國立虎尾科技大學 |

Sets for mathematics /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Sets for mathematics // F. William Lawvere, Robert Rosebrugh.
作者:	Lawvere, F. W.,
其他作者:	Rosebrugh, Robert,
面頁冊數:	1 online resource (xiii, 261 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Set theory. -
電子資源:	https://doi.org/10.1017/CBO9780511755460
ISBN:	9780511755460 (ebook)

Sets for mathematics /
Lawvere, F. W.,

Sets for mathematics /F. William Lawvere, Robert Rosebrugh. - 1 online resource (xiii, 261 pages) :digital, PDF file(s).

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. This book, first published in 2003, 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.

ISBN: 9780511755460 (ebook)Subjects--Topical Terms:

579942
Set theory.

LC Class. No.: QA248 / .L28 2003

Dewey Class. No.: 511.3/22

Sets for mathematics /
LDR:02168nam a2200289 i 4500 001 1127242
003 UkCbUP
005 20151005020622.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 240926s2003||||enk o ||1 0|eng|d
020 $a 9780511755460 (ebook)
020 $z 9780521804448 (hardback)
020 $z 9780521010603 (paperback)
035 $a CR9780511755460
040 $a UkCbUP $b eng $e rda $c UkCbUP
050 0 0 $a QA248 $b .L28 2003
082 0 0 $a 511.3/22 $2 21
100 1 $a Lawvere, F. W., $e author. $3 1446514
245 1 0 $a Sets for mathematics / $c F. William Lawvere, Robert Rosebrugh.
264 1 $a Cambridge : $b Cambridge University Press, $c 2003.
300 $a 1 online resource (xiii, 261 pages) : $b digital, PDF file(s).
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
520 $a Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. This book, first published in 2003, 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.
650 0 $a Set theory. $3 579942
700 1 $a Rosebrugh, Robert, $d 1948- $e author. $3 1446515
776 0 8 $i Print version: $z 9780521804448
856 4 0 $u https://doi.org/10.1017/CBO9780511755460