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- W3104555150 abstract "Let R be a real closed field. We prove that if R is uncountable, then any separately Nash (respectively, arc-Nash) function defined over R is semialgebraic (respectively, continuous semialgebraic). To complete the picture, we provide an example showing that the assumption on R to be uncountable cannot be dropped. Moreover, even if R is uncountable but non-Archimedean, then the shape of the domain of a separately Nash function matters for the conclusion. For R = R , we prove that arc-Nash functions coincide with arc-analytic semialgebraic functions." @default.
- W3104555150 created "2020-11-23" @default.
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- W3104555150 date "2020-11-09" @default.
- W3104555150 modified "2023-09-26" @default.
- W3104555150 title "Separately Nash and arc‐Nash functions over real closed fields" @default.
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- W3104555150 doi "https://doi.org/10.1112/blms.12432" @default.
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