Real Analytic and Algebraic Geometry pp 206-222
Slices: Functions for abstract real analysis
- First Online:
- 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
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.
Unable to display preview. Download preview PDF.