The author considers necessary and sufficient conditions for a set

$\phi $ of n functions

${\phi}_{i}:{E}^{m}\to {E}^{1}$, 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

$\phi =({\phi}_{1}\left(t\right),\xb7\xb7\xb7,{\phi}_{n}\left(t\right))$,

$(t=({t}_{1},\xb7\xb7\xb7,{t}_{m}))$ in an open set

$G\subset {E}^{m}$ 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

$\phi $ is linearly independent, (2) the union of these components is dense in G.