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The visible part of plane self-similar sets
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dc.contributor.author | Falconer, Kenneth John | |
dc.contributor.author | Fraser, Jonathan Macdonald | |
dc.date.accessioned | 2012-06-13T10:31:01Z | |
dc.date.available | 2012-06-13T10:31:01Z | |
dc.date.issued | 2013 | |
dc.identifier.citation | Falconer , K J & Fraser , J M 2013 , ' The visible part of plane self-similar sets ' , Proceedings of the American Mathematical Society , vol. 141 , no. 1 , pp. 269-278 . https://doi.org/10.1090/S0002-9939-2012-11312-7 | en |
dc.identifier.issn | 0002-9939 | |
dc.identifier.other | PURE: 5014744 | |
dc.identifier.other | PURE UUID: 5fdbfe84-647b-4c98-b821-91ff94d5e825 | |
dc.identifier.other | Scopus: 84868153101 | |
dc.identifier.other | ORCID: /0000-0001-8823-0406/work/58055267 | |
dc.identifier.other | ORCID: /0000-0002-8066-9120/work/58285486 | |
dc.identifier.uri | https://hdl.handle.net/10023/2756 | |
dc.description | JMF was supported by an EPSRC grant whilst undertaking this work. | en |
dc.description.abstract | Given a compact subset F of R2, the visible part VθF of F from direction θ is the set of x in F such that the half-line from x in direction θ intersects F only at x. It is suggested that if dimH F ≥ 1 then dimH VθF = 1 for almost all θ , where dimH denotes Hausdorff dimension. We conrm this when F is a self-similar set satisfying the convex open set condition and such that the orthogonal projection of F onto every line is an interval. In particular the underlying similarities may involve arbitrary rotations and F need not be connected. | |
dc.language.iso | eng | |
dc.relation.ispartof | Proceedings of the American Mathematical Society | en |
dc.rights | © Copyright 2012 American Mathematical Society. First published in Proceedings of the American Mathematical Society 2012, published by the American Mathematical Society) | en |
dc.subject | Metric Geometry | en |
dc.subject | QA Mathematics | en |
dc.subject.lcc | QA | en |
dc.title | The visible part of plane self-similar sets | en |
dc.type | Journal article | en |
dc.description.version | Publisher PDF | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | https://doi.org/10.1090/S0002-9939-2012-11312-7 | |
dc.description.status | Peer reviewed | en |
dc.identifier.url | http://arxiv.org/pdf/1004.5067.pdf | en |
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