  Suppose that Y is a complex manifold with the property that any holomorphic
map from a compact convex set in a complex Euclidean space C^n (for any n) to Y
is a uniform limit of entire maps from C^n to Y. We prove that a holomorphic
map from a closed complex subvariety X_0 in a Stein manifold X to the manifold
Y extends to a holomorphic map of X to Y provided that it extends to a
continuous map. We then establish the equivalence of four Oka-type properties
of a complex manifold. We also generalize a theorem of Siu and Demailly on the
existence of open Stein neighborhoods of Stein subvarieties in complex spaces.
