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Beschreibung
This is the first comprehensive collection of problems in set theory. But rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution. This is destined to become a classic, and will be an important resource for students and researchers. It follows a tradition of Hungarian mathematics started with Pólya-Szegõ's problem book in analysis and continued with Lovász' problem book in combinatorics.
This is the first comprehensive collection of problems in set theory. But rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution. This is destined to become a classic, and will be an important resource for students and researchers. It follows a tradition of Hungarian mathematics started with Pólya-Szegõ's problem book in analysis and continued with Lovász' problem book in combinatorics.
Zusammenfassung
This is the first comprehensive collection of problems in set theory. But rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution. This is destined to become a classic, and will be an important resource for students and researchers. It follows a tradition of Hungarian mathematics started with Pólya-Szegõ's problem book in analysis and continued with Lovász' problem book in combinatorics.
Inhaltsverzeichnis
Problems.- Operations on sets.- Countability.- Equivalence.- Continuum.- Sets of reals and real functions.- Ordered sets.- Order types.- Ordinals.- Ordinal arithmetic.- Cardinals.- Partially ordered sets.- Transfinite enumeration.- Euclidean spaces.- Zorn¿s lemma.- Hamel bases.- The continuum hypothesis.- Ultrafilters on ?.- Families of sets.- The Banach-Tarski paradox.- Stationary sets in ?1.- Stationary sets in larger cardinals.- Canonical functions.- Infinite graphs.- Partition relations.- ?-systems.- Set mappings.- Trees.- The measure problem.- Stationary sets in [?]^- The Banach-Tarski paradox.- Stationary sets in ?1.- Stationary sets in larger cardinals.- Canonical functions.- Infinite graphs.- Partition relations.- ?-systems.- Set mappings.- Trees.- The measure problem.- Stationary sets in [?]^
Details
| Erscheinungsjahr: | 2010 |
|---|---|
| Fachbereich: | Grundlagen |
| Genre: | Importe, Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Problem Books in Mathematics |
| Inhalt: |
xii
516 S. |
| ISBN-13: | 9781441921406 |
| ISBN-10: | 1441921400 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: |
Komjath, Peter
Totik, Vilmos |
| Hersteller: |
Springer
Copernicus Springer US, New York, N.Y. Problem Books in Mathematics |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 29 mm |
| Von/Mit: | Peter Komjath (u. a.) |
| Erscheinungsdatum: | 24.11.2010 |
| Gewicht: | 0,791 kg |
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