Density of polynomials in classes of functions on products of planar domains

For planar domains ΩiΩi, i∈Ii∈I, where I   is an arbitrary set, we give sufficient conditions for the density of polynomials in A(∏i∈IΩi)A(∏i∈IΩi) as well as in A∞(∏i∈IΩi)A∞(∏i∈IΩi), endowed with their natural topologies. We also characterize the uniform limits, with respect to the chordal metric, of polynomials on ∏i∈IΩ‾i. Moreover, we discuss sets of uniqueness.