On the Vertical Similarly Homogeneous R-Trees

We study the class of similarly homogeneous locally complete ℝ-trees with some additional requirements. In particular, vertical and strictly vertical ℝ-trees are defined. The metric classification of strictly vertical ℝ-trees is made: it is shown that every such ℝ-tree is isometric to some model ℝ-t...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2019-02, Vol.40 (2), p.127-139
Main Authors: Andreev, P. D., Bulygin, A. I.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Trees
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Summary:We study the class of similarly homogeneous locally complete ℝ-trees with some additional requirements. In particular, vertical and strictly vertical ℝ-trees are defined. The metric classification of strictly vertical ℝ-trees is made: it is shown that every such ℝ-tree is isometric to some model ℝ-tree. For the vertical ℝ-trees which are not strictly vertical it is shown that their branching number is at least continuum.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080219020033