2022/07/27 by Dydak, Jerzy, Rashed, Hussain
#FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT) #Metric Geometry (math.MG) #Primary 20F65 #Secondary 20F67
paper · doi:10.48550/arxiv.2207.13672
For every proper geodesic space X we introduce its quasi-geometric boundary ∂QGX with the following properties: 1. Every geodesic ray g in X converges to a point of the boundary ∂QGX and for every point p in ∂QGX there is a geodesic ray in X converging to p, 2. The boundary ∂QGX is compact metric, 3. The boundary ∂QGX is an invariant under quasi-isometric equivalences, 4. A quasi-isometric embedding induces a continuous map of quasi-geodesic boundaries, 5. If X is Gromov hyperbolic, then ∂QGX is the Gromov boundary of X. 6. If X is a Croke-Kleiner space, then ∂QGX is a point.