Abstract
Let F be a real closed field and let 
. If 
in an open constructible set, an abstract function on V is a section of the natural projection π : 
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 
-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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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. https://doi.org/10.1007/BFb0083922
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DOI: https://doi.org/10.1007/BFb0083922
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