Usco sections and Choquet-completeness
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.