Metrizability of Mahavier Products Indexed by Partial Orders - Clontz, Steven; Dunham, Jacob (Topology Proceedings, 2022)
Let X be separable metrizable, and let f X^2 be a non-trivial relation on X. For a given partial order P, ≤, the Mahavier product MX, f, PX^P (also known as a generalized inverse limit) collects functions such that x(p) f(x(q)) for all p ≤ q. Steven Clontz and Scott Varagona [Topology Proc. 54 (2019), 259-269] previously showed that for well orders P, MX, f, P is separable metrizable exactly when P is countable and f satisfies condition Γ; we extend this result to hold for all partial orders.