  On a flat plane, convexity of a set is preserved by both radial expansion and
contraction of the set about any point inside it. Using the Poincar\'e disk
model of hyperbolic geometry, we prove that radial expansion of a hyperbolic
convex set about a point inside it always preserves hyperbolic convexity. Using
stereographic projection of a sphere, we prove that radial contraction of a
spherical convex set about a point inside it, such that the initial set is
contained in the closed hemisphere centred at that point, always preserves
spherical convexity.
