Foundations of analysis over surreal number fields [electronic resource] / Norman L. Alling.
Material type:
TextSeries: North-Holland mathematics studies ; 141. | Notas de matem�atica (Rio de Janeiro, Brazil) ; no. 117.Publication details: 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. Description: 1 online resource (xvi, 373 p.)Content type: text Media type: computer Carrier type: online resourceISBN: 9780444702265; 0444702261; 9780080872520 (electronic bk.); 0080872522 (electronic bk.); 1281798053; 9781281798053Subject(s): 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 fieldsGenre/Form: Electronic books. | Surrealer Zahlk�orper.Additional physical formats: Print version:: Foundations of analysis over surreal number fields.DDC classification: 510 | 512/.3 LOC classification: QA1 | .N86 no. 117ebQA241 | .A45 1987ebOther classification: MAT 260f | SI 867 Online resources: ScienceDirect | Volltext Action note: digitized 2011 committed to preserveSummary: 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.
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.
Includes bibliographical references (p. 353-358) and index.
Description based on print version record.
Use copy Restrictions unspecified star MiAaHDL
Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2011. MiAaHDL
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. MiAaHDL
http://purl.oclc.org/DLF/benchrepro0212
digitized 2011 HathiTrust Digital Library committed to preserve pda MiAaHDL
There are no comments on this title.