Slices: Functions for abstract real analysis

  • Robert O. Robson
Conference paper

DOI: 10.1007/BFb0083922

Volume 1420 of the book series Lecture Notes in Mathematics (LNM)
Cite this paper as:
Robson R.O. (1990) Slices: Functions for abstract real analysis. In: Galbiati M., Tognoli A. (eds) Real Analytic and Algebraic Geometry. Lecture Notes in Mathematics, vol 1420. Springer, Berlin, Heidelberg

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.

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

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