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arXiv · 2606.01447

Constructing Discontinuous but Locally Bounded Rational Functions using \L ojasiewicz Inequalities

Adam Coffman·Yifei Pan
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Abstract

For real multivariate polynomials $P$ and $Q$ both vanishing at a point, if the zero set of $Q$ is contained in the zero set of $P$, then there exists a rational function of the form $P^{p}/Q^{q}$ which is locally bounded and such that its extension that vanishes on the zero set of $Q$ is discontinuous. The proof uses inequalities of Lojasiewicz.

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BibTeXRIS

Adam Coffman, Yifei Pan. 2026-05-31. Constructing Discontinuous but Locally Bounded Rational Functions using \L ojasiewicz Inequalities. https://arxiv.org/abs/2606.01447

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