For a totally disconnected compact set E in the extended z-plane C, we denote by M_E the totality of meromorphic functions each of which is defined in the domain complementary to E and has E as the set of transcendental singularities. A meromorphic function f(z) of M_E is said to be exceptionally ramified at a singularity ζ ∈E, if there exist values w_i, 1≦ i ≦ q, and positive integers ν_i ≧ 2, 1 ≦ i≦ q, with ∑ form i=1 to q of (1-1/(ν_i)) > 2 such that, in some neighborhood of ζ, the multiplicity of any w_i-point of f(z) is not less than ν_i. Recently, we have shown that, for Cantor sets E with successive ratios {ξ_n} satisfying ξ_(n+1)=0(ξ_n~2), any function of M_E cannot be exceptionally ramified at any singularity ζ∈E(Theorem in [5]).
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