Geodesic
Dimensions of $\mathbb R$-Trees and Self-Similar Fractal Spaces of Nonpositive Curvature
Matematičeskie trudy, Tome 9 (2006) no. 2, pp. 3-22.

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We study various dimensions of spaces with nonpositive curvature in the A. D. Alexandrov sense, in particular, of $\mathbb R$-trees. We find some conditions necessary and sufficient for the metric space to be an $\mathbb R$-tree and clarify relations between the topological, Hausdorff, entropy, and rough dimensions. We build the examples of $\mathbb R$-trees and CAT(0)-spaces in which strict inequalities between the topological, Hausdorff, and entropy dimensions hold; we also show that the Hausdorff and entropy dimensions can be arbitrarily large while the topological dimension remains fixed. 
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P. D. Andreev; V. N. Berestovskii. Dimensions of $\mathbb R$-Trees and Self-Similar Fractal Spaces of Nonpositive Curvature. Matematičeskie trudy, Tome 9 (2006) no. 2, pp. 3-22. http://geodesic.mathdoc.fr/item/MT_2006_9_2_a0/

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