J Austral Math Soc Ser A 59 pp273--282, 1995.

The Urysohn-Menger Sum Formula: An Extension of the Dydak-Walsh Theorem to Dimension One

Aleksander N. Dranisnikov and Dusan Repovs

(Received 5 January 1993; revised 20 September 1993)

Abstract

Let X be a finite-dimensional separable metric space, presented as a disjoint union of subsets, X = AÈB. We prove the following theorem: For every prime p, c-dim_{Z_p} X £ c-dim_{Z_p} A + c-dim_{Z_p} B + 1. This improves upon some of the earlier work by Dydak and Walsh.

1991 AMS Subject Classification: primary 55M10, 55M20; secondary 54F45, 55P99

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Authors

Aleksander N. Dranisnikov: Department of Mathematics, Cornell University, White Hall, Ithaca, NY 14853-7901, USA.
mailto:dranish@math.cornell.edu
Dusan Repovs: Institute for Mathematics Physics and Mechanics, University of Ljubljana, P. O. Box 64 Ljubjana 61111, Slovenia.
mailto:dusan.repovs@uni-lj.si

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Last Modified: Thu Jan 9 9:04:24 2003