منابع مشابه
Möbius Invariant Metrics Bilipschitz Equivalent to the Hyperbolic Metric
We study three Möbius invariant metrics, and three affine invariant analogs, all of which are bilipschitz equivalent to the Poincaré hyperbolic metric. We exhibit numerous illustrative examples.
متن کاملThe metric dimension and girth of graphs
A set $Wsubseteq V(G)$ is called a resolving set for $G$, if for each two distinct vertices $u,vin V(G)$ there exists $win W$ such that $d(u,w)neq d(v,w)$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. The minimum cardinality of a resolving set for $G$ is called the metric dimension of $G$, and denoted by $dim(G)$. In this paper, it is proved that in a connected graph $...
متن کاملEquivalent metrics and compactifications
Let (X, d) be a metric space and m ∈ X. Suppose that φ : X×X → R is a nonnegative symmetric function. We define a metric d on X which is equivalent to d. If d is totally bounded, its completion is a compactification of (X, d). As examples, we construct two compactifications of (R, dE), where dE is the Euclidean metric and s ≥ 2. key words. equivalent metric; completion; compactification Mathema...
متن کاملthe metric dimension and girth of graphs
a set $wsubseteq v(g)$ is called a resolving set for $g$, if for each two distinct vertices $u,vin v(g)$ there exists $win w$ such that $d(u,w)neq d(v,w)$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. the minimum cardinality of a resolving set for $g$ is called the metric dimension of $g$, and denoted by $dim(g)$. in this paper, it is proved that in a connected graph $...
متن کاملNote on Metric Dimension
The metric dimension of a compact metric space is defined here as the order of growth of the exponential metric entropy of the space. The metric dimension depends on the metric, but is always bounded below by the topological dimension. Moreover, there is always an equivalent metric in which the metric and topological dimensions agree. This result may be used to define the topological dimension ...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1968
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-62-1-1-5