  By a geodesic subspace of a metric space $X$ we mean a subset $A$ of $X$ such
that any two points in $A$ can be connected by a geodesic in $A$. It is easy to
check that a geodesic metric space $X$ is an $\mathbb{R}$-tree (that is, a
$0$-hyperbolic space in the sense of Gromov) if and only if the union of any
two intersecting geodesic subspaces is again a geodesic subspace. In this
paper, we prove an analogous characterization of general Gromov hyperbolic
spaces, where we replace geodesic subspaces by quasigeodesic subspaces.
