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Let j be a positive integer. For each integer n &gt; j we consider the connectedness locus M(n) of the family of polynomials P(c)(z)=z(n) - cz(n-j), where c is a complex parameter. We prove that lim n→∞ M(n) = D in the Hausdorff topology, where D is the unitary closed disk {c;|c|≤1}.

A note on the connectedness locus of the families of polynomials Pc(z)=z n - cz n-j