Cardinality bound for Urysohn spaces with an H-closed π-base using wL, t, and ψ_c

Determine whether the cardinality inequality |X| ≤ 2^{wL(X) t(X) ψ_c(X)} holds for every Urysohn Hausdorff topological space X that admits a π-base whose elements have H-closed closures.

Background

The paper studies cardinal bounds for spaces with a π-base whose elements have H-closed closures. For quasiregular spaces in this class, Carlson establishes |X| ≤ 2^{wL(X) t(X) ψ_c(X)}. For Urysohn spaces, the authors prove a different bound |X| ≤ 2^{wL(X) k(X)}, where k(X) is a cardinal function introduced by Alas and Kocinac, and present examples showing k(X) may be strictly smaller than χ(X). Whether the stronger inequality with t(X) and ψ_c(X) also holds for Urysohn spaces remains explicitly questioned by the authors.