Completions of partial metrics into value lattices |
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Authors: | RD Kopperman SG Matthews |
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Institution: | a Department of Mathematics, City College of City University of New York, New York, NY 10031, USA b Department of Computer Science, University of Warwick, Coventry, CV4 7AL, UK c Department of Mathematics, Medgar Evers College, CUNY, 1650 Bedford Av., Brooklyn, NY 11225, USA |
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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 poset, but whose spherical completion is not a continuous poset. |
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