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Completions of partial metrics into value lattices
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Kopperman, R. D., Matthews, Stephen G. and Pajoohesh, H. (2009) Completions of partial metrics into value lattices. Topology and its Applications, Vol.156 (No.8). pp. 1534-1544. doi:10.1016/j.topol.2009.01.002 ISSN 0166-8641.
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Official URL: http://dx.doi.org/10.1016/j.topol.2009.01.002
Abstract
In this paper we investigate some notions of completion of partial metric spaces. including the bicompletion, the Smyth completion, and a new "spherical completion". Given an auxiliary relation, we show that it arises from a totally bounded partial metric space, and the spherical completion of such a space is its round ideal completion. We also give an example of a totally bounded partial metric space whose bicompletion and Smyth completion are not continuous posets. Finally, we present an example of a totally bounded partial metric giving rise to the Scott and lower topologies of a continuous poser. but whose spherical completion is not a continuous poser. (C) 2009 Elsevier B.V. All rights reserved.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||
Journal or Publication Title: | Topology and its Applications | ||||
Publisher: | Elsevier Science BV | ||||
ISSN: | 0166-8641 | ||||
Official Date: | 15 April 2009 | ||||
Dates: |
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Volume: | Vol.156 | ||||
Number: | No.8 | ||||
Number of Pages: | 11 | ||||
Page Range: | pp. 1534-1544 | ||||
DOI: | 10.1016/j.topol.2009.01.002 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Funder: | PSC-CUNY |
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