Łojasiewicz, Stanisław Sur la séparation régulière. (Regular separation). (French) Zbl 0612.32008 Semin. Geom., Univ. Studi Bologna 1985, 119-121 (1986). The author proves the following version of the type of inequalities, which are named by Hörmander and himself. Theorem: Let A be relatively compact subanalytic in an analytic variety V and let \(\phi\),\(\psi\) : \(A\to {\mathbb{R}}\) be continuous and subanalytic. If \(\{\phi =0\}\subset \{\psi =0\}\), then \(| \psi (x)| \leq c | \phi (x)|^{\alpha}\) on A for some \(c,\alpha >0.\) First it is shown, that a subanalytic set which is contained in a semianalytic set of dim\(\leq 2\) is itself semianalytic. This is applied for the image of A in \({\mathbb{R}}^ 2\) under (\(\phi\),\(\psi)\); from which the Theorem follows in the usual way. Reviewer: H.-J. Nastold Cited in 2 Documents MSC: 32B20 Semi-analytic sets, subanalytic sets, and generalizations 32C05 Real-analytic manifolds, real-analytic spaces 58A07 Real-analytic and Nash manifolds Keywords:Hörmander-Lojasiewicz inequality; regular separation; subanalytic set PDFBibTeX XMLCite \textit{S. Łojasiewicz}, Semin. Geom., Univ. Studi Bologna 1985, 119--121 (1986; Zbl 0612.32008)