  In this paper we first consider the class of minimal time functions in the
general setting of locally convex topological vector (LCTV) spaces. The results
obtained in this framework are based on a novel notion of closedness of target
sets with respect to constant dynamics. Then we introduce and investigate a new
class of signed minimal time functions, which are generalizations of the signed
distance functions. Subdifferential formulas for the signed minimal time and
distance functions are obtained under the convexity assumptions on the given
data.
