Dimensions of products of hyperbolic spaces

We give estimates on asymptotic dimensions of products of general hyperbolic spaces with following applications to the hyperbolic groups. We give examples of strict inequality in the product theorem for the asymptotic dimension in the class of the hyperbolic groups; and examples of strict inequality in the product theorem for the hyperbolic dimension. We prove that R is dimensionally full for the asymptotic dimension in the class of the hyperbolic groups

Locally homogeneous C0C^0-Riemannian manifolds

We show that locally homogeneous $\mathcal{C}^0$-Riemannian manifolds are smooth.Comment: 17 page

5-point CAT(0) spaces after Tetsu Toyoda

We give another proof of Toyoda's theorem that describes 5-point subpaces in CAT(0) length spacesComment: 9 pages, 8 figure

Trees meet octahedron comparison

We show that trees and their products meet octahedron comparison.Comment: 4 pages, 4 figure