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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
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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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