
Foundations of Analysis over Surreal Number Fields
Description
Table of Contents
- Introduction. 1. Preliminaries. 2. The &xgr;-Topology. 3. The &xgr;-Topology on Affine n-Space. 4. Introduction to the Surreal Field No. 5. The Surreal Fields &xgr;No, and Related Topics. 6. The Valuation Theory of Ordered Fields, Applied to No and &xgr;No. 7. Power Series: Formal and Hyper-Convergent. 8. A Primer on Analytic Functions of a Surreal Variable. Bibliography. Index.
Product details
- No. of pages: 372
- Language: English
- Copyright: © North Holland 1987
- Published: April 1, 1987
- Imprint: North Holland
- eBook ISBN: 9780080872520
About the Author
N.L. Alling
Ratings and Reviews
Latest reviews
(Total rating for all reviews)
Alec R. Wed Feb 21 2018
Beautiful beginnings of a theory
Alling's book provides an excellent first pass at a theory of analysis over the Surreal numbers, utilizing tools from classical ordered group/ring valuation theory together with set theory. Although the exponential function developed within only holds for infinitesimal Surreals, and a more comprehensive exponential theory is developed in other texts on Surreals, Alling's construction of Surreal numbers as Hahn series over the reals is fascinating and enlightening -- a must read for anyone wanting to gain a foothold in the strange world of Surreal analysis. There are minor typos in the text, some of them significant in proofs, for which I have deducted one star.