A central set of dimension $2$
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- by Christopher J. Bishop and Hrant Hakobyan
- Proc. Amer. Math. Soc. 136 (2008), 2453-2461
- DOI: https://doi.org/10.1090/S0002-9939-08-09173-9
- Published electronically: March 7, 2008
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Abstract:
The central set of a domain $D$ is the set of centers of maximal discs in $D$. Fremlin proved that the central set of a planar domain has zero area and asked whether it can have Hausdorff dimension strictly larger than $1$. We construct a planar domain with central set of Hausdorff dimension $2$.References
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Bibliographic Information
- Christopher J. Bishop
- Affiliation: Department of Mathematics, SUNY Stony Brook, Stony Brook, New York 11790
- MR Author ID: 37290
- Email: bishop@math.sunysb.edu
- Hrant Hakobyan
- Affiliation: Department of Mathematics, University of Toronto, Toronto, ON, Canada M5S 2E4
- Received by editor(s): February 1, 2007
- Published electronically: March 7, 2008
- Additional Notes: The first author was partially supported by NSF Grant DMS 04-05578.
- Communicated by: Juha M. Heinonen
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 2453-2461
- MSC (2000): Primary 28A78; Secondary 28A75
- DOI: https://doi.org/10.1090/S0002-9939-08-09173-9
- MathSciNet review: 2390513