The "Research Group on Ordered Structures with Applications", which will be held on 5 October 2023 at 2:00 PM CET with the use of the ZOOM platform. 

SpeakerPr. Jan Harm Van Der Walt , University of Pretoria,Tunisia. 

Title of the lecture: Category measures, the dual of $C(K)^\delta$ and hyper-Stonean spaces. 

Seminar working language: English. 


For a compact Hausdorff space $K$, we give descriptions of the dual of $C(K)^\delta$, the Dedekind completion of the Banach lattice $C(K)$ of continuous, real-valued functions on $K$.  We characterize those functionals which are $\sigma$-order continuous and order continuous, respectively, in terms of Oxtoby's category measures.  As applications, we give a purely topological characterization of hyper-Stonean spaces, and characterize those spaces $K$ for which $C(K)$ admits a strictly positive order continuous functional.

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