Calibres, Diagonals, and Generalizing Schneider's Theorem

A classic metrization theorem due to Schneider says that any compact space with a $G_\delta$ diagonal is metrizable. Here, the diagonal of a space $X$ refers to the set of all points of the form $(x,x)$ in $X^2$. Research into the relationship between metrizability and diagonals has uncovered several generalizations of Schneider's theorem, at least one of which was discovered in the context of functional analysis. In this talk, I will introduce the notion of calibres of a partially-ordered set and discuss how these order properties lead to a new generalization of Schneider's theorem that is, in some sense, "optimal."