Gabriel Saadia: Ultra

Abstract

Just as metric spaces can be described in terms of the convergence of their ℕ-indexed sequences, we’ll see that any topological space can be described via the ultraconvergence of their ultrasequences. We will categorify this result and establish connections with topos theory and model theory.

This talk is constructed in dual to Errol's talk “Points are overrated: An introduction to pointfree topology”; opens are "overrated" if we allow ourselves to work ultra.