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MacLane(1) has introduced the class of functions 
with a dense set of asymptotic values on {|z| = 1} in the following sense:
Definition. Let f(z) be regular and not constant in the unit disc and let ξ be a point of {|z| = 1}. Suppose that there exists a curve Γξ in {|z| < 1} and a in the closed complex plane such that f(z) → a as z → ξ along Γξ. Then we say ξ ∈ Aa.
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