Localic completion of generalized metric spaces

Theory and Applications of Categories

Volumn 14, Issue 15, 2005, Pages

  Vickers, Steven ^a  

^a UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

Completion; Enriched category; Geometric logic; Locale; Metric; Quasimetric; Topology

Indexed keywords

EID: 27844462025     PISSN: 1201561X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. [BvBR98] M.M. Bonsangue, F. van Breugel, and J.J.M.M. Rutten, Generalized metric spaces: Completion, topology, and powerdomains via the Yoneda embedding, Theoret. Comput. Sci. 193 (1998), 1-51.
2. [CSSV03] T. Coquand, G. Sambin, J. Smith, and S. Valentini, Inductively generated formal topologies, Annals of Pure and Applied Logic 124 (2003), 71-106.
3. [Joh82] P.T. Johnstone, Stone spaces, Cambridge Studies in Advanced Mathematics, no. 3, Cambridge University Press, 1982.
4. [Joh89] P.T. Johnstone, A constructive 'closed subgroup' theorem for localic groups and groupoids, Cahiers Topologie Géom. Differentielle Catégoriques 30 (1989), 3-23.
5. [JT84] A. Joyal and M. Tierney, An extension of the Galois theory of Grothendieck, Memoirs of the American Mathematical Society 309 (1984).
6. [KS02] H.P. Künzi and M.P. Schellekens, On the Yoneda completion of a quasi-metric space, Theoretical Computer Science 278 (2002), 159-194.
7. [Law73] F.W. Lawvere, Metric spaces, generalised logic, and closed categories, Rend. del Sem. Mat. e Fis. di Milano 43 (1973), reissued as [Law02].
8. [Law02] F.W. Lawvere, Metric spaces, generalised logic, and closed categories, Reprints in Theory and Applications of Categories 1 (2002), 1-37, originally published as [Law73].
9. [MLM92] S. Mac Lane and I. Moerdijk, Sheaves in geometry and logic, Springer-Verlag, 1992.
10. [MP91] C.J. Mulvey and J. Wick-Pelletier, A globalization of the Hahn-Banach theorem, Advances in Mathematics 89 (1991), 1-59.
11. [Sam87] G. Sambin, Intuitionistic formal spaces - a first communication, Mathematical Logic and its Applications (Dimiter G. Skordev, ed.), Plenum, 1987, pp. 187-204.
12. [Smy91] M. Smyth, Totally bounded spaces and compact ordered spaces as domains of computation, Topology and Category Theory in Computer Science (G.M. Reed, A.W. Roscoe, and R.F. Wachter, eds.), Oxford University Press, 1991, pp. 207-229.
13. [Vic89] S. Vickers, Topology via logic, Cambridge University Press, 1989.
14. [Vic93] S. Vickers, Information systems for continuous posets, Theoretical Computer Science 114 (1993), 201-229.
15. [Vic98] S. Vickers, Localic completion of quasimetric spaces, Tech. Report DoC 97/2, Department of Computing, Imperial College, London, 1998.
16. [Vic99] S. Vickers, Topical categories of domains, Mathematical Structures in Computer Science 9 (1999), 569-616.
17. [Vic03] S. Vickers, Localic completion of generalized metric spaces II: Powerlocales, draft available on web at http://www.cs.bham.ac.uk/~sjv, 2003.
18. [Vic04] S. Vickers, The double powerlocale and exponentiation: A case study in geometric reasoning, Theory and Applications of Categories 12 (2004), 372-422.