Selection properties of the split interval and the Continuum Hypothesis
General Topology
2021-11-01 v1 Logic
Abstract
We prove that every usco multimap from a metrizable separable space to a GO-space has an -measurable selection. On the other hand, for the split interval and the projection of its square onto the unit square , the usco multimap has a Borel (-measurable) selection if and only if the Continuum Hypothesis holds. This CH-example shows that know results on Borel selections of usco maps into fragmentable compact spaces cannot be extended to a wider class of compact spaces.
Cite
@article{arxiv.1905.02243,
title = {Selection properties of the split interval and the Continuum Hypothesis},
author = {Taras Banakh},
journal= {arXiv preprint arXiv:1905.02243},
year = {2021}
}
Comments
10 pages