Subfields of R with arbitrary Hausdorff dimension
Assuming CH, the continuum hypothesis, holds we show, by completing an attack first discovered by Roy Davies, that for each α between 0 and 1 there is a subring, in fact a subfield, of R with Hausdorff dimension α.
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| Veröffentlicht in: | Mathematical proceedings of the Cambridge Philosophical Society 2016-07, Vol.161 (1), p.157-165 |
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| Format: | Artikel |
| Sprache: | eng |
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| Online-Zugang: | Volltext |
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| Zusammenfassung: | Assuming CH, the continuum hypothesis, holds we show, by completing an attack first discovered by Roy Davies, that for each α between 0 and 1 there is a subring, in fact a subfield, of R with Hausdorff dimension α. |
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| ISSN: | 0305-0041 1469-8064 |
| DOI: | 10.1017/S0305004116000207 |