Abstract
We introduce the notion of large scale dimensiongrad as a large scale invariant of asymptotic resemblance spaces. Consequently it can be considered as a large scale invariant of metric spaces. The large scale dimensiongrad is a way of counting dimension in large scale but it is different from asymptotic dimension in general, as we show in the paper, too.
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Kalantari, S. A new inductive approach for counting dimension in large scale. Arch. Math. 110, 403–412 (2018). https://doi.org/10.1007/s00013-017-1140-2
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DOI: https://doi.org/10.1007/s00013-017-1140-2
Keywords
- Asymptotic dimension
- Asymptotic resemblance
- Coarse Structure
- Large scale dimensiongrad
- Large scale geometry