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On contractible $n$-dimensional compacta, non-embeddable into $\mathbb{R}^{2n}$

Author(s): Dusan Repovs; Arkady Skopenkov
Journal: Proc. Amer. Math. Soc. 129 (2001), 627-628.
MSC (1991): Primary 54C25; Secondary 55S91
Posted: October 2, 2000
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Abstract: We present a very short proof of a well-known result, that for each $n$ there exists a contractible $n$-dimensional compactum, non-embeddable into $\mathbb{R}^{2n}$.

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Additional Information:

Dusan Repovs
Affiliation: Institute of Mathematics, Physics and Mechanics, University of Ljubljana, P.O. Box 2964, Ljubljana, Slovenia 1001
Email: dusan.repovs@fmf.uni-lj.si

Arkady Skopenkov
Affiliation: Department of Differential Geometry, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia 119899
Email: skopenko@mccme.ru, skopenko@aesc.msu.ru

DOI: 10.1090/S0002-9939-00-05972-4
PII: S 0002-9939(00)05972-4
Keywords: Embedding in euclidean space, contractible compactum, equivariant map, involution, Borsuk-Ulam theorem, antipode
Received by editor(s): January 6, 2000
Received by editor(s) in revised form: April 1, 2000
Posted: October 2, 2000
Additional Notes: The first author was supported in part by the Ministry for Science and Technology of the Republic of Slovenia research grant No. J1-0885-0101-98. The second author was supported in part by the Russian Fundamental Research Grant No.~99-01-00009.
Communicated by: Alan Dow
Copyright of article: Copyright 2000, American Mathematical Society

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