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Linear dependence of a function set of m variables with vanishing generalized Wronskians. (English) Zbl 0724.15004
The author considers necessary and sufficient conditions for a set ϕ of n functions ϕ i :E m 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 ϕ=(ϕ 1 (t),···,ϕ n (t)), (t=(t 1 ,···,t m )) in an open set GE 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 ϕ is linearly independent, (2) the union of these components is dense in G.
15A03Vector spaces, linear dependence, rank
53A45Vector and tensor analysis
26B12Calculus of vector functions