On the Vertical Similarly Homogeneous R-Trees

Resumo

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.