Embeddability on functions: Order and chaos

Raphäel Carroy, Yann Pequignot, Z. Vidnyánszky

Research output: Contribution to journalArticle


We study the quasi-order of topological embeddability on definable functions between Polish 0-dimensional spaces. We consider the descriptive complexity of this quasi-order restricted to the space of continuous functions. Our main result is the following dichotomy: the embeddability quasi-order restricted to continuous functions from a given compact space to another is either an analytic complete quasi-order or a wellquasi- order. We also investigate the existence of maximal elements with respect to embeddability in a given Baire class. We prove that no Baire class admits a maximal element, except for the class of continuous functions which admits a maximum element.

Original languageEnglish
Pages (from-to)6711-6738
Number of pages28
JournalTransactions of the American Mathematical Society
Issue number9
Publication statusPublished - Jan 1 2019


ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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