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arXiv · 2504.09351

A small Radon-Nikod\'ym compact space from a parametrized diamond

Arturo Martínez-Celis·Adam Morawski
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Abstract

A compact space $K$ is Radon-Nikod\'{y}m if there is a lower semi-continuous metric fragmenting $K$. In this note, we show that, under $\diamondsuit (\mathrm{non}{\mathcal{M}})$, there is a Radon-Nikod\'{y}m compact space of weight $\aleph_1$ with a continuous image that is not Radon-Nikod\'{y}m, which partially answers a question posed in arXiv:1112.4152 [math.FA].

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Arturo Martínez-Celis, Adam Morawski. 2025-04-12. A small Radon-Nikod\'ym compact space from a parametrized diamond. https://arxiv.org/abs/2504.09351

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