Planar finitely Suslinian compacta
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- by Alexander Blokh, Michał Misiurewicz and Lex Oversteegen PDF
- Proc. Amer. Math. Soc. 135 (2007), 3755-3764 Request permission
Abstract:
We show that a planar unshielded compact set $X$ is finitely Suslinian if and only if there exists a closed set $F\subset \mathbb {S}^1$ 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.References
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Additional Information
- Alexander Blokh
- Affiliation: Department of Mathematics, University of Alabama in Birmingham, University Station, Birmingham, Alabama 35294-2060
- MR Author ID: 196866
- Email: ablokh@math.uab.edu
- Michał Misiurewicz
- Affiliation: Department of Mathematical Sciences, IUPUI, 402 N. Blackford Street, Indianapolis, Indiana 46202-3216
- MR Author ID: 125475
- Email: mmisiure@math.iupui.edu
- Lex Oversteegen
- Affiliation: Department of Mathematics, University of Alabama in Birmingham, University Station, Birmingham, Alabama 35294-2060
- MR Author ID: 134850
- Email: overstee@math.uab.edu
- 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
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 3755-3764
- MSC (2000): Primary 54F15, 54D05, 37F10
- DOI: https://doi.org/10.1090/S0002-9939-07-08953-8
- MathSciNet review: 2336592