Approximation of metric spaces by partial metric spaces. (English) Zbl 0993.54029

Heckmann, Reinhold

Appl. Categ. Struct. 7, No. 1-2, 71-83 (1999).

Summary: Partial metrics are generalized metrics with non-zero self-distances. We slightly generalize Matthews’s original definition of partial metrics [S. G. Matthews, Ann. N.Y. Acad. Sci. 728, 183-197 (1994; Zbl 0911.54025)], 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.

MSC:

54E35	Metric spaces, metrizability
06B35	Continuous lattices and posets, applications

Keywords:

generalized metric spaces; Scott topology; preorder; weak partial metric

Citations:

Zbl 0911.54025