In this note we prove that a complex manifold
X
X
is Kobayashi hyperbolic if and only if the space
Hol
(
Δ
,
X
)
\operatorname {Hol} (\Delta ,X)
of holomorphic maps of the unit disk
Δ
\Delta
into
X
X
is relatively compact (with respect to the compact-open topology) in the space
C
(
Δ
,
X
∗
)
C(\Delta ,{X^{\ast }})
of continuous maps from
Δ
\Delta
into the one-point compactification
X
∗
{X^{\ast }}
of
X
X
.