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The closure of convergence sets for continued fractions are convergence sets

Published online by Cambridge University Press:  20 January 2009

Lisa Lorentzen
Lisa Lorentzen
Affiliation:
Division of Mathematical Sciences, University of Trondheim, NTH, N-7034 Trondheim, Norway
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Abstract

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We prove that if Ω is a simple convergence set for continued fractions K(an/bn), then the closure of Ω is also such a convergence set. Actually, we prove more: every continued fraction K(an/bn) has a “neighbourhood” where rn>0 and sn>0, with the following property: Every continued fraction from {n} converges if and only if K(an/bn) converges.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 37 , Issue 1 , February 1994 , pp. 39 - 46
Copyright
Copyright © Edinburgh Mathematical Society 1994

References

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