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Having cut-points is not a Whitney reversible property
Author(s):
Eiichi
Matsuhashi
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3543-3545.
MSC (2000):
Primary 54B20;
Secondary 54F15
Posted:
May 6, 2009
MathSciNet review:
2515424
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Abstract:
We show that the property of having cut-points is not a Whitney reversible property. This answers in the negative a question posed by Illanes and Nadler.
References:
-
- 1.
- R. D. Anderson, Atomic decompositions of continua, Duke Math. J. 23 (1956), 507-514. MR 0082668 (18:590c)
- 2.
- A. Illanes and S.B. Nadler Jr., Hyperspaces: Fundamentals and Recent Advances, in: Pure Appl. Math. Ser., Vol. 216, Marcel Dekker, New York, 1999. MR 1670250 (99m:54006)
- 3.
- S.B. Nadler Jr., Continuum Theory: An Introduction, Marcel Dekker, New York, 1992. MR 1192552 (93m:54002)
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Additional Information:
Eiichi
Matsuhashi
Affiliation:
Faculty of Engineering, Yokohama National University, Yokohama, 240-8501, Japan
Email:
mateii@ynu.ac.jp
DOI:
10.1090/S0002-9939-09-09895-5
PII:
S 0002-9939(09)09895-5
Keywords:
Whitney reversible property,
cut-point,
terminal continuum,
atomic map.
Received by editor(s):
December 23, 2008,
Received by editor(s) in revised form:
January 6, 2009
Posted:
May 6, 2009
Communicated by:
Alexander N. Dranishnikov
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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