  The contracting boundary of a proper geodesic metric space generalizes the
Gromov boundary of a hyperbolic space. It consists of contracting geodesics up
to bounded Hausdorff distances. Another generalization of the Gromov boundary
is the $\kappa$-Morse boundary with a sublinear function $\kappa$. The two
generalizations model the Gromov boundary based on different characteristics of
geodesics in Gromov hyperbolic spaces. It was suspected that the $\kappa$-Morse
boundary contains the contracting boundary. We will prove this conjecture: when
$\kappa =1$ is the constant function, the 1-Morse boundary and the contracting
boundary are equivalent as topological spaces.
