Two Constructive Embedding-Extension Theorems with Applications to Continuity Principles and to Banach-Mazur Computability

With Alex Simpson.

Abstract: We prove two embedding and extension theorems in the context of the constructive theory of metric spaces. The first states that Cantor space embeds in any inhabited complete separable metric space (CSM) without isolated points, `X`, in such a way that every sequentially continuous function from Cantor space to `ZZ` extends to a [...]