Review on: The Baire property in hit and miss topologies

The paper is a contribution to the classical problem: When is the hyper- space of a topological space X a Baire space? This problem was first treated by McCoy in [Pacific