Geodesic
Remarks on WDC sets
Commentationes Mathematicae Universitatis Carolinae, Tome 62 (2021) no. 1, pp. 81-94.

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We study WDC sets, which form a substantial generalization of sets with positive reach and still admit the definition of curvature measures. Main results concern WDC sets $A\subset {\mathbb R}^2$. We prove that, for such $A$, the distance function $d_A= {\rm dist}(\cdot,A)$ is a ``DC aura'' for $A$, which implies that each closed locally WDC set in ${\mathbb R}^2$ is a WDC set. Another consequence is that compact WDC subsets of ${\mathbb R}^2$ form a Borel subset of the space of all compact sets.
DOI : 10.14712/1213-7243.2021.006
Classification : 26B25
Keywords: distance function; WDC set; DC function; DC aura; Borel complexity 
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Pokorný, Dušan; Zajíček, Luděk. Remarks on WDC sets. Commentationes Mathematicae Universitatis Carolinae, Tome 62 (2021) no. 1, pp. 81-94. doi : 10.14712/1213-7243.2021.006. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2021.006/

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