The Structure of the Real Line [recurso electrónico] / by Lev Bukovský.
Tipo de material: TextoSeries Monografie Matematyczne ; 71Editor: Basel : Springer Basel, 2011Descripción: XIV, 542 p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783034800068Tema(s): Mathematics | Global analysis (Mathematics) | Mathematics | AnalysisFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 515 Clasificación LoC:QA299.6-433Recursos en línea: Libro electrónicoTipo de ítem | Biblioteca actual | Colección | Signatura | Copia número | Estado | Fecha de vencimiento | Código de barras |
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Libro Electrónico | Biblioteca Electrónica | Colección de Libros Electrónicos | QA299.6 -433 (Browse shelf(Abre debajo)) | 1 | No para préstamo | 373037-2001 |
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QA299.6 -433 A Sequence of Problems on Semigroups | QA299.6 -433 Essentials of Integration Theory for Analysis | QA299.6 -433 Dimensional Analysis | QA299.6 -433 The Structure of the Real Line | QA299.6 -433 Modern Aspects of the Theory of Partial Differential Equations | QA299.6 -433 Weights, Extrapolation and the Theory of Rubio de Francia | QA299.6 -433 Notions of Positivity and the Geometry of Polynomials |
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.
The rapid development of set theory in the last fifty years, mainly in 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, descriptive set theory are revisited with the purpose to eliminate 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 it is shortly explained in the appendix. Each section contains a series of exercises with additional results.
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