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Foundations of analysis over surreal number fields

Author: Norman L Alling
Publisher: Amsterdam ; New York : North-Holland ; New York, N.Y., U.S.A. : Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1987.
Series: North-Holland mathematics studies, 141.; Notas de matemática (Rio de Janeiro, Brazil), no. 117.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Surrealer Zahlkörper
Additional Physical Format: Print version:
Alling, Norman L.
Foundations of analysis over surreal number fields.
Amsterdam ; New York : North-Holland ; New York, N.Y., U.S.A. : Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1987
(DLC) 87006735
(OCoLC)15629532
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Norman L Alling
ISBN: 9780444702265 0444702261 9780080872520 0080872522 1281798053 9781281798053
OCLC Number: 316553001
Reproduction Notes: Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2011. MiAaHDL
Description: 1 online resource (xvi, 373 pages).
Details: 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.
Series Title: North-Holland mathematics studies, 141.; Notas de matemática (Rio de Janeiro, Brazil), no. 117.
Responsibility: Norman L. Alling.

Abstract:

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.

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