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.


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