On metrizable subsets of hereditarily normal compact spaces
Keywords:
hereditarily normal, $\omega_1$-compact, rim-LindelöfAbstract
Let $X$ be a metrizable space which has a hereditarily normal $\omega_1$-compactification. We show that $X$ is rim-separable and that if $X$ is also connected, then $w(X) \leq \omega_1$ and $X$ has a $\sigma$-point-finite base by sets with separable boundaries.
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