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# Asymptotic Dimension of Proper CAT(0) Spaces that are Homeomorphic to the Plane

Published:2010-07-26
Printed: Dec 2010
• Naotsugu Chinen,
Hiroshima Institute of Technology, Hiroshima 731-5193, Japan
• Tetsuya Hosaka,
Department of Mathematics, Faculty of Education, Utsunomiya University, Utsunomiya, 321-8505, Japan
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## 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]