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Let X be a reduced Stein space and L a holomorphic line bundle on X. L is spanned by its global sections and the associated holomorphic map hL : X ! P(H0(X;L)¤) is an embed-ding. Choose any locally convex vector topology ¿ on H0(X;L)¤ stronger than the weak-topology. Here we prove that hL(X) is sequentially closed in P(H0(X;L)¤) and arithmetically Cohen - Macaulay, i.e. for all integers k ¸ 1 the restriction map ½k : H0(P(H0(X;L)¤);OP(H0(X;L)¤)(k)) ! H0(hL(X);OhL(X)(k)) »= H0(X;Lk) is surjective.
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