Alling, Norman L.
Foundations of analysis over surreal number fields / Norman L. Alling. - 1 online resource (xvi, 373 pages) - North-Holland mathematics studies ; 141 Notas de matemática ; 117 . - North-Holland mathematics studies ; 141. Notas de matemática (Rio de Janeiro, Brazil) ; no. 117. .
Includes bibliographical references (p. 353-358) and index.
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.
9780444702265 0444702261
127713:122763 Elsevier Science & Technology http://www.sciencedirect.com
Surreal numbers.
Algebraic fields.
Mathematical analysis.
Nombres surréels.
Corps algébriques.
Analyse mathématique.
Algebraic fields.
Mathematical analysis.
Surreal numbers.
Electronic books.
QA1 / .N86 no. 117eb QA241 / .A45 1987eb
510 512/.3
Foundations of analysis over surreal number fields / Norman L. Alling. - 1 online resource (xvi, 373 pages) - North-Holland mathematics studies ; 141 Notas de matemática ; 117 . - North-Holland mathematics studies ; 141. Notas de matemática (Rio de Janeiro, Brazil) ; no. 117. .
Includes bibliographical references (p. 353-358) and index.
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.
9780444702265 0444702261
127713:122763 Elsevier Science & Technology http://www.sciencedirect.com
Surreal numbers.
Algebraic fields.
Mathematical analysis.
Nombres surréels.
Corps algébriques.
Analyse mathématique.
Algebraic fields.
Mathematical analysis.
Surreal numbers.
Electronic books.
QA1 / .N86 no. 117eb QA241 / .A45 1987eb
510 512/.3