We say a function \(f\) embeds (topologically) in a function \(g\) when there are two topological embeddings \(\sigma\) and \(\tau\) satisfying \(\tau \circ f = g \circ \sigma\). I will prove the following dichotomy: the quasi-order of topological embeddability between continuous functions on compact zero-dimensional Polish spaces is either an analytic complete quasi-order, or a well-quasi-order.
This is a joint work with Yann Pequignot and Zoltán Vidnyánszky.
A video recording of this talk is available on YouTube.