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A counterexample related to topological sums

Author(s): Shuji Yamamoto; Atsushi Yamashita
Journal: Proc. Amer. Math. Soc. 134 (2006), 3715-3719.
MSC (2000): Primary 54B99, 54G15, 54G20
Posted: June 15, 2006
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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: 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
Posted: 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
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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