| Title:
|
Remarks on WDC sets (English) |
| Author:
|
Pokorný, Dušan |
| Author:
|
Zajíček, Luděk |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
62 |
| Issue:
|
1 |
| Year:
|
2021 |
| Pages:
|
81-94 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
distance function |
| Keyword:
|
WDC set |
| Keyword:
|
DC function |
| Keyword:
|
DC aura |
| Keyword:
|
Borel complexity |
| MSC:
|
26B25 |
| idZBL:
|
Zbl 07396212 |
| idMR:
|
MR4270468 |
| DOI:
|
10.14712/1213-7243.2021.006 |
| . |
| Date available:
|
2021-07-26T11:13:07Z |
| Last updated:
|
2023-04-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148938 |
| . |
| Reference:
|
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