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Universal Entire Functions That Define Order Isomorphisms of Countable Real Sets

Part of: Miscellaneous topics of analysis in the complex domain Universal holomorphic functions

Published online by Cambridge University Press:  10 April 2019

P. M. Gauthier
P. M. Gauthier*
Affiliation:
Département de mathématiques et de statistique, Université de Montréal, CP-6128 Centreville, Montréal, H3C3J7 Email: gauthier@dms.umontreal.ca
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Abstract

In 1895, Cantor showed that between every two countable dense real sets, there is an order isomorphism. In fact, there is always such an order isomorphism that is the restriction of a universal entire function.

Keywords

universal function

MSC classification

Primary: 30E10: Approximation in the complex domain
Secondary: 30K20: Compositional universality
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 4 , December 2019 , pp. 767 - 779
Copyright
© Canadian Mathematical Society 2019 

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Footnotes

Research supported by NSERC (Canada) grant RGPIN-2016-04107.

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