Balogh, Zoltán M.; Züst, Roger (2020). Box-counting by Hölder's traveling salesman. Archiv der Mathematik, 114(5), pp. 561-572. Birkhäuser 10.1007/s00013-019-01415-5
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We provide a sufficient Dini-type condition for a subset of a complete, quasiconvex metric space to be covered by a Hölder curve. This implies in particular that if the upper box-counting dimension is less than d≥1, then it can be covered by an 1/d-Hölder curve. On the other hand, for each 1≤d<2 we give an example of a compact set in the plane with lower box-counting dimension equal to zero and upper box-counting dimension equal to d, just failing the above Dini-type condition, that can not be covered by a countable collection of 1/d-Hölder curves.
Item Type: |
Journal Article (Original Article) |
|---|---|
Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Balogh, Zoltan, Züst, Roger |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
0003-889X |
Publisher: |
Birkhäuser |
Funders: |
[4] Swiss National Science Foundation |
Language: |
English |
Submitter: |
Sebastiano Don |
Date Deposited: |
28 Jan 2021 17:59 |
Last Modified: |
14 Dec 2023 00:25 |
Publisher DOI: |
10.1007/s00013-019-01415-5 |
ArXiv ID: |
1907.05227 |
Uncontrolled Keywords: |
Hausdorff dimension, Box-counting dimension, Fractals, Hölder maps |
BORIS DOI: |
10.48350/151223 |
URI: |
https://boris.unibe.ch/id/eprint/151223 |
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