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A quasi-order on continuous functions

Published online by Cambridge University Press:  12 March 2014

Raphaël Carroy
Raphaël Carroy*
Affiliation:
Équipe de Logique Mathématique, Université Paris Diderot Paris 7, Ufr de Mathématiques Case 7012. Site Chevaleret, 75205 Paris Cedex 13France, E-mail:carroy@math.univ-paris-diderot.fr
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Abstract

We define a quasi-order on Borel functions from a zero-dimensional Polish space into another that both refines the order induced by the Baire hierarchy of functions and generalises the embeddability order on Borel sets. We study the properties of this quasi-order on continuous functions, and we prove that the closed subsets of a zero-dimensional Polish space are well-quasi-ordered by bi-continuous embeddability.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 2 , June 2013 , pp. 633 - 648
Copyright
Copyright © Association for Symbolic Logic 2013

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References

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