Domain Theory as a Tool for Topology - a Case Study

• Autorzy: Waszkiewicz P.
• Języki publikacji: PL

Abstrakty

EN

In this paper we adopt a certain view on continuous posets and see them as models of their spaces of maximal elements, which are most often topologies rich in structure. Adopting this perspective seems to be fruitful: we are often able to match structural properties of the modelling poset to properties of the modelled space. It was discovered by Mike Reed and Keye Martin two years ago that existence of a measurement on the model corresponds to existence of a development for the modelled topological space. We present an elementary proof of this fact and show how one can use this result to give a new proof to one of the first metrization theorems in Topology.

Słowa kluczowe

EN

Continuous dcpo; domain; development; metrization

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Schedae Informaticae
• Rocznik: 2003
• Tom: Vol. 12
• Strony: 17--26
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Waszkiewicz P.

• Institute of Computer Science, Jagiellonian University, Nawojki 11, Kraków, 30-072 Poland,

Bibliografia

• [1] Abramsky S., Jung A.; Domain Theory, in: S. Abramsky, D.M. Gabbay and T.S.E. Maibaum, (eds.), Handbook of Logic in Computer Science, Clarendon Press, Vol. 3, 1994, pp. 1–168.
• [2] Edalat A., Heckmann R.; A computational model for metric spaces, Theoretical Computer Science, Vol. 193(1–2), 1998, pp. 53–73.
• [3] Engelking R.; General Topology, Heldermann Verlag, 1989.
• [4] Heckmann R.; Power Domain Constructions (Potenzbereich-Konstruktionen),Ph.D. thesis, Universit¨at des Saarlandes, December 1990.
• [5] Martin K.; A Foundation for Computation, Ph.D. thesis, Department of Mathematics, Tulane University, New Orleans 2000.
• [6] Waszkiewicz P.; Quantitative Continuous Domains, Ph.D. thesis, School of Computer Science, The University of Birmingham, May 2002.
• [7] Willard S.; General Topology, Addison-Wesley, 1970.