Complete partial metric spaces have partially metrizable computational models

References

• Ali-Akbari , M. , Honari , B. , Pourmahdian , M. and Rezaii , M. M. 2009 . The space of formal balls and models of quasi-metric spaces . Math. Struct. Comput. Sci , 19 : 337 – 355 .
   Google Scholar
• Edalat , A. and Heckmann , R. 1998 . A computational model for metric spaces . Theoret. Comput. Sci , 193 : 53 – 73 .
   Google Scholar
• Edalat , A. and Sünderhauf , Ph. 1999 . Computable Banach spaces via domain theory . Theoret. Comput. Sci. 219 , : 169 – 184 .
   Google Scholar
• Engelking , R. 1977 . General Topology, Monografie Mat. Tom 60 , Warszawa : PWN-Polish Scientific Publishers .
   Google Scholar
• Flagg , B. and Kopperman , R. 1997 . Computational models for ultrametric spaces . Electron. Notes Theoret. Comput. Sci , 6 : 151 – 159 .
   Google Scholar
• Gierz , G. , Hofmann , K. H. , Keimel , K. , Lawson , J. D. , Mislove , M. and Scott , D. S. 2003 . “ Continuous Lattices and Domains ” . In Encyclopedia of Mathematics and its Applications , Vol. 93 , Cambridge : Cambridge University Press .
   Google Scholar
• Heckmann , R. 1999 . Approximation of metric spaces by partial metric spaces . Appl.Cat. Struct , 7 : 71 – 83 .
   Google Scholar
• Kopperman , R. , Künzi , H. P. and Waszkiewicz , P. 2004 . Bounded complete models of topological spaces . Topol. Appl , 139 : 285 – 297 .
   Google Scholar
• Krötzsch , M. 2006 . Generalized ultrametric spaces in quantitative domain theory . Theoret. Comput. Sci , 368 : 30 – 49 .
   Google Scholar
• Künzi , H. P.A. 2001 . “ Nonsymmetric distances and their associated topologies: About the origins of basic ideas in the area of asymmetric topology ” . In Handbook of the History of General Topology , Edited by: Aull , C. E. and Lowen , R. vol. 3 , 853 – 968 . Dordrecht : Kluwer .
   Google Scholar
• Lawson , J. 1997 . Spaces of maximal points . Math. Struct. Comput. Sci , 7 : 543 – 556 .
   Google Scholar
• Martin , K. 1998 . Domain theoretic models of topological spaces . Electron. Notes Theoret. Comput. Sci , 13 : 173 – 181 .
   Google Scholar
• Matthews , S. G. Partial metric topology . Procedings of the 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci. 728 (1994), pp. 183–197
   Google Scholar
• Rodríguez-López , J. , Romaguera , S. and Valero , O. 2008 . Denotational semantics for programming languages, balanced quasi-metrics and fixed points . Internat. J. Comput. Math , 85 : 623 – 630 .
   Web of Science ®Google Scholar
• Romaguera , S. 2009 . “ On Computational Models for the Hyperspace ” . In Advances in Mathematics Research , Vol. 8 , 277 – 294 . New York : Nova Science Publishers .
   Google Scholar
• Romaguera , S. and Valero , O. 2009 . A quasi-metric computational model from modular functions on monoids . Internat. J. Comput. Math , 86 : 1668 – 1677 .
   Web of Science ®Google Scholar
• Romaguera , S. and Valero , O. 2009 . A quantitative computational model for complete partial metric spaces via formal balls . Math. Struct. Comput. Sci , 19 : 541 – 563 .
   Web of Science ®Google Scholar
• Romaguera , S. and Valero , O. 2010 . Domain theoretic characterisations of quasi-metric completeness in terms of formal balls . Math. Struct. Comput. Sci , 20 : 453 – 472 .
   Web of Science ®Google Scholar
• Rutten , J. J.M.M. 1998 . Weighted colimits and formal balls in generalized metric spaces . Topol. Appl , 89 : 179 – 202 .
   Google Scholar
• Schellekens , M. 2003 . A characterization of partial metrizability. Domains are quantifiable . Theoret. Comput. Sci , 305 : 409 – 432 .
   Google Scholar
• Smyth , M. B. 2006 . The constructive maximal point space and partial metrizability . Ann. Pure Appl. Logic , 137 : 360 – 379 .
   Google Scholar
• Waszkiewicz , P. 2003 . Quantitative continuous domains . Appl. Cat. Struct , 11 : 41 – 67 .
   Google Scholar
• Waszkiewicz , P. 2006 . Partial metrisability of continuous posets . Math. Struct. Comput. Sci , 16 : 359 – 372 .
   Google Scholar