A function algebra providing new Mergelyan type theorems in several complex variables

The celebrated theorem of Mergelyan states that, if K is a compact subset the complex plane with connected complement, then every continuous function on which holomorphic its interior can be uniformly approximated by polynomials. This paper concerned polynomial and rational approximation in several variables, where situation much more complicated far from being understood. In particular, we introduce natural algebra allows us to obtain new type theorems for certain graphs as well Cartesian products an arbitrary (possibly infinite) indexed family planar sets. Finally, identify mistake classical result 1969 correct it within framework our algebra.