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The local behavior of principal and chordal principal cluster sets

1972
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Transactions of the American Mathematical Society
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Let K be the unit circle, and let/ be a function whose domain is the open unit disk and whose range is a subset of the Riemann sphere. We define a set, called the boundary principal cluster set of/at £0 6 K, which characterizes the behavior of the principal cluster sets of fat points £ s K which are near £0 and distinct from £0. It is shown that iff is continuous, then the principal and boundary principal cluster sets off at £o are equal for nearly every point i0 6 Í. A similar result holds for

doi:10.1090/s0002-9947-1972-0294643-3
fatcat:62pey2cspnbxplsfrpzzgbhjzy