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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On Curvilinear cluster sets on open Riemann surfaces


Author: Mikio Niimura
Journal: Proc. Amer. Math. Soc. 62 (1977), 117-118
MSC: Primary 30A72
MathSciNet review: 0425127
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Abstract: Every boundary point of the Kerékjártó-Stoïlow compactification of an open Riemann surface is the limit of a Jordan arc with this property: for every nonempty continuum in the extended complex plane there is a holomorphic function on the surface having the continuum as its cluster set along the arc.


References [Enhancements On Off] (What's this?)

  • [1] L. V. Ahlfors and Leo Sario, Riemann surfaces, Princeton Univ. Press, Princeton, N.J., 1960. MR 22 #5729. MR 0114911 (22:5729)
  • [2] Errett Bishop, Subalgebras of functions on a Riemann surface, Pacific J. Math. 8 (1958), 29-50. MR 20 #3300. MR 0096818 (20:3300)
  • [3] E. F. Collingwood and A. J. Lohwater, The theory of cluster sets, Cambridge Univ. Press, New York, 1966. MR 38 #325. MR 0231999 (38:325)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0425127-7
PII: S 0002-9939(1977)0425127-7
Keywords: Bishop's approximation theorem, open Riemann surface, holomorphic function, curvilinear cluster set, continuum
Article copyright: © Copyright 1977 American Mathematical Society