# 2018 seminar talk: A dichotomy for topological embeddability between continuous functions

Talk held by Raphaël Carroy (KGRC) at the KGRC seminar on 2018-11-22.

### Abstract

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.