Foundations of analysis over surreal number fields
Alling, Norman L.
Foundations of analysis over surreal number fields [electronic resource] / Norman L. Alling. - Amsterdam ; New York : New York, N.Y., U.S.A. : North-Holland ; Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1987. - 1 online resource (xvi, 373 p.) - North-Holland mathematics studies ; 141 Notas de matem�atica ; 117 . - North-Holland mathematics studies ; 141. Notas de matem�atica (Rio de Janeiro, Brazil) ; no. 117. .
Includes bibliographical references (p. 353-358) and index.
Use copy
In this volume, a tower of surreal number fields is defined, each being a real-closed field having a canonical formal power series structure and many other higher order properties. Formal versions of such theorems as the Implicit Function Theorem hold over such fields. The Main Theorem states that every formal power series in a finite number of variables over a surreal field has a positive radius of hyper-convergence within which it may be evaluated. Analytic functions of several surreal and surcomplex variables can then be defined and studied. Some first results in the one variable case are derived. A primer on Conway's field of surreal numbers is also given. Throughout the manuscript, great efforts have been made to make the volume fairly self-contained. Much exposition is given. Many references are cited. While experts may want to turn quickly to new results, students should be able to find the explanation of many elementary points of interest. On the other hand, many new results are given, and much mathematics is brought to bear on the problems at hand.
Electronic reproduction.
[S.l.] :
HathiTrust Digital Library,
2011.
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
http://purl.oclc.org/DLF/benchrepro0212
9780444702265 0444702261 9780080872520 (electronic bk.) 0080872522 (electronic bk.) 1281798053 9781281798053
127713:122763 Elsevier Science & Technology http://www.sciencedirect.com
Surreal numbers.
Algebraic fields.
Mathematical analysis.
Nombres surr�eels.
Corps alg�ebriques.
Analyse math�ematique.
Algebraic fields.
Mathematical analysis.
Surreal numbers.
MATHEMATICS--Algebra--Intermediate.
s�erie formelle.
s�erie puissance.
espace affine.
topologie.
nombre r�eel.
Corps alg�ebriques.
Analyse math�ematique.
Zahlk�orper.
Algebraic number fields
Electronic books.
Surrealer Zahlk�orper.
QA1 / .N86 no. 117eb QA241 / .A45 1987eb
510 512/.3
Foundations of analysis over surreal number fields [electronic resource] / Norman L. Alling. - Amsterdam ; New York : New York, N.Y., U.S.A. : North-Holland ; Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1987. - 1 online resource (xvi, 373 p.) - North-Holland mathematics studies ; 141 Notas de matem�atica ; 117 . - North-Holland mathematics studies ; 141. Notas de matem�atica (Rio de Janeiro, Brazil) ; no. 117. .
Includes bibliographical references (p. 353-358) and index.
Use copy
In this volume, a tower of surreal number fields is defined, each being a real-closed field having a canonical formal power series structure and many other higher order properties. Formal versions of such theorems as the Implicit Function Theorem hold over such fields. The Main Theorem states that every formal power series in a finite number of variables over a surreal field has a positive radius of hyper-convergence within which it may be evaluated. Analytic functions of several surreal and surcomplex variables can then be defined and studied. Some first results in the one variable case are derived. A primer on Conway's field of surreal numbers is also given. Throughout the manuscript, great efforts have been made to make the volume fairly self-contained. Much exposition is given. Many references are cited. While experts may want to turn quickly to new results, students should be able to find the explanation of many elementary points of interest. On the other hand, many new results are given, and much mathematics is brought to bear on the problems at hand.
Electronic reproduction.
[S.l.] :
HathiTrust Digital Library,
2011.
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
http://purl.oclc.org/DLF/benchrepro0212
9780444702265 0444702261 9780080872520 (electronic bk.) 0080872522 (electronic bk.) 1281798053 9781281798053
127713:122763 Elsevier Science & Technology http://www.sciencedirect.com
Surreal numbers.
Algebraic fields.
Mathematical analysis.
Nombres surr�eels.
Corps alg�ebriques.
Analyse math�ematique.
Algebraic fields.
Mathematical analysis.
Surreal numbers.
MATHEMATICS--Algebra--Intermediate.
s�erie formelle.
s�erie puissance.
espace affine.
topologie.
nombre r�eel.
Corps alg�ebriques.
Analyse math�ematique.
Zahlk�orper.
Algebraic number fields
Electronic books.
Surrealer Zahlk�orper.
QA1 / .N86 no. 117eb QA241 / .A45 1987eb
510 512/.3
