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Cover: 9783034800051 | The Structure of the Real Line | Lev Bukovský | Buch | xiv | Englisch
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The Structure of the Real Line
Buch von Lev Bukovský
Sprache: Englisch

105,95 €*

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Lieferzeit 1-2 Wochen

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Beschreibung
The rapid development of set theory in the last fifty years, mainly by obtaining plenty of independence results, strongly influenced an understanding of the structure of the real line. This book is devoted to the study of the real line and its subsets taking into account the recent results of set theory. Whenever possible the presentation is done without the full axiom of choice. Since the book is intended to be self-contained, all necessary results of set theory, topology, measure theory, and descriptive set theory are revisited with the purpose of eliminating superfluous use of an axiom of choice. The duality of measure and category is studied in a detailed manner. Several statements pertaining to properties of the real line are shown to be undecidable in set theory. The metamathematics behind set theory is shortly explained in the appendix. Each section contains a series of exercises with additional results.
The rapid development of set theory in the last fifty years, mainly by obtaining plenty of independence results, strongly influenced an understanding of the structure of the real line. This book is devoted to the study of the real line and its subsets taking into account the recent results of set theory. Whenever possible the presentation is done without the full axiom of choice. Since the book is intended to be self-contained, all necessary results of set theory, topology, measure theory, and descriptive set theory are revisited with the purpose of eliminating superfluous use of an axiom of choice. The duality of measure and category is studied in a detailed manner. Several statements pertaining to properties of the real line are shown to be undecidable in set theory. The metamathematics behind set theory is shortly explained in the appendix. Each section contains a series of exercises with additional results.
Zusammenfassung

Study of the real line taking into account recent results of set theory Self-contained, all necessary results being revisited Appendix with short explanation of the metamathematics behind set theory Execercises with additional results at the end of each section

Includes supplementary material: [...]

Inhaltsverzeichnis
Preface.- 1 Introduction.- 2 The Real Line.- 3 Topology of Euclidean Spaces.- 4 Measure Theory.- 5 Useful Tools and Technologies.- 6 Descriptive Set Theory.- 7 Decline and Fall of the Duality.- 8 Special Sets of Reals.- 9 Additional Axioms.- 10 Undecidable Statements.- 11 Appendix.- Bibliography.- Index of Notation.- Index.
Details
Erscheinungsjahr: 2011
Fachbereich: Topologie
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xiv
542 S.
ISBN-13: 9783034800051
ISBN-10: 3034800053
Sprache: Englisch
Herstellernummer: 80014197
Einband: Gebunden
Autor: Bukovský, Lev
Hersteller: Springer Basel
Birkhäuser Basel
Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße: 241 x 160 x 35 mm
Von/Mit: Lev Bukovský
Erscheinungsdatum: 04.03.2011
Gewicht: 0,992 kg
Artikel-ID: 107411273
Zusammenfassung

Study of the real line taking into account recent results of set theory Self-contained, all necessary results being revisited Appendix with short explanation of the metamathematics behind set theory Execercises with additional results at the end of each section

Includes supplementary material: [...]

Inhaltsverzeichnis
Preface.- 1 Introduction.- 2 The Real Line.- 3 Topology of Euclidean Spaces.- 4 Measure Theory.- 5 Useful Tools and Technologies.- 6 Descriptive Set Theory.- 7 Decline and Fall of the Duality.- 8 Special Sets of Reals.- 9 Additional Axioms.- 10 Undecidable Statements.- 11 Appendix.- Bibliography.- Index of Notation.- Index.
Details
Erscheinungsjahr: 2011
Fachbereich: Topologie
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xiv
542 S.
ISBN-13: 9783034800051
ISBN-10: 3034800053
Sprache: Englisch
Herstellernummer: 80014197
Einband: Gebunden
Autor: Bukovský, Lev
Hersteller: Springer Basel
Birkhäuser Basel
Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße: 241 x 160 x 35 mm
Von/Mit: Lev Bukovský
Erscheinungsdatum: 04.03.2011
Gewicht: 0,992 kg
Artikel-ID: 107411273
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