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

 

Extension of the Borsuk theorem on non-embeddability of spheres


Authors: Józef Krasinkiewicz and Stanisław Spież
Journal: Proc. Amer. Math. Soc. 140 (2012), 4035-4040
MSC (2010): Primary 54E45, 57N35; Secondary 55M10, 57Q05
Published electronically: March 16, 2012
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Abstract: It is proved by elementary techniques that the suspension $ \sum M$ of a closed $ n$-dimensional manifold $ M$, $ n\ge 1$, does not embed in a product of $ n+1$ curves. Thus we get in particular an elementary proof of a far-reaching generalization of the Borsuk theorem on non-embeddability of the sphere $ \mathbb{S}^{n+1}$ in a product of $ n+1$ curves. The ultimate results are even more general; they complement and extend some principal results of Koyama, Krasinkiewicz, and Spież.


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Additional Information

Józef Krasinkiewicz
Affiliation: The Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-950, Warsaw, Poland
Email: jokra@impan.gov.pl

Stanisław Spież
Affiliation: The Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-950, Warsaw, Poland
Email: spiez@impan.gov.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11238-9
PII: S 0002-9939(2012)11238-9
Keywords: Embeddings, locally connected continua, weak manifolds, ramified manifolds, products of curves
Received by editor(s): April 8, 2010
Received by editor(s) in revised form: May 5, 2011
Published electronically: March 16, 2012
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.