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Covering the real line with translates of a zero-dimensional compact set
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Máthé, András (2011) Covering the real line with translates of a zero-dimensional compact set. Fundamenta Mathematicae , Vol.213 (No.3). pp. 213-219. doi:10.4064/fm213-3-2
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Official URL: http://dx.doi.org/10.4064/fm213-3-2
Abstract
We construct a compact set C of Hausdorff dimension zero such that cof(N) many translates of C cover the real line. Hence it is consistent with ZFC that less than continuum many translates of a zero-dimensional compact set can cover the real line. This answers a question of Dan Mauldin.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Fundamenta Mathematicae | ||||
| Publisher: | Polska Akademia Nauk | ||||
| ISSN: | 0016-2736 | ||||
| Official Date: | 2011 | ||||
| Dates: |
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| Volume: | Vol.213 | ||||
| Number: | No.3 | ||||
| Number of Pages: | 7 | ||||
| Page Range: | pp. 213-219 | ||||
| DOI: | 10.4064/fm213-3-2 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | Hungarian Scientific Research Fund | ||||
| Grant number: | T 72655 |
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