Testing math in abstract

Abstract

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.