## Dušan Pokorný, Luděk Zajíček

*Remarks on WDC sets*

Comment.Math.Univ.Carolin. 62,1 (2021) 81-94.**Abstract: **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.

**Keywords:** distance function; WDC set; DC function; DC aura; Borel complexity

**DOI:** DOI 10.14712/1213-7243.2021.006

**AMS Subject Classification:** 26B25

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