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Slices: Functions for abstract real analysis

  • Robert O. Robson
Conference paper
  • 315 Downloads
Part of the Lecture Notes in Mathematics book series (LNM, volume 1420)

Abstract

Let F be a real closed field and let Open image in new window . If Open image in new window in an open constructible set, an abstract function on V is a section of the natural projection π : Open image in new window over V. In this paper we undertake a study of abstract functions in general, extending the notions of boundedness and compatibility from the work of N. Schwartz, H. Delfs, and others. We then introduce of a nice a class of abstract functions, called slices, whose values are determined by semialgebraic approximations. Familiar transcendental functions provide examples over R. We give criteria for extending Open image in new window -valued functions on Fn to slices for arbitrary F. This paper is in its final form and no similar paper has been submitted elsewhere.

Keywords

Open Neighborhood Abstract Function Real Analytic Function Real Spectrum Quotient Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Robert O. Robson
    • 1
  1. 1.Department of MathematicsOregon State UniversityCorvallis

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