Author | Bishop, Errett. author |
---|---|
Title | Constructive Analysis [electronic resource] / by Errett Bishop, Douglas Bridges |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1985 |
Connect to | http://dx.doi.org/10.1007/978-3-642-61667-9 |
Descript | XII, 477 p. online resource |
Prolog -- 1 A Constructivist Manifesto -- 1. The Descriptive Basis of Mathematics -- 2. The Idealistic Component of Mathematics -- 3. The Constructivization of Mathematics -- Notes -- 2 Calculus and the Real Numbers -- 1. Sets and Functions -- 2. The Real Number System -- 3. Sequences and Series of Real Numbers -- 4. Continuous Functions -- 5. Differentiation -- 6. Integration -- 7. Certain Important Functions -- Problems -- Notes -- 3 Set Theory -- 1. Some Basic Notions of the Theory of Sets -- 2. Complemented Sets -- 3. Neighborhood Spaces and Function Spaces -- Problems -- Notes -- 4 Metric Spaces -- 1. Fundamental Definitions and Constructions -- 2. Associated Structures -- 3. Completeness -- 4. Total Boundedness and Compactness -- 5. Spaces of Functions -- 6. Locally Compact Spaces -- Problems -- Notes -- 5 Complex Analysis -- 1. The Complex Plane -- 2. Derivatives -- 3. Integration -- 4. The Winding Number -- 5. Estimates of Size, and the Location of Zeros -- 6. Singularities and Picardโs Theorem -- 7. The Riemann Mapping Theorem -- Problems -- Notes -- 6 Integration -- 1. Integration Spaces -- 2. Complete Extension of an Integral -- 3. Integrable Sets -- 4. Profiles -- 5. Positive Measures on IR -- 6. Approximation by Compact Sets -- 7. Measurable Functions -- 8. Convergence of Functions and Integrals -- 9. Product Integrals -- 10. Measure Spaces -- Problems -- Notes -- 7 Normed Linear Spaces -- 1. Definitions and Examples -- 2. Finite-Dimensional Spaces -- 3. The Lp Spaces and the Radon-Nikodym Theorem -- 4. The Extension of Linear Functionals -- 5. Quasinormed Linear Spaces; the Space L? -- 6. Dual Spaces -- 7. Extreme Points -- 8. Hilbert Space and the Spectral Theorem -- Problems -- Notes -- 8 Locally Compact Abelian Groups -- 1. Haar Measure -- 2. Convolution Operators -- 3. The Character Group -- 4. Duality and the Fourier Transform -- Problems -- Notes -- 9 Commutative Banach Algebras -- 1. Definitions and Examples -- 2. Linear Equations in a Banach Algebra -- Problems -- Notes -- References -- Symbols