Asymptotic dimension of proper CAT(0) spaces which are homeomorphic to the plane

TL;DR

This paper proves that proper CAT(0) spaces homeomorphic to the plane have an asymptotic dimension exactly equal to 2, linking geometric properties to topological structure.

Contribution

It establishes that the asymptotic dimension of proper CAT(0) spaces homeomorphic to the plane is precisely 2, a new result connecting topology and large-scale geometry.

Findings

asdim(X,d) = 2 for such spaces

connects topological homeomorphism to asymptotic dimension

advances understanding of CAT(0) space geometry

Abstract

In this paper, we investigate a proper CAT(0) space $(X,d)$ which is homeomorphic to $R^2$ and we show that the asymptotic dimension $asdim (X,d)$ is equal to 2.