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Alexandroff and Scott Topologies for Generalized Metric Spaces
Author(s) -
BONSANGUE M.M.,
BREUGEL F.,
RUTTEN J.J.M.M.
Publication year - 1996
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1996.tb49159.x
Subject(s) - mathematics , metric space , convex metric space , compact open topology , topology (electrical circuits) , injective metric space , general topology , ball (mathematics) , equivalence of metrics , fisher information metric , intrinsic metric , topological space , pure mathematics , mathematical analysis , combinatorics , interpolation space , functional analysis , biochemistry , chemistry , gene
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 ε‐ball topology; 2. a topology for algebraic generalized metric spaces generalizing both the Scott topology for algebraic complete partial orders and the ε‐ball topology for metric spaces.