Generalizations of metrics and partial metrics
نویسندگان
چکیده
منابع مشابه
Cones of partial metrics
A partial semimetric on a set X is a function (x, y) 7→ p(x, y) ∈ R≥0 satisfying p(x, y) = p(y, x), p(x, y) ≥ p(x, x) and p(x, z) ≤ p(x, y) + p(y, z) − p(y, y) for all x, y, z ∈ X. Using computations done for n ≤ 6, we study the polyhedral convex cone PMETn of all partial semimetrics on n points and its subcone l1-PMETn generated by all {0, 1}-valued, i.e., contaning {0, 1}-valued element, extr...
متن کاملPartial quasi-metrics
In this article we introduce and investigate the concept of a partial quasi-metric and some of its applications. We show that many important constructions studied in Matthews’s theory of partial metrics can still be used successfully in this more general setting. In particular we consider the bicompletion of the quasi-metric space that is associated with a partial quasi-metric space and study i...
متن کاملMetrics and Embeddings of Generalizations of Thompson’s Group F
The distance from the origin in the word metric for generalizations F (p) of Thompson’s group F is quasi-isometric to the number of carets in the reduced rooted tree diagrams representing the elements of F (p). This interpretation of the metric is used to prove that every F (p) admits a quasiisometric embedding into every F (q), and also to study the behavior of the shift maps under these embed...
متن کاملPartial Metrics and Quantale-valued Sets (Preprint)
It is observed that the axioms for partial metrics with values in quantales coincide with the axioms for Q-sets (M -valued sets, sets with fuzzy equality, quantale-valued sets) for commutative quantales. Ω-sets correspond to the case of partial ultrametrics.
متن کاملThe correspondence between partial metrics and semivaluations
Partial metrics, or the equivalent weightable quasi-metrics, have been introduced in [Mat94] as part of the study of the denotational semantics of data flow networks (cf. also [Mat95]). The interest in valuations in connection to Domain Theory derives from e.g. [JP89], [Jon89], [Eda94] and [Hec95]. Connections between partial metrics and valuations have been discussed in the literature, e.g. [O...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Hacettepe Journal of Mathematics and Statistics
سال: 2017
ISSN: 1303-5010
DOI: 10.15672/hjms.2016.394