Abstract
Partial metrics are generalised metrics with non-zero self-distances. We slightly generalise Matthews' original definition of partial metrics, yielding a notion of weak partial metric. After considering weak partial metric spaces in general, we introduce a weak partial metric on the poset of formal balls of a metric space. This weak partial metric can be used to construct the completion of classical metric spaces from the domain-theoretic rounded ideal completion.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Edalat, A. and Heckmann, R.: A computational model for metric spaces, Theoretical Computer Science 193 (1998), 53–73.
Matthews, S. G.: Partial metric topology, in Proceedings of the 8th Summer Conference on Topology and its Applications, Annals of the New York Academy of Sciences 728, 1992, pp. 183–197.
O'Neill, S. J.: Two topologies are better than one, Technical Report, University of Warwick, April 1995.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Heckmann, R. Approximation of Metric Spaces by Partial Metric Spaces. Applied Categorical Structures 7, 71–83 (1999). https://doi.org/10.1023/A:1008684018933
Issue Date:
DOI: https://doi.org/10.1023/A:1008684018933