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Weighted Quasi‐Metrics
Author(s) -
KÜNZI HANSPETER A.,
VAJNER VÁCLAV
Publication year - 1994
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.1749-6632.1994.tb44134.x
Subject(s) - metric (unit) , disjoint sets , base (topology) , mathematics , metric space , class (philosophy) , denotational semantics , space (punctuation) , discrete mathematics , equivalence of metrics , network topology , topology (electrical circuits) , semantics (computer science) , combinatorics , computer science , convex metric space , artificial intelligence , operational semantics , mathematical analysis , programming language , operations management , economics , operating system
We study the class of topologies which are induced by weighted quasi‐metrics (equivalently, partial metrics). Partial metrics were introduced by S. Matthews in his study of topological models appropriate for the denotational semantics of programming languages. It follows from our results that each T 0 ‐space with a s̀‐disjoint base admits a weightable quasi‐metric and that each weightable quasi‐metric space is quasi‐developable. Those partially ordered sets whose Alexandrov topology admits a weightable quasi‐metric are characterized. We also show that the Pixley‐Roy space over the reals does not admit a weightable quasi‐metric.