Linearly-ordered Radon-Nidkod\'ym compact spaces
Antonio Avil\'es
TL;DR
This paper proves that fragmentable linearly ordered compact spaces are almost totally disconnected and shows that certain quasi Radon-Nikodym compact spaces are Radon-Nikodym, advancing understanding of their structure.
Contribution
It establishes a new connection between fragmentability and total disconnectedness in linearly ordered compact spaces and confirms a partial case of the Radon-Nikodym problem.
Findings
Fragmentable linearly ordered compact spaces are almost totally disconnected.
Quasi Radon-Nikodym compact spaces are Radon-Nikodym under certain conditions.
Provides partial answers to the Radon-Nikodym problem.
Abstract
We prove that every fragmentable linearly ordered compact space is almost totally disconnected. This combined with a result of Arvanitakis yields that every linearly ordered quasi Radon-Nikodym compact space is Radon-Nikodym, providing a new partial answer to the problem of continuous images of Radon-Nikodym compacta.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Banach Space Theory