Lpt 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 $h_L;:;X{ o}P(H^0(X, L)^{ast})$ is an embedding. Choose any locally convex vector topology ${ au};on;H^0(X, L)^{ast}$ stronger than the weak-topology. Here we prove that $h_L(X)$ is sequentially closed in $P(H^0(X, L)^{ast})$ and arithmetically Cohen -Macaulay. i.e. for all integers $k{ge}1$ the restriction map ${ ho}_k;:;H^0(P(H^0(X, L)^{ast}),;O_{P(H^0(X, L)^{ast})}(k)){ o}H^0(h_L(X),O_{hL_(X)}(k)){cong}H^0(X, L^{otimes{k}})$ is surjective.