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Domain theoretic characterisations of quasi-metric completeness in terms of formal balls†

Published online by Cambridge University Press:  07 April 2010

SALVADOR ROMAGUERA  and
OSCAR VALERO
SALVADOR ROMAGUERA
Affiliation:
Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, 46071 Valencia, Spain Email: sromague@mat.upv.es
OSCAR VALERO
Affiliation:
Departamento de Ciencias Matemáticas e Informática, Universidad de las Islas Baleares, 07122 Palma de Mallorca, Baleares, Spain Email: o.valero@uib.es
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Abstract

We characterise those quasi-metric spaces (X, d) whose poset BX of formal balls satisfies the condition(*)From this characterisation, we then deduce that a quasi-metric space (X, d) is Smyth-complete if and only if BX is a dcpo satisfying condition (*). We also give characterisations in terms of formal balls for sequentially Yoneda complete quasi-metric spaces and for Yoneda complete T1 quasi-metric spaces. Finally, we discuss several properties of the Heckmann quasi-metric on the formal balls of any quasi-metric space.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 20 , Issue 3 , June 2010 , pp. 453 - 472
Copyright
Copyright © Cambridge University Press 2010

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