BONSANGUE, M. M.---van BREUGEL, F.---RUTTEN, J. J. M. M. : Alexandroff and Scott Topologies for Generalized Metric Spaces, In: Andima, S. et al. (Eds.), Papers on General Topology and Applications: Eleventh Summer Conference at University of Southern Maine, Annals of the New York Academy of Sciences, Vol. 806, 1996, pp. 49--68. Home/Search Document Details and Download
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A "Converse" of the Banach Contraction Mapping Theorem - Hitzler, Seda (2001) (Correct)
....on order. Nevertheless, in recent years there has been a significant movement towards the use of theorems, such as the Banach contraction mapping theorem, which apply to metric spaces and especially to ultrametric spaces, and to variants and generalizations of ultrametric spaces, see for example [3, 4, 15]. This is particularly so in the case of logic programming, where the presence of negation may restrict the use of order theory. Fixed point theorems on metric spaces and on generalized metric spaces provide an alternative and have indeed been applied successfully in the area of logic programming ....
BONSANGUE, M. M.---van BREUGEL, F.---RUTTEN, J. J. M. M. : Alexandroff and Scott Topologies for Generalized Metric Spaces, In: Andima, S. et al. (Eds.), Papers on General Topology and Applications: Eleventh Summer Conference at University of Southern Maine, Annals of the New York Academy of Sciences, Vol. 806, 1996, pp. 49--68.
Generalized Metric Spaces: Completion, Topology, and.. - Bonsangue, van.. Self-citation (Bonsangue Van breugel Rutten) (Correct)
....on metric spaces; 3. the definition and characterization of three powerdomains generalizing on the one hand the familiar lower, upper, and convex powerdomains from order theory; and on the other hand the metric powerdomain of compact subsets. The present paper is a reworking of an earlier report [BBR95] in which generalized ultrametric spaces are considered, satisfying X(x; z) maxfX(x; y) X(y; z)g, for all x, y, and z in X . There is but little difference between the two papers: as it turns out, none of the proofs about ultrametrics relies essentially on the strong triangle inequality. ....
....which generalized ultrametric spaces are considered, satisfying X(x; z) maxfX(x; y) X(y; z)g, for all x, y, and z in X . There is but little difference between the two papers: as it turns out, none of the proofs about ultrametrics relies essentially on the strong triangle inequality. See also [BBR] which contains part of the present paper. As mentioned above, generalized metric spaces and the constructions that are given in the present paper both unify and generalize a substantial part of order theoretic and metric domain theory. Both disciplines play a central role in (to a large extent ....
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M.M. Bonsangue, F. van Breugel, and J.J.M.M. Rutten. Alexandroff and Scott topologies for generalized metric spaces. To appear in S. Andima, B. Flagg, J. Itzkowitz, R. Kopperman, P. Misra, and Y. Kong, editors, Proceedings of the 11th Summer Conference on General Topology and Applications, Annals of the New York Academy of Sciences.
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