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Modern Analysis and Topology - nuovo libro

1995, ISBN: 9780387979861

Kartoniert, 440 Seiten, 235mm x 155mm x 24mm, Sprache(n): eng The purpose of this book is to provide an integrated development of modern analysis and topology through the integrating vehi… Altro …

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1995, ISBN: 0387979867

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ISBN: 9780387979861

The purpose of this book is to provide an integrated development of modern analysis and topology through the integrating vehicle of uniform spaces. It is intended that the material be acc… Altro …

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Howes, Norman R.:
Modern analysis and topology. Universitext - libri usati

1995, ISBN: 0387979867

8° Broschiert XXVIII, 403 S. ; 24 cm Broschiert ISBN: 0387979867 Analysis; Topologie; Uniformer Raum ; Integration , Mathematik 1, [PU:New York ; Berlin ; Heidelberg ; London ; Paris ; … Altro …

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Howes, Norman R.:
Modern Analysis and Topology - edizione con copertina flessibile

1995, ISBN: 9780387979861

Secaucus, New Jersey, U.S.A.: Springer Verlag, 1995. Trade paperback in near fine condition.. Soft cover. Fine., Secaucus, New Jersey, U.S.A.: Springer Verlag, 1995, 5

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Dettagli del libro
Modern Analysis and Topology Norman R. Howes Author

The purpose of this book is to provide an integrated development of modern analysis and topology through the integrating vehicle of uniform spaces. The reader should have taken an advanced calculus course and an introductory topology course. It is intended that a subset of the book could be used for an upper-level undergraduate course whereas much of the full text would be suitable for a one-year graduate class. An attempt has been made to document the history of all the central ideas and references and historical notes are embedded in the text. These can lead the interested reader to the foundational sources where these ideas emerged.

Informazioni dettagliate del libro - Modern Analysis and Topology Norman R. Howes Author


EAN (ISBN-13): 9780387979861
ISBN (ISBN-10): 0387979867
Copertina rigida
Copertina flessibile
Anno di pubblicazione: 1995
Editore: Springer New York Core >1 >T
444 Pagine
Peso: 0,661 kg

Libro nella banca dati dal 2007-04-29T22:35:18+02:00 (Rome)
Pagina di dettaglio ultima modifica in 2023-12-29T13:54:54+01:00 (Rome)
ISBN/EAN: 9780387979861

ISBN - Stili di scrittura alternativi:
0-387-97986-7, 978-0-387-97986-1
Stili di scrittura alternativi e concetti di ricerca simili:
Autore del libro : howes, norman, hewitt
Titolo del libro: topology and analysis, have never been modern


Dati dell'editore

Autore: Norman R. Howes
Titolo: Universitext; Modern Analysis and Topology
Editore: Springer; Springer US
444 Pagine
Anno di pubblicazione: 1995-06-23
New York; NY; US
Peso: 1,370 kg
Lingua: Inglese
53,49 € (DE)
54,99 € (AT)
59,00 CHF (CH)
POD
XXVIII, 444 p.

BC; Analysis; Hardcover, Softcover / Mathematik/Analysis; Mathematische Analysis, allgemein; Verstehen; Banach Space; Compact space; Compactification; Derivative; Hilbert space; Homeomorphism; Maximum; Metrization theorem; calculus; compactness; differential equation; measure; Topology; Analysis; Topology; Topologie; EA

