Remarks on WDC sets
Dušan Pokorný, Luděk Zajíček (2021)
Commentationes Mathematicae Universitatis Carolinae
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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 . We prove that, for such , the distance function is a “DC aura” for , which implies that each closed locally WDC set in is a WDC set. Another consequence is that compact WDC subsets of form a Borel subset of the space of all compact sets.