Extension of the Borsuk theorem on non-embeddability of spheres
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- by Józef Krasinkiewicz and Stanisław Spież
- Proc. Amer. Math. Soc. 140 (2012), 4035-4040
- DOI: https://doi.org/10.1090/S0002-9939-2012-11238-9
- 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.References
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Bibliographic 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
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 4035-4040
- MSC (2010): Primary 54E45, 57N35; Secondary 55M10, 57Q05
- DOI: https://doi.org/10.1090/S0002-9939-2012-11238-9
- MathSciNet review: 2944743