Another Remark on "some Problems in Conformal Mapping"

In a great many cases the methods used in the proofs of the above theorems can be used to determine whether a given continuum is a Wn set. In particular, they can be used to prove that no W-¡ set, M, has a complementary domain whose boundary, /, contains three limit points of B(M) — J, no Wi set has a complementary domain whose boundary contains five such points, and that there exists a Wo set whose outer boundary contains three such points.