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Proceedings of the American Mathematical Society

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A construction of a subspace in Euclidean space with designated values of dimension and metric dimension


Author: Tatsuo Goto
Journal: Proc. Amer. Math. Soc. 118 (1993), 1319-1321
MSC: Primary 54F45; Secondary 55M10
MathSciNet review: 1189543
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Abstract: For every integer $ m,k$, and $ n$ such that $ 0 \leqslant m \leqslant n - 1$ and $ m \leqslant k \leqslant \min \{ 2m,n - 1\} $, we construct a subspace $ S_{m,k}^n$ in Euclidean $ n$space $ {{\mathbf{R}}^n}$ satisfying the conditions that $ \mu \dim S_{m,k}^n = m$ and $ \dim S_{m,k}^n = k$, where $ \mu \dim $ denotes the metric dimension.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1189543-X
Keywords: Dimension, metric dimension, Euclidean space, Nöbeling's space
Article copyright: © Copyright 1993 American Mathematical Society