Let [X,A] be a natural syslem
such that X is locally compact and every open subset of X is σ-compact. Let 𝒜 be
the sheaf on X generated by the presheaf {U → AU≡A|U}. If p ∈ X,V is a
subvariety of an open sei in Cn which contains 0 and if there exists an algebra
homomorphism φ : 𝒜p→V𝒪0 having rank greater than one, lken there exists a
neighborhood U of p in X, a neighborhood of 0 in Cn and a continuous map
τ;V ∩ ω → U sueh that (1) τ(0) = p, (2) if f ∈ AU, lhen f ∘t is holomorphic on
V ∩ ω (3) if f ∈ AU, then (f ∘ τ)0= φ((f)p), where (f ∘ τ)0 is the germ at 0 of
f ∘ τ and (f)p is the elemeRl of 𝒜p (the stalk of 𝒜 above p) determined by
f.
