Eva Kallin's Lemma On Polynomial Convexity

We give a survey on the use of Eva Kallin's lemma. This lemmagives a condition on two polynomially convex sets in Cⁿ underwhich their union is polynomially convex. This result has provedto be a useful tool in different areas of complex function theoryof several variables, for instance in the study of polynomialconvexity of the union of totally real surfaces, and in approximationproblems in function algebras.