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arXiv · 2410.13150

A well-quasi-order for continuous functions

Raphaël Carroy·Yann Pequignot
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Abstract

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.

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Raphaël Carroy, Yann Pequignot. 2024-10-17. A well-quasi-order for continuous functions. https://arxiv.org/abs/2410.13150

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