semimetric

semimetric

[¦sem·i′me·trik]
(mathematics)
A real valued function d (x,y) on pairs of points from a topological space which has all the same properties as a metric save that d (x,y) may be zero even if x and y are distinct points. Also known as pseudometric.
Mentioned in ?
References in periodicals archive ?
Gabeleh, "On cyclic relatively nonexpansive mappings in generalized semimetric spaces," Applied General Topology, vol.
In this paper we introduce the notion of subordinate semimetric space; such concept is a generalization of the notion of RS-space.
Fitting multivariate models to semimetric distances: A comment on distance-based redundancy analysis.
In their paper they define two concepts: semimetric and metric.
Since the pioneer works of [1, 2], the nonparametric estimation of the regression function has been very widely studied for real and vectorial regressors (see, e.g., [3-8]) and, more recently, the case when the regressor takes values in a semimetric space of infinite dimension has been addressed.
The following lemma is a corollary of Blumenthal's solution of the problem of isometric embedding of semimetric spaces in the Euclidean spaces, see [[6], p.105].
The Sorensen (Bray & Curtis) distance measure was used to calculate the A values because it is semimetric in nature, employing a domain range of 0 [less than or equal to] d [less than or equal to] 1.
If, in addition, d is reflexive [d(x, x) = 0, [for all]x [member of] M], triangular [d(x, z) [less than or equal to] d(x, y) + d(y, z), [for all]x, y, z [member of] M] and symmetric [d(x, y) = d(y, x), [for all]x, y [member of] M], we say that it is a semimetric (on M).
Despite the seeming impossibility of joining metric and non-metric properties in "one package", Smarandache semimetric spaces can easily be introduced even by means of "classical" General Relativity.
Let us recall that a semimetric space (X, d), also often referred to as apseudometric space, is defined exactly like a metric space, except that the condition d(x,y) = 0 for a pair of points x,y [member of] X does not imply that x = y.
(ii) On each fibre of X over Z, R defines a semimetric