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On a Hopf Homotopy Classification Theorem

Published online by Cambridge University Press:  22 January 2016

Hiroshi Uehara
Hiroshi Uehara*
Affiliation:
Mathematical Institute, Nagoya University
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There are various generalizations of Hopf’s brilliant theorem, which may be stated, as newly formulated by Alexandroff; all the homotopy classes of the mappings of a compact Hausdorff space X with dim X≦n into an n-sphere Sn are in a (1-1) -correspondence with the elements of the n-dimensional Čech cohomology group Hn(X) with integer coefficients.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 3 , October 1951 , pp. 49 - 54
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1951

References

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[3] Hurewicz, W. and Wallman, H., Dimension theory, Princeton, 1941.Google Scholar
[4] Spanier, E., Borsuk’s Cohomotopy Groups, Ann. of Math. 50 (1949), 203–245.Google Scholar