The author considers necessary and sufficient conditions for a set
of n functions
, which together with their partial derivatives of order at least n-1 are continuous, to be linearly dependent. After giving some definitions he shows that the vanishing of all generalized Wronskians of
in an open set
implies that G contains a countable set of disjoint, open, connected components of the interiors of set of constant order such that (1) on each such component
is linearly independent, (2) the union of these components is dense in G.