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The Urysohn-Menger sum formula: an extension of the Dydak-Walsh theorem to dimension one

Part of: Special properties Homotopy theory Classical Topics in Algebraic Topology

Published online by Cambridge University Press:  09 April 2009

Aleksander N. Dranišnikov  and
Dušan Repovš
Aleksander N. Dranišnikov
Affiliation:
Department of Mathematics, Cornell University, White Hall, Ithaca, NY 14853-7901, USA, e-mail: [email protected]
Dušan Repovš
Affiliation:
Institute for Mathematics Physics and Mechanics, University of Ljubljana, P. O. Box 64 Ljubljana 61111, Slovenia, e-mail: [email protected]
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Abstract

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Let X be a finite-dimensional separable metric space, presented as a disjoint union of subsets, X = A∪B. We prove the following theorem: For every prime p, c-dimZpX≦c-dimZpA + c–dimZpB + 1. This improves upon some of the earlier work by Dydak and Walsh.

Keywords

Urysohn-Menger sum formulacohomological dimensionfinite groupsBock-stein ringsMoore spacesEilenberg-MacLane complexesBlakers-Massey theorem.

MSC classification

Secondary: 55M10: Dimension theory 55P20: Eilenberg-Mac Lane spaces 54F45: Dimension theory 55P99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 2 , October 1995 , pp. 273 - 282
Copyright
Copyright © Australian Mathematical Society 1995

References

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