Work

On quasi-regulous functions

Year: 2026

Type: article

Abstract: Let X be a real algebraic set. In the literature, a (real-valued) function $$\varphi $$ on X is called regulous if its restriction to each algebraic subset of X is a continuous rational function. A function f on X is called quasi-regulous if it is continuous and $$f^2=\varphi ^2$$ for some regulous function $$\varphi $$ on X . Assuming X is nonsingular, we prove that a function f on X is quasi-regulous if and only if its restriction to each algebraic curve in X is quasi-regulous. We also prove three other variants of this result.

Source: Annali di Matematica Pura ed Applicata (1923 -)

Authors: Wojciech Kucharz, Krzysztof Kurdyka

Institutions: Jagiellonian University, Centre National de la Recherche Scientifique, Le LAMA, Université Savoie Mont Blanc

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Narodowe Centrum Nauki

Award: G1520158475