A small Radon-Nikodým compact space from a parametrized diamond

Abstract

A compact space $K$ is Radon-Nikodým if there is a lower semi-continuous metric fragmenting $K$. In this note, we show that, under $♢(\mathrm{non}\mathcal{M})$, 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 in arXiv:1112.4152 [math.FA].

11 pages