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International Journal of Mathematics and Mathematical Sciences
Volume 28, 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 Hindawi Publishing Corporation. 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.