On Curvilinear cluster sets on open Riemann surfaces
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- by Mikio Niimura
- Proc. Amer. Math. Soc. 62 (1977), 117-118
- DOI: https://doi.org/10.1090/S0002-9939-1977-0425127-7
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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
- Lars V. Ahlfors and Leo Sario, Riemann surfaces, Princeton Mathematical Series, No. 26, Princeton University Press, Princeton, N.J., 1960. MR 0114911
- Errett Bishop, Subalgebras of functions on a Riemann surface, Pacific J. Math. 8 (1958), 29–50. MR 96818
- E. F. Collingwood and A. J. Lohwater, The theory of cluster sets, Cambridge Tracts in Mathematics and Mathematical Physics, No. 56, Cambridge University Press, Cambridge, 1966. MR 0231999
Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 62 (1977), 117-118
- MSC: Primary 30A72
- DOI: https://doi.org/10.1090/S0002-9939-1977-0425127-7
- MathSciNet review: 0425127