Remarks on WDC sets
| Autor: | Pokorný, Dušan, Zajíček, Luděk |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 locally WDC set in $\mathbb{R}^2$ is a WDC set. An another consequence is that compact WDC subsets of $\mathbb{R}^2$ form a Borel subset of the space of all compact sets. |
| Databáze: | arXiv |
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