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Sets for mathematics /
Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. For the first time in a text, this book uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically commo...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, UK ; New York :
Cambridge University Press,
2003.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Lawvere, F. W. | |
| 245 | 1 | 0 | |a Sets for mathematics / |c F. William Lawvere, Robert Rosebrugh. |
| 260 | |a Cambridge, UK ; |a New York : |b Cambridge University Press, |c 2003. | ||
| 300 | |a 1 online resource (xiii, 261 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 504 | |a Includes bibliographical references (pages 253-255) and index. | ||
| 505 | 0 | 0 | |t Abstract sets and mappings -- |t Sums, monomorphisms and parts -- |t Finite inverse limits -- |t Colimits, epimorphisms and the axiom of choice -- |t Mapping sets and exponentials -- |t Summary of the axioms and an example of variable sets -- |t Consequences and uses of exponentials -- |t More on power sets -- |t Introduction to variable sets -- |t Models of additional variation. |
| 588 | 0 | |a Print version record. | |
| 520 | |a Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. For the first time in a text, this book uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the algebra of mappings is introduced and developed as a unifying basis for advanced mathematical subjects such as algebra, geometry, analysis, and combinatorics. The formal study evolves from general axioms which express universal properties of sums, products, mapping sets, and natural number recursion. The distinctive features of Cantorian abstract sets, as contrasted with the variable and cohesive sets of geometry and analysis, are made explicit and taken as special axioms. Functor categories are introduced in order to model the variable sets used in geometry, and to illustrate the failure of the axiom of choice. An appendix provides an explicit introduction to necessary concepts from logic, and an extensive glossary provides a window to the mathematical landscape. | ||
| 546 | |a English. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Set theory. | |
| 650 | 6 | |a Théorie des ensembles. | |
| 650 | 7 | |a MATHEMATICS |x Set Theory. |2 bisacsh | |
| 650 | 7 | |a Set theory. |2 fast |0 (OCoLC)fst01113587 | |
| 650 | 7 | |a Mengenlehre |2 gnd | |
| 650 | 1 | 7 | |a Verzamelingen (wiskunde) |2 gtt |
| 650 | 7 | |a Ensembles, Théorie des. |2 ram | |
| 650 | 7 | |a Logique symbolique et mathématique. |2 ram | |
| 700 | 1 | |a Rosebrugh, Robert, |d 1948- | |
| 776 | 0 | 8 | |i Print version: |a Lawvere, F.W. |t Sets for mathematics. |d Cambridge, UK ; New York : Cambridge University Press, 2003 |z 0521804442 |z 0521010608 |w (DLC) 2002071478 |w (OCoLC)49820963 |
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