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BISECTORS IN VECTOR GROUPS OVER INTEGERS

Part of: Graph theory Metric geometry

Published online by Cambridge University Press:  15 August 2019

SHENG BAU  and
YIMING LEI
SHENG BAU*
Affiliation:
School of Mathematics, Statistics and Computer Science, University of Kwazulu Natal, Pietermaritzburg, South Africa email [email protected]
YIMING LEI
Affiliation:
School of Mathematics, Statistics and Computer Science, University of Kwazulu Natal, Pietermaritzburg, South Africa email [email protected]
*
✉[email protected]
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Abstract

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We present an example of an isometric subspace of a metric space that has a greater metric dimension. We also show that the metric spaces of vector groups over the integers, defined by the generating set of unit vectors, cannot be resolved by a finite set. Bisectors in the spaces of vector groups, defined by the generating set consisting of unit vectors, are completely determined.

Keywords

basismetric dimensionmonotonicityresolutionvector semigroups

MSC classification

Primary: 05C12: Distance in graphs
Secondary: 51F99: None of the above, but in this section
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 100 , Issue 3 , December 2019 , pp. 353 - 361
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

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