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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A counterexample related to topological sums


Authors: Shuji Yamamoto and Atsushi Yamashita
Journal: Proc. Amer. Math. Soc. 134 (2006), 3715-3719
MSC (2000): Primary 54B99, 54G15, 54G20
Published electronically: June 15, 2006
MathSciNet review: 2240688
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Abstract | Similar Articles | Additional Information

Abstract: In this paper we construct compact metric spaces $ X$, $ Y$ which are topologically distinct but whose topological sums $ X \sqcup X$ and $ Y\sqcup Y$ are homeomorphic.


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Additional Information

Shuji Yamamoto
Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo 153–8914, Japan
Email: yamashu@ms.u-tokyo.ac.jp

Atsushi Yamashita
Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo 153–8914, Japan
Email: yonster@ms.u-tokyo.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08596-0
PII: S 0002-9939(06)08596-0
Keywords: Topological sum, disjoint union, counterexample
Received by editor(s): September 27, 2004
Received by editor(s) in revised form: July 9, 2005
Published electronically: June 15, 2006
Additional Notes: The authors are pleased to thank the referee and K. Sakai for their useful comments. The authors also thank S. Saito, who corrected English expressions and many errors in the preliminary version of this paper.
Communicated by: Alexander Dranishnikov
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.