Weighted colimits and formal balls in generalized metric spaces

Topology and its Applications

Volumn 89, Issue 1-2, 1998, Pages 179-202

  Rutten, J J M M ^a  

^a CWI   (Netherlands)

Author keywords

Enriched categories; Formal balls; Generalized metric spaces; Weighted limits

Indexed keywords

EID: 15944422937     PISSN: 0016660X     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0166-8641(97)00224-1     Document Type: Article

References (17)

1. M.M. Bonsangue, F. van Breugel and J.J.M.M. Rutten, Generalized metric spaces: completion, topology, and powerdomains via the Yoneda embedding, Report CS-R9636, CWI (1996); also: Theoretical Computer Science 193 (1998) 1-51. FTP-available via www.cwi.nl/∼janr. This report extends CS-R9560, where similar results are given for ultrametric spaces.
2. M.M. Bonsangue, F. van Breugel and J.J.M.M. Rutten, Generalized metric spaces: completion, topology, and powerdomains via the Yoneda embedding, Report CS-R9636, CWI (1996); also: Theoretical Computer Science 193 (1998) 1-51. FTP-available via www.cwi.nl/∼janr. This report extends CS-R9560, where similar results are given for ultrametric spaces.
3. F. Borceux and G.M. Kelly, A notion of limit for enriched categories, Bull. Austral. Math. Soc. 12 (1975) 49-72.
4. F. Borceux, Handbook of Categorical Algebra 2: Categories and Structures, Encyclopedia Math. Appl. 51 (Cambridge University Press, 1994).
5. A. Edalat and R. Heckmann, A computational model for metric spaces, Theoretical Computer Science 193 (1998) 53-73.
6. S. Eilenberg and G.M. Kelly, Closed categories, in: S. Eilenberg, D.K. Harrison, S. MacLane and H. Röhrl, eds., Proceedings of the Conference on Categorical Algebra (Springer, Berlin, 1966) 421-562.
7. B. Flagg and R. Kopperman, Computational models for ultrametric spaces, in: Proceedings MFPS'97, Electronic Notes in Theoret. Comput. Sci. (1997); URL: http://www. elsevier.nl/locate/entcs/volume6.html.
8. G.M. Kelly, Basic Concepts of Enriched Category Theory, London Math. Soc. Lecture Note Series 64 (Cambridge University Press, 1982).
9. F.W. Lawvere, Metric spaces, generalized logic, and closed categories, Rendiconti del Semi-nario Matematico e Fisico di Milano 43 (1973) 135-166.
10. F.W. Lawvere, Taking categories seriously, Revista Colombiana de Matemáticas XX (1986) 147-178.
11. J.D. Lawson, Spaces of maximal points, Math. Structures Comput. Sci. 7 (1997) 543-555.
12. J.J.M.M. Rutten, Elements of generalized ultrametric domain theory, Theoret. Comput. Sci. 170 (1996) 349-381.
13. M.B. Smyth, Totally bounded spaces and compact ordered spaces as domains of computation, in: G.M. Reed, A.W. Roscoe and R.F. Wachter, eds., Topology and Category Theory in Computer Science (Oxford University Press, 1991) 207-229.
14. K.R. Wagner, Liminf convergence in w-categories, Technical Report, Cambridge University (1995); also: Theoretical Computer Science 184 (1997) 61-104.
15. K.R. Wagner, Liminf convergence in w-categories, Technical Report, Cambridge University (1995); also: Theoretical Computer Science 184 (1997) 61-104.
16. K.R. Wagner, Some well-known facts about adjoint bimodules, Preprint, 1995.
17. K. Weihrauch and U. Schreiber, Embedding metric spaces into cpo's, Theoret. Comput. Sci. 16 (1) (1981) 5-24.