Curve-rational function

Time: 10:00 to  12:00 Ngày 25/02/2016

Venue/Location: C2

Organisers: GS. Krzysztof Kurdyka

Content:

Let $X$ be an algebraic subset of $\R^n$, and $f \colon X \to \R$ a function. We prove that if $f$ is continuous rational on each curve $C \subset X$ then:

1) $f$ is arc-analytic,

2) $f$ is continuous rational on $X$. As a consequence we obtain a characterization of hereditarily rational functions recently studied by J. Koll\'ar and K. Nowak. These functions appeared in a recent work of C. Fefferman and J. Kollar on continous solutions of linear systems with regular coefficients. (joint work with W. Kucharz and J. Kollar)