeness Theorem -- 6.4 Points at Infinity and Tamanoโs Theorem -- 6.5 Paracompactifications -- 6.6 The Spectrum of ?X -- 6.7 The Tamano-Morita Paracompactification -- 7: Realcompactifications -- 7.1 Introduction -- 7.2 Realcompact Spaces -- 7.3 Realcompactifications -- 7.4 Realcompact Spaces and Lindelรถf Spaces -- 7.5 Shirotaโs Theorem -- 8: Measure And Integration -- 8.1 Introduction -- 8.2 Measure Rings and Algebras -- 8.3 Properties of Measures -- 8.4 Outer Measures -- 8.5 Measurable Functions -- 8.6 The Lebesgue Integral -- 8.7 Negligible Sets -- 8.8 Linear Functional and Integrals -- 9: Haar Measure In Uniform Spaces -- 9.1 Introduction -- 9.2 Haar Integrals and Measures -- 9.3 Topological Groups and Uniqueness of Haar Measures -- 10: Uniform Measures -- 10.1 Introduction -- 10.2 Prerings and Loomis Contents -- 10.3 The Haar Functions -- 10.4 Invariance and Uniqueness of Loomis Contents and Haar Measures -- 10.5 Local Compactness and Uniform Measures -- 11: Spaces Of Functions -- 11.1 LP -spaces -- 11.2 The Space L2(?) and Hilbert Spaces -- 11.3 The Space LP(?) and Banach Spaces -- 11.4 Uniform Function Spaces -- 12: Uniform Differentiation -- 12.1 Complex Measures -- 12.2 The Radon-Nikodym Derivative -- 12.3 Decompositions of Measures and Complex Integration -- 12.4 The Riesz Representation Theorem -- 12.5 Uniform Derivatives of Measures