English

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

Functional Analysis 2025-04-15 v1

Abstract

A compact space KK is Radon-Nikod\'{y}m if there is a lower semi-continuous metric fragmenting KK. In this note, we show that, under (nonM)\diamondsuit (\mathrm{non}{\mathcal{M}}), there is a Radon-Nikod\'{y}m compact space of weight 1\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].

Cite

@article{arxiv.2504.09351,
  title  = {A small Radon-Nikod\'ym compact space from a parametrized diamond},
  author = {Arturo Martínez-Celis and Adam Morawski},
  journal= {arXiv preprint arXiv:2504.09351},
  year   = {2025}
}

Comments

11 pages

R2 v1 2026-06-28T22:56:10.689Z