  We first provide an approach to the recent conjecture of
Bierstone-Milman-Pawlucki on Whitney's old problem on smooth extendability of
functions defined on a closed subset of a Euclidean space, using higher order
paratangent bundle they introduced. For example, the conjecture is affirmative
for classical fractal sets. Next, we give a sharpened form of Spallek's theorem
on controllability of flatness by the values on a closed set. The
multi-dimensional Vandermonde matrix plays an important role in both cases.
