On metrizable subsets of hereditarily normal compact spaces - Junnila, Heikki; Tomoyasu, Kazuo (Topology Proceedings, 2021)
Let X be a metrizable space which has a hereditarily normal ω_1-compactification. We show that X is rim-separable and that if X is also connected, then w(X) ≤ ω_1 and X has a σ-point-finite base by sets with separable boundaries.