Constructing Discontinuous but Locally Bounded Rational Functions using Łojasiewicz Inequalities
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917552922296320 |
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| author | Coffman, Adam Pan, Yifei |
| author_facet | Coffman, Adam Pan, Yifei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01447 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Constructing Discontinuous but Locally Bounded Rational Functions using Łojasiewicz Inequalities Coffman, Adam Pan, Yifei Classical Analysis and ODEs Algebraic Geometry 26C15 (Primary) 14P10, 26B05 (Secondary) 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. |
| title | Constructing Discontinuous but Locally Bounded Rational Functions using Łojasiewicz Inequalities |
| topic | Classical Analysis and ODEs Algebraic Geometry 26C15 (Primary) 14P10, 26B05 (Secondary) |
| url | https://arxiv.org/abs/2606.01447 |