International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 11, Pages 663-672
Precompactness and total boundedness in products of metric spaces
Department of Mathematics and Computer Science, University of Antwerpen-Ruca, Groenenborgerlaan 171, Antwerpen 2020, Belgium
Received 16 February 2001
Copyright © 2001 Bart Windels. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We show that the canonical quantifications of uniform properties
such as precompactness and total boundedness, which were already
studied by Kuratowski and Hausdorff in the setting of complete
metric spaces, can be generalized in the setting of products of
metric spaces in an intuitively appealing way.