1: Metric Spaces.- 1.1 Metric and Pseudo-Metric Spaces.- Distance Functions, Spheres, Topology of Pseudo-Metric Spaces, The Ring C*(X), Real Hilbert Space, The Distance from a Point to a Set, Partitions of Unity.- 1.2 Stone’s Theorem.- Refinements, Star Refinements and ?-Refinements, Full Normality, Paracompactness, Shrinkable Coverings, Stone’s Theorem.- 1.3 The Metrization Problem.- Functions That Can Distinguish Points from Sets, ?-Local Finiteness, Urysohn’s Metrization Theorem, The Nagata-Smirnov Metrization Theorem, Local Starrings, Arhangel’skil’s Metrization Theorem.- 1.4 Topology of Metric Spaces.- Complete Normality and Perfect Normality, First and Second Countable Spaces, Separable Spaces, The Diameter of a Set, The Lebesgue Number, Precompact Spaces, Countably Compact and Sequentially Compact Spaces.- 1.5 Uniform Continuity and Uniform Convergence.- Uniform Continuity, Uniform Homeomorphisms and Isomorphisms, Isometric Functions, Uniform Convergence.- 1.6 Completeness.- Convergence and Clustering of Sequences, Cauchy Sequences and Cofinally Cauchy, Sequences, Complete and Cofinally Complete Spaces, The Lebesgue Property, Borel Compactness, Regularly Bounded Metric Spaces.- 1.7 Completions.- The Completion of a Metric Space, Uniformly Continuous Extensions.- 2: Uniformities.- 2.1 Covering Uniformities.- Uniform Spaces, Normal Sequences of Coverings, Bases and Subbases for Uniformities, Normal Coverings, Uniform Topology.- 2.2 Uniform Continuity.- Uniform Continuity, Uniform Homeomorphisms, Pseudo-Metrics Determined by Normal Sequences.- 2.3 Uniformizability and Complete Regularity.- Uniformizable Spaces, The Equivalence of Uniformizability and Complete Regularity, Regularly Open Sets and Coverings, Open and Closed Bases of Uniformities, Regularly Open Bases of Uniformities, Universal or Fine Uniformities.- 2.4 Normal Coverings.- The Unique Uniformity of a Compact Hausdorff Space, Tukey’s Characterization of Normal Spaces, Star-Finite Coverings, Precise Refinements, Some Results of K. Morita, Some Corrections of Tukey’s Theorems by Morita.- 3: Transfinite Sequences.- 3.1 Background.- 3.2 Transfinite Sequences in Uniform Spaces.- Cauchy and Cofinally Cauchy Transfinite Sequences, A Characterization of Paracompactness in Terms of Transfinite Sequences, Shirota’s e Uniformity, Some Characterizations of the Lindelöf Property in Terms of Transfinite Sequences, The ? Uniformity, A Characterization of Compactness in Terms of Transfinite Sequences.- 3.3 Transfinite Sequences and Topologies.- Characterizations of Open and Closed Sets in Terms of Transfinite Sequences, A Characterization of the Hausdorff Property in Terms of Transfinite Sequences, Cluster Classes and the Characterization of Topologies, A Characterization of Continuity in Terms of Transfinite Sequences.- 4: Completeness, Cofinal Completeness And Uniform Paracompactness.- 4.1 Introduction.- 4.2 Nets.- Convergence and Clustering of Nets, Characterizations of Open and Closed Sets in Terms of Nets, A Characterization of the Hausdorff Property in Terms of Nets, Subnets, A Characterization of Compactness in Terms of Nets, A Characterization of Continuity in Terms of Nets, Convergence Classes and the Characterization of Topologies, Universal Nets, Characterizations of Paracompactness, the Lindelöf Property and Compactness in Terms of Nets.- 4.3 Completeness, Cofinal Completeness and Uniform Paracompactness.- Cauchy and Cofinally Cauchy Nets, Completeness and Cofinal Completeness, The Lebesgue Property, Precompactness, Uniform Paracompactness.- 4.4 The Completion of a Uniform Space.- Fundamental Nets, Completeness in Terms of Fundamental Nets, The Construction of the Completion with Fundamental Nets, The Uniqueness of the Completion.- 4.5 The Cofinal Completion or Uniform Paracompactification.- The Topological Completion, Preparacompactness, Countable Bound-edness and the Lindelöf Property, A Necessary and Sufficient Condition for a Uniform Space to Have a Paracompact Completion, A Necessary and Sufficient Condition for a Uniform Space to Have a Lindelöf Completion, The Existence of the Cofinal Completion, A Characterization of Preparacompactness.- 5: Fundamental Constructions.- 5.1 Introduction.- 5.2 Limit Uniformities.- Infimum and Supremum Topologies, Infimum and Supremum Uniformities, Projective and Inductive Limit Topologies, Projective and Inductive Limit Uniformities.- 5.3 Subspaces, Sums, Products and Quotients.- Uniform Product Spaces, Uniform Subspaces, Quotient Uniform Spaces, The Uniform Sum.- 5.4 Hyperspaces.- The Hyperspace of a Uniform Space, Supercompleteness, Burdick’s Characterization of Supercompleteness, Other Characterizations of Supercompleteness, Supercompleteness and Cofinal Completeness, Paracompactness and Supercompleteness.- 5.5 Inverse Limits and Spectra.- Inverse Limit Sequences, Inverse Limit Systems, Inverse Limit Systems of Uniform Spaces, Morita’s Weak Completion, The Spectrum of Weakly Complete Uniform Spaces, Morita’s and Pasynkov’s Characterizations of Closed Subsets of Products of Metric Spaces.- 5.6 The Locally Fine Coreflection.- Uniformly Locally Uniform Coverings, Locally Fine Uniform Spaces, The Derivative of a Uniformity, Partially Cauchy Nets, Injective Uniform Spaces, Subfine Uniform Spaces, The Subfine Coreflection.- 5.7 Categories and Functors.- Concrete Categories, Objects, Morphisms, Covariant Functors, Isomorphisms, Monomorphisms, Duality, Subcategories, Reflection, Coreflection.- 6: Paracompactifications.- 6.1 Introduction.- Some Problems of K. Morita and H. Tamano, Topological Completion, Paracompactifications, Compactifications, Samuel Compactifications, The Stone-?ech Compactification, Uniform Paracompactifications, Tamano’s Paracompactification Problem.- 6.2 Compactifications.- Extensions of Open Sets, Extensions of Coverings, The Extent of a Covering, Stable Coverings, Star-Finite Partitions of Unity.- 6.3 Tamano’s Completeness Theorem.- The Radical of a Uniform Space, Tamano’s Completeness Theorem, Necessary and Sufficient Conditions for Topological Completeness.- 6.4 Points at Infinity and Tamano’s Theorem.- Points and Sets at Infinity, Some Characterizations of Paracompactness by Tamano, Tamano’s Theorem.- 6.5 Paracompactifications.- Completions of Uniform Spaces as Subsets of ?X, A Solution of Tamano’s Paracompactification Problem, The Tamano-Morita Paracompactification, Characterizations of Paracompactness, the Lindelöf Property and Compactness in Terms of Supercompleteness, Another Necessary and Sufficient Condition for a Uniform Space to Have a Paracompact Completion, Another Necessary and Sufficient Condition for a Uniform Space to Have a Lindelöf Completion, The Definition and Existence of the Supercompletion.- 6.6 The Spectrum of ?X.- The Spectrum of ?X, The Spectrum of uX, Monta’s Weak Completion.- 6.7 The Tamano-Morita Paracompactification.- M-spaces, Perfect and Quasi-perfect Mappings, The Topological Completion of an M-space, The Tamano-Morita Paracompactification of an M-space.- 7: Realcompactifications.- 7.1 Introduction.- Another Characterization of ?X, Q-spaces, CZ-maximal Families.- 7.2 Realcompact Spaces.- Realcompact Spaces, The Hewitt Realcompactification, Characterizations of Realcompactness, Properties of Realcompact Spaces, Pseudo-metric Uniformities, The c and c* Uniformities.- 7.3 Realcompactifications.- Realcompactifications, The Equivalence of uX and eX, The Uniqueness of the Hewitt Realcompactification, Characterizations of uX, Properties of uX, Hereditary Realcompactness.- 7.4 Realcompact Spaces and Lindelöf Spaces.- Tamano’s Characterization of Realcompact Spaces, A Necessary and Sufficient Condition for the Realcompactification to be Lindelöf, Tamano’s Characterization of Lindelöf Spaces.- 7.5 Shirota’s Theorem.- Measurable Cardinals, {0,1} Measures, The Relationship of Non-Zero {0,1} Measures and CZ-maximal Families, A Necessary and Sufficient Condition for Discrete Spaces to be Realcompact, Closed Classes of Cardinals, Shirota’s Theorem.- 8: Measure And Integration.- 8.1 Introduction.- Riemann Integration, Lebesgue Integration, Measures, Invariant Integrals.- 8.2 Measure Rings and Algebras.- Rings, Algebras, ?-Rings, ?-Algebras, Borel Sets, Baire Sets, Measures, Measure Rings, Measurable Sets, Measure Algebras, Measure Spaces, Complete Measures, The Completion of a Measure, Borel Measures, Lebesgue Measure, Baire Measures, The Lebesgue Ring, Lebesgue Measurable Sets, Finite Measures, Infinite Measures.- 8.3 Properties of Measures.- Monotone Collections, Continuous from Below, Continuous from Above.- 8.4 Outer Measures.- Hereditary Collections, Outer Measures, Extensions of Measures, ?*-Measurability.- 8.5 Measurable Functions.- Measurable Spaces, Measurable Sets, Measurable Functions, Borel Functions, Limits Superior, Limits Inferior, Point-wise Limits of Functions, Simple Functions, Simple Measurable Functions.- 8.6 The Lebesgue Integral.- Development of the Lebesgue Integral.- 8.7 Negligible Sets.- Negligible Sets, Almost Everywhere, Complete Measures, Completion of a Measure.- 8.8 Linear Functional and Integrals.- Linear Functionals, Positive Linear Functionals, Lower Semi-continuous, Upper Semi-continuous, Outer Regularity, Inner Regularity, Regular Measures, Almost Regular Measures, The Riesz Representation Theorem.- 9: Haar Measure In Uniform Spaces.- 9.1 Introduction.- Isogeneous Uniform Spaces, Isomorphisms, Homogeneous Spaces, Translations, Rotations, Reflections, Haar Integral, Haar Measure.- 9.2 Haar Integrals and Measures.- Development of the Haar integral on Locally Compact Isogeneous Uniform Spaces.- 9.3 Topological Groups and Uniqueness of Haar Measures.- Topological Groups, Abelian Topological Groups, Open at 0, Right Uniformity, Left Uniformity, Right Coset, Left Coset, Quotient of a Topological Group, A Necessary and Sufficient Condition for a Locally Compact Space to Have a Topological Group Structure.- 10: Uniform Measures.- 10.1 Introduction.- Uniform Measures, The Congruence Axiom, Loomis Contents.- 10.2 Prerings and Loomis Contents.- Prerings, Hereditary Open Prerings, Loomis Contents, Uniformly Separated, Left Continuity, Invariant Loomis Contents, Zero-boundary Sets.- 10.3 The Haar Functions.- The Haar Covering Function, The Haar Function, Extension of Loomis Contents to Finitely Additive Measures.- 10.4 Invariance and Uniqueness of Loomis Contents and Haar Measures.- Invariance with Respect to a Uniform Covering, Invariance on Compact Spheres, Development of Loomis Contents on Suitably Restricted Uniform Spaces..- 10.5 Local Compactness and Uniform Measures.- Almost Uniform Measures, Uniform Measures, Jordan Contents, Monotone Sequences of Sets, Monotone Classes, Development of Uniform Measures on Suitably Restricted Uniform Spaces.- 11: Spaces Of Functions.- 11.1 LP -spaces.- Conjugate Exponents, LP-norm, The Essential Supremum, Essentially Bounded, Minkowski’s Inequality Hölder’s Inequality, The Supremum Norm, The Completion of CK(X) with Respect to the LP-norm.- 11.2 The Space L2(?) and Hilbert Spaces.- Square Integrable Functions, Inner Product, Schwarz Inequality, Hilbert Space, Orthogonality, Orthogonal Projections, Linear Combinations, Linear Independence, Span, Basis of a Vector Space, Orthonormal Sets, Orthonormal Bases, Bessel’s Inequality, Riesz-Fischer Theorem, Hilbert Space Isomorphism.- 11.3 The Space LP(?) and Banach Spaces.- Normed Linear Space, Banach Space, Linear Operators, Kernel of a Linear Operator, Bounded Linear Operators, Dual Spaces, Hahn-Banach Theorem, Second Dual Space, Baire’s Category Theorem, Nowhere Dense Sets, Open Mapping Theorem, Closed Graph Theorem, Uniform Boundedness Principle, Banach-Steinhaus Theorem.- 11.4 Uniform Function Spaces.- Uniformity of Pointwise Convergence, Uniformity of Uniform Convergence, Joint Continuity, Uniformity of Uniform Convergence on Compacta, Topology of Compact Convergence, Compact-Open Topology, Joint Continuity on Compacta, Ascoli Theorem, Equicontinuity.- 12: Uniform Differentiation.- 12.1 Complex Measures.- Complex Measure, Total Variation, Absolute Continuity, Concentration of a Measure on a Subset, Orthogonality of Measures.- 12.2 The Radon-Nikodym Derivative.- Radon-Nikodym Derivative and its Applications.- 12.3 Decompositions of Measures and Complex Integration.- Polar Decomposition, Lebesgue Decomposition, Complex Integration.- 12.4 The Riesz Representation Theorem.- Regular and Almost Regular Complex Measures, The Riesz Representation Theorem.- 12.5 Uniform Derivatives of Measures.- Differentiation of a Measure at a Point, Differentiable Measures, L1-differentiable Measures, Uniformly Differentiable Measures, Fubini’s Theorem.

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