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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 homeomorphism on $ s$ not conjugate to an extendable homeomorphism


Author: Jan van Mill
Journal: Proc. Amer. Math. Soc. 105 (1989), 250-253
MSC: Primary 54H15; Secondary 57S05, 58B05
MathSciNet review: 931739
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Abstract: Consider $ s = \Pi _{i = 1}^\infty {( - 1,1)_i}$ and its compactification $ Q = \Pi _{i = 1}^\infty {\left[ { - 1,1} \right]_i}$. Anderson and Bing asked whether for every homeomorphism $ f:s \to s$ there is a homeomorphism $ \phi :s \to s$ such that $ {\phi ^{ - 1}}f\phi $ is extendable to a homeomorphism $ \overline {{\phi ^{ - 1}}f\phi :\;} Q \to Q$. The aim of this note is to construct a counterexample to this question.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0931739-2
PII: S 0002-9939(1989)0931739-2
Keywords: Hilbert cube, isotopy, conjugation, capset
Article copyright: © Copyright 1989 American Mathematical Society