Mergelyan's theorem
Mergelyan's theorem is a result from approximation by polynomials in complex analysis proved by the Armenian mathematician Sergei Mergelyan in 1951. == Statement == Let K {\displaystyle K} be a compact subset of the complex plane C {\displaystyle \mathbb {C} } such that C ∖ K {\displaystyle \mathbb {C} \setminus K} is connected.