DMS Topology Seminar

Speaker: Steven Clontz, University of South Alabama

Title: Metrizability of Mahavier products indexed by partial orders

Abstract: Let $X$ be separable metrizable, and let $f\subseteq X^2$ be a non-trivial relation on $X$. For a given partial order $(P,\leq)$, the Mahavier product $M(X,f,P)\subseteq X^P$ (also known as a generalized inverse limit) collects functions such that $x(p)\in f(x(q))$ for all $p<q$. We will show that whenever $f$ satisfies condition $\Gamma$, $M(X,f,P)$ is separable metrizable if and only if $P$ is countable.