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A continuous circle of pseudo-arcs filling up the annulus
Author(s):
Janusz
R.
Prajs
Journal:
Trans. Amer. Math. Soc.
352
(2000),
1743-1757.
MSC (1991):
Primary 54F15;
Secondary 54F50, 54B15
Posted:
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.
References:
- 1.
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- 2.
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- 4.
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- M. Brown, Continuous collections of higher dimensional continua, Ph. D. Thesis, University of Wisconsin, 1958.
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- B. Knaster, Un continu dont tout sous-continu est indecomposable, Fund. Math. 3(1922), 247-286.
- 7.
- W. Lewis, Continuous curves of pseudo-arcs, Houston J. Math. 11(1985), 91-99. MR 86e:54038
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- List of the works achieved in the field of mathematics and sciences in Poland during the German occupation, 1939-1945, Polish Academy of Sciences and Letters, Kraków 1947. MR 10:276e
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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:
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
Posted:
July 1, 1999
Dedicated:
To the memory of Professor Bronislaw Knaster
Copyright of article:
Copyright
2000,
American Mathematical Society
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