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On the decomposition of spaces in Cartesian products and unions

Published online by Cambridge University Press:  24 October 2008

Tudor Ganea  and
Peter J. Hilton
Tudor Ganea
Affiliation:
The University of BucarestCornell UniversityUniversity of Birmingham
Peter J. Hilton
Affiliation:
The University of BucarestCornell UniversityUniversity of Birmingham
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Extract

The present paper is concerned with particular cases, obtained by suitably restricting the spaces involved, of the following general problem.

Given a topological space X, we ask whether there exist integers n ≥ 2 and non-contractible spaces X1, …, Xn such that X has the homotopy type of the Cartesian product X1, × … × Xn or of the union X1, v … v Xn.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 55 , Issue 3 , July 1959 , pp. 248 - 256
Copyright
Copyright © Cambridge Philosophical Society 1959

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References

REFERENCES

(1)Berstein, I.On the dimension of modules and algebras IX (Direct limita). Nagoya Math. J. 13 (1958), 83–4.Google Scholar
(2)Dowker, C. H.Topology of metrio complexes. Amer. J. Math. 74 (1952), 555–77.CrossRefGoogle Scholar
(3)Eckmann, B. and Helton, P. J.Groupes d'homotopie et dualité. C.R. Acad. Sci. Paris, 246 (1958), 2444–7, 2555–8, 2991–3.Google Scholar
(4)Eilenberg, S. and Ganea, T.On the Lusternik–Schnirelmann category of abstract groups. Ann. Math. 65 (1957), 517–18.Google Scholar
(5)Fox, R. H.On the Lusternik–Schnirelmann category. Ann. Math. 42 (1941), 333–70.Google Scholar
(6)Giever, J. B.On the equivalence of two singular homology theories. Ann. Math. 51 (1950), 178–91.CrossRefGoogle Scholar
(7)Hilton, P. J.On divisore and multiples of continuous maps. Fundam. Math. 43 (1956), 358–86.Google Scholar
(8)Van Kampen, E. R.On the connection between the fundamental groups of some related spaces. Amer. J. Math. 55 (1933), 261–7.Google Scholar
(9)Kurosch, A. G.Gruppentheorie (Berlin, 1953).Google Scholar
(10)Borsite, K.Über einige Probleme der anschaulichen Topologie. Jber. Dtsch. Mat Ver. 60 (1958), 101–14.Google Scholar