Usco sections and Choquet-completeness
Volume 242 / 2018
Fundamenta Mathematicae 242 (2018), 93-102
MSC: 54B20, 54C60, 54E50, 91A44.
DOI: 10.4064/fm411-11-2017
Published online: 30 March 2018
Abstract
We show that a regular space which admits an usco section for its Vietoris hyperspace of countable discrete sets is Choquet-complete. For metrizable spaces, Choquet-completeness is equivalent to Čech-completeness. Thus, the above result provides a natural generalization of several known results for metrizable spaces. It also has several applications for nonmetrizable spaces.
