S-Algebras on Sets in C to the power of n

We give conditions which are necessary and sufficient for polynomial approximation of any continuous function on a compact subset of Cn

On a theorem of Rudin

We give short proofs of a theorem of Rudin about polynomial approximation in R 2 + n {R^{2 + n}} and a corollary of this theorem which says that any function algebra on [0, 1] generated by one complex-valued function and n real functions is all continuous functions. At the same time our proof shows that both results hold with n replaced by an arbitrary index set Λ \Lambda .</p

𝑆-algebras on sets in 𝐶ⁿ

We give conditions which are necessary and sufficient for polynomial approximation of any continuous function on a compact subset of C n {C^n} .</p