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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A continuous circle of pseudo-arcs
filling up the annulus


Author: Janusz R. Prajs
Journal: Trans. Amer. Math. Soc. 352 (2000), 1743-1757
MSC (1991): Primary 54F15; Secondary 54F50, 54B15
Published electronically: July 1, 1999
MathSciNet review: 1608498
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Abstract: We prove an early announcement by Knaster on a decomposition of the plane. Then we establish an announcement by Anderson saying that the plane annulus admits a continuous decomposition into pseudo-arcs such that the quotient space is a simple closed curve. This provides a new plane curve, ``a selectible circle of pseudo-arcs", and answers some questions of Lewis.


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Additional Information

Janusz R. Prajs
Affiliation: Institute of Mathematics, Opole University, ul. Oleska 48, 45-052 Opole, Poland
Email: jrprajs@math.uni.opole.pl

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02330-2
PII: S 0002-9947(99)02330-2
Keywords: continuous decomposition, continuum, plane, pseudo-arc
Received by editor(s): May 25, 1994
Received by editor(s) in revised form: February 3, 1998
Published electronically: July 1, 1999
Dedicated: To the memory of Professor Bronisław Knaster
Article copyright: © Copyright 2000 American Mathematical Society