Continuous rational functions on real and $p$-adic varieties

Abstract

This note studies, and partially solves, 3 elementary questions about continuous rational functions on real (and p-adic) algebraic varieties: Can one restrict such a function to a subvariety? Can one extend such a function from a subvariety? Which linear equations can be solved using such functions?

This paper, while correct, is superseded by 1301.5048: Kollár--Nowak: Continuous rational functions on real and $p$-adic varieties II

Cited by in corpus (7)

• Curve-rational functions
• Some results of algebraic geometry over Henselian rank one valued fields
• A uniform classification of discrete series representations of affine Hecke algebras
• Continuous functions in the plane regular after one blowing-up
• Some results from algebraic geometry over complete discretely valued fields
• On solutions of linear equations with polynomial coefficients
• Real rational surfaces