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Planar finitely Suslinian compacta
Author(s):
Alexander
Blokh;
Michal\
Misiurewicz;
Lex
Oversteegen
Journal:
Proc. Amer. Math. Soc.
135
(2007),
3755-3764.
MSC (2000):
Primary 54F15, 54D05, 37F10
Posted:
August 15, 2007
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Abstract:
We show that a planar unshielded compact set  is finitely Suslinian if and only if there exists a closed set  and a lamination  of  such that  is homeomorphic to  . If  is a continuum, the analogous statement follows from Carathéodory theory and is widely used in polynomial dynamics.
References:
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- 2.
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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:
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
Posted:
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
Copyright of article:
Copyright
2007,
American Mathematical Society
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