Differences between the uniform diameter two properties

Abraham Rueda Zoca

Differences between the uniform diameter two properties

Functional Analysis 2026-07-15 v1

Authors: Abraham Rueda Zoca

Abstract

We study uniform versions of the diameter two properties, that is, the uniform slice-D2P, the uniform D2P and the uniform SD2P, as the property that every ultrapower over any free ultrafilter over $\mathbb N$ has the respective diameter two property. The aim of this note is to prove that all the uniform diameter two properties are different eachother.

Cite

@article{arxiv.2607.13788,
  title  = {Differences between the uniform diameter two properties},
  author = {Abraham Rueda Zoca},
  journal= {arXiv preprint arXiv:2607.13788},
  year   = {2026}
}

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21 pages