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Asymptotic Dimension of Proper CAT(0) Spaces that are Homeomorphic to the Plane |
Canad. Math. Bull. 53(2010), 629-638
Published:2010-07-26
Printed: Dec 2010
Printed: Dec 2010
- Naotsugu Chinen,
- Tetsuya Hosaka,
Abstract
In this paper, we investigate
a proper CAT(0) space $(X,d)$
that is homeomorphic to $\mathbb R^2$ and
we show that the asymptotic dimension $\operatorname{asdim} (X,d)$ is
equal to $2$.
| Keywords: | asymptotic dimension, CAT(0) space, plane |
| MSC Classifications: |
20F69 - Asymptotic properties of groups 54F45 - Dimension theory [See also 55M10] 20F65 - Geometric group theory [See also 05C25, 20E08, 57Mxx] |