Set theory : with an introduction to real point sets / Abhijit Dasgupta.
Tipo de material: TextoIdioma: Inglés Fecha de copyright: New York : Birkhäuser, 2014Edición: First EditionDescripción: xv, 444 pages : illustrations ; 24 cmISBN:- 9781461488538 (hbk. : acidfree paper)
- 1461488532 (hbk. : acidfree paper)
- 23 511.322
- QA248 .D26 2014
Tipo de ítem | Biblioteca actual | Signatura | Copia número | Estado | Fecha de vencimiento | Código de barras | Reserva de ítems | |
---|---|---|---|---|---|---|---|---|
Colección general | Biblioteca Yachay Tech | 511.322 D2296s 2014 (Navegar estantería(Abre debajo)) | Ej. 1 | Disponible | 005808 |
Includes index.
Includes bibliographical references (pages 423-425).
1 Preliminaries: Sets, Relations, and Functions -- Part I Dedekind: Numbers -- 2 The Dedekind-Peano Axioms -- 3 Dedekind's Theory of the Continuum -- 4 Postscript I: What Exactly Are the Natural Numbers? -- Part II Cantor: Cardinals, Order, and Ordinals -- 5 Cardinals: Finite, Countable, and Uncountable -- 6 Cardinal Arithmetic and the Cantor Set -- 7 Orders and Order Types -- 8 Dense and Complete Orders -- 9 Well-Orders and Ordinals -- 11 Posets, Zorn's Lemma, Ranks, and Trees -- 12 Postscript II: Infinitary Combinatorics -- Part III Real Point Sets -- 13 Interval Trees and Generalized Cantor Sets -- 14 Real Sets and Functions -- 15 The Heine-Borel and Baire Category Theorems -- 16 Cantor-Bendixson Analysis of Countable Closed Sets -- 17 Brouwer's Theorem and Sierpinski's Theorem -- 18 Borel and Analytic Sets -- 19 Postscript III: Measurability and Projective Sets -- Part IV Paradoxes and Axioms -- 20 Paradoxes and Resolutions -- 21 Zermelo-Fraenkel System and von Neumann Ordinals -- 22 Postscript IV: Landmarks of Modern Set Theory
What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner.
No hay comentarios en este titulo.