Centre for Discrete and Applicable Mathematics |
|
CDAM Research Report, LSE-CDAM-98-19October 1998 |
A.J. Ostaszewski
Abstract
A Roy space is a zero-dimensional 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 aleph1 (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 2aleph0. In our case CH is unnecessary (since one does not need to map aleph1 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.
Compressed (gzip) PostScript files with the full contents of this report can be downloaded by clicking here for the text (111 kB) and clicking here for the figures (12 kB).
Alternatively, if you like a free hard copy of this report, please send the number of this report, LSE-CDAM-98-19, together with your name and postal address to:
CDAM Research Reports Series Centre for Discrete and Applicable Mathematics London School of Economics Houghton Street London WC2A 2AE, U.K. |
||
Phone: +44(0)-171-955 7732. Fax: +44(0)-171-955 6877. Email: info@maths.lse.ac.uk |
Introduction to the CDAM Research Report Series. | ||
CDAM Homepage. |
Last changed: Wed 9 Feb 2005
For comments go to:
http://www.maths.lse.ac.uk/webmaster.html