منابع مشابه
Indivisible Ultrametric Spaces
Ametric space is indivisible if for any partition of it into finitely many pieces one piece contains an isometric copy of the whole space. Continuing our investigation of indivisible metric spaces [1], we show that a countable ultrametric space embeds isometrically into an indivisible ultrametric metric space if and only if it does not contain a strictly increasing sequence of balls.
متن کاملAsynchronous iterations in ultrametric spaces
Some iterative calculations can be carried out by parallel communicating processors, and yield the same results whether or not the processors are synchronized. We show that this is the case if and only if the iteration is a contraction that is strict on orbits, with respect to an ultrametric defined on the state space. The maximum number of independent processors is given by the dimension of th...
متن کاملCompleteness in Generalized Ultrametric Spaces
Γ-ultrametric spaces are spaces which satisfy all the axioms of an ultrametric space except that the distance function takes values in a complete lattice Γ instead of R≥0. Γ-ultrametric spaces have been extensively studied as a way to weaken the notion of an ultrametric space while still providing enough structure to be useful (see for example [17], [18], [8]). The many uses of Γ-ultrametric sp...
متن کاملUltrametric Spaces in Continuous Logic
We investigate the continuous model theory of ultrametric spaces of diameter ≤ 1. There is no universal Polish ultrametric space of diameter 1; but there is a Polish ultrametric space, Umax, taking distances in Q∩[0, 1], which is universal for all such Polish ultrametric spaces. We show that in the continuous theory of Umax, nonforking is characterized by a stable independence relation, which i...
متن کاملRamsey Degrees of Finite Ultrametric Spaces, Ultrametric Urysohn Spaces and Dynamics of Their Isometry Groups
We study Ramsey-theoretic properties of several natural classes of finite ultrametric spaces, describe the corresponding Urysohn spaces and compute a dynamical invariant attached to their isometry groups.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1996
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0380