The metric dimension of metric spaces
S Bau, AF Beardon - Computational Methods and Function Theory, 2013 - Springer
S Bau, AF Beardon
Computational Methods and Function Theory, 2013•SpringerAbstract Let (X, d)(X, d) be a metric space. A subset AA of XX resolves XX if each point xx in
XX is uniquely determined by the distances d (x, a) d (x, a), where a ∈ A a∈ A. The metric
dimension of (X, d)(X, d) is the smallest integer kk such that there is a set AA of cardinality kk
that resolves X X. Much is known about the metric dimension when XX is the vertex set of a
graph, but very little seems to be known for a general metric space. Here we provide some
basic results for general metric spaces.
XX is uniquely determined by the distances d (x, a) d (x, a), where a ∈ A a∈ A. The metric
dimension of (X, d)(X, d) is the smallest integer kk such that there is a set AA of cardinality kk
that resolves X X. Much is known about the metric dimension when XX is the vertex set of a
graph, but very little seems to be known for a general metric space. Here we provide some
basic results for general metric spaces.
Abstract
Let be a metric space. A subset of resolves if each point in is uniquely determined by the distances , where . The metric dimension of is the smallest integer such that there is a set of cardinality that resolves . Much is known about the metric dimension when is the vertex set of a graph, but very little seems to be known for a general metric space. Here we provide some basic results for general metric spaces.
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