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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: [email protected]
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Abstract

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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 

Footnotes

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

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