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Let f be & real convex function defined near 0', /(0)=/'(0)=0, />0 otherwise. The family of curves, /(0) = y(l-r), 0<y<oe, in the unit disc is investigated. The union of the w* closures in the maximal ideal space of if00 of these curves is seen to be a union of nontrivial parts and each such part is hit by the closure of each such curve. Using results of Hoffman and the Wermer map onto such a part, nets in the disc tending to points of the part are located on the curves as explicitly as can bedoi:10.2307/2038833 fatcat:seybmw6uefgmpfg5xsognyztii