Intersections of Arc-Cluster Sets for Meromorphic Functions
1970 ◽
Vol 40
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pp. 213-220
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Let D and C denote the open unit disk and the unit circle in the complex plane, respectively; and let f be a function from D into the Riemann sphere Ω. An arc γ⊂D is said to be an arc at p∈C if γ∪{p} is a Jordan arc; and, for each t (0<t<1), the component of γ∩{z: t≤|z|<1} which has p as a limit point is said to be a terminal subarc of γ. If γ is an arc at p, the arc-cluster set C(f, p,γ) is the set of all points a∈Ω for which there exists a sequence {zk}a⊂γ with zk→p and f(zk)→a.
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1969 ◽
Vol 34
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pp. 105-119
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1969 ◽
Vol 35
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pp. 151-157
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1966 ◽
Vol 18
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pp. 256-264
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