Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Having cut-points is not a Whitney reversible property


Author: Eiichi Matsuhashi
Journal: Proc. Amer. Math. Soc. 137 (2009), 3543-3545
MSC (2000): Primary 54B20; Secondary 54F15
DOI: https://doi.org/10.1090/S0002-9939-09-09895-5
Published electronically: May 6, 2009
MathSciNet review: 2515424
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • R. D. Anderson, Atomic decompositions of continua, Duke Math. J. 23 (1956), 507–514. MR 82668
  • Alejandro Illanes and Sam B. Nadler Jr., Hyperspaces, Monographs and Textbooks in Pure and Applied Mathematics, vol. 216, Marcel Dekker, Inc., New York, 1999. Fundamentals and recent advances. MR 1670250
  • Sam B. Nadler Jr., Continuum theory, Monographs and Textbooks in Pure and Applied Mathematics, vol. 158, Marcel Dekker, Inc., New York, 1992. An introduction. MR 1192552

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 54B20, 54F15

Retrieve articles in all journals with MSC (2000): 54B20, 54F15


Additional Information

Eiichi Matsuhashi
Affiliation: Faculty of Engineering, Yokohama National University, Yokohama, 240-8501, Japan
Email: mateii@ynu.ac.jp

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
Published electronically: May 6, 2009
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.