A well-quasi-order for continuous functions

Raphaël Carroy, Yann Pequignot

Published 2024-10-17Version 1

We prove that continuous reducibility is a well-quasi-order on the class of continuous functions between separable metrizable spaces with analytic zero-dimensional domain. To achieve this, we define scattered functions, which generalize scattered spaces, and describe exhaustively scattered functions between zero-dimensional separable metrizable spaces up to continuous equivalence.