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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Planar finitely Suslinian compacta


Authors: Alexander Blokh, Michal\ Misiurewicz and Lex Oversteegen
Journal: Proc. Amer. Math. Soc. 135 (2007), 3755-3764
MSC (2000): Primary 54F15, 54D05, 37F10
Published electronically: August 15, 2007
MathSciNet review: 2336592
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Abstract: We show that a planar unshielded compact set $ X$ is finitely Suslinian if and only if there exists a closed set $ F\subset \sone$ and a lamination $ \sim$ of $ F$ such that $ F/\sim$ is homeomorphic to $ X$. If $ X$ is a continuum, the analogous statement follows from Carathéodory theory and is widely used in polynomial dynamics.


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Additional Information

Alexander Blokh
Affiliation: Department of Mathematics, University of Alabama in Birmingham, University Station, Birmingham, Alabama 35294-2060
Email: ablokh@math.uab.edu

Michal\ Misiurewicz
Affiliation: Department of Mathematical Sciences, IUPUI, 402 N. Blackford Street, Indianapolis, Indiana 46202-3216
Email: mmisiure@math.iupui.edu

Lex Oversteegen
Affiliation: Department of Mathematics, University of Alabama in Birmingham, University Station, Birmingham, Alabama 35294-2060
Email: overstee@math.uab.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08953-8
PII: S 0002-9939(07)08953-8
Keywords: Finitely Suslinian, unshielded, locally connected, lamination
Received by editor(s): January 4, 2006
Received by editor(s) in revised form: September 8, 2006
Published electronically: August 15, 2007
Additional Notes: The first author was partially supported by NSF grant DMS 0456748
The second author was partially supported by NSF grant DMS 0456526
The third author was partially supported by by NSF grant DMS 0405774
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2007 American Mathematical Society