A small Radon–Nikodým compact space from a parametrized diamond
Fundamenta Mathematicae
MSC: Primary 03E35; Secondary 54A35, 54D30, 03E17
DOI: 10.4064/fm251021-2-3
Published online: 21 September 2026
Abstract
A compact space $K$ is Radon–Nikodým if there is a lower semicontinuous metric fragmenting $K$. In this note, we show that, under $\diamondsuit (\mathrm{non}(\mathcal M))$, there is a Radon–Nikodým compact space of weight $\aleph _1$ with a continuous image that is not Radon–Nikodým, which partially answers a question posed by Avilés and Koszmider in 2013.
