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Nash regulous functions

Volume 119 / 2017

Wojciech Kucharz Annales Polonici Mathematici 119 (2017), 275-289 MSC: 14P20, 14P10, 14P99. DOI: 10.4064/ap170601-21-8 Published online: 21 September 2017


A real-valued function on $\mathbb {R}^n$ is $k$-regulous, where $k$ is a nonnegative integer, if it is of class $\mathcal {C}^k$ and can be represented as a quotient of two polynomial functions on $\mathbb {R}^n$. Several interesting results involving such functions have been obtained recently. Some of them (Nullstellensatz, Cartan’s theorems A and B, etc.) can be carried over to a new setting of Nash $k$-regulous functions, introduced in this paper. Here a function on a Nash manifold $X$ is called Nash $k$-regulous if it is of class $\mathcal {C}^k$ and can be represented as a quotient of two Nash functions on $X$.


  • Wojciech KucharzInstitute of Mathematics
    Faculty of Mathematics and Computer Science
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland

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