Centre for Discrete and Applicable Mathematics 

CDAM Research Report, LSECDAM9819October 1998 
A.J. Ostaszewski
Abstract
A Roy space is a zerodimensional metric space having covering dimension at least 1. Using the technique introduced by Mrówka [4], we prove the following.
Theorem The two known Roy spaces of weight aleph_{1} (Kulesza [2] and Ostaszewski [7]) have squares of covering dimension 1.
We also show how to generalize the result to arbitrary finite powers by indicating the changes needed in the case of cubing. Assuming the Continuum Hypothesis (CH), the corresponding theorem for the square was proved by Mrówka [4] in the case of the other then known Roy spaces, which are of weight 2^{aleph0}. In our case CH is unnecessary (since one does not need to map aleph_{1} onto the line). There is resurgent interest in the problem of constructing Roy spaces with dimensional discrepancy larger than 1, so the current contribution presents what is hoped to be a more readable account of [4] by elucidating some of the finer details.
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