Alexandroff and Scott topologies for generalized metric spaces (1996) [3 citations — 2 self]
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by M. M. Bonsangue, F. Van Breugel, J. J. M. M. Rutten
Proceedings of the 11th Summer Conference on General Topology and Applications, Annals of the New York Academy of Sciences
http://www.cs.vu.nl/ftp/bonsangue/top_gms.ps.Z
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Abstract:
Generalized metric spaces are a common generalization of preorders and ordinary metric spaces. Every generalized metric space can be isometrically embedded in a complete function space by means of a metric version of the categorical Yoneda embedding. This simple fact gives naturally rise to: 1. a topology for generalized metric spaces which for arbitrary preorders corresponds to the Alexandroff topology and for ordinary metric spaces reduces to the ffl-ball topology; 2. a topology for algebraic generalized metric spaces generalizing both the Scott topology for algebraic complete partial orders and the ffl-ball topology for metric spaces.
