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

By J. Kollár, Krzysztof Jan Nowak. 2011

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Strictly speaking, a rational function f is not really a function on Rn in general since it is defined only on the dense open set where q = 0. Nonetheless, even if q vanishes at some points of Rn , it can happen that f extends to an everywhere defined continuous function f c; such an f c is unique. It is customary to identify f with f c and call f itself a continuous rational function on Rn . For instance, p(x1, . . . , xn) x2m 1 + · · · + x2m n

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c67ceaca711fcce47e9064b60399fce94460d14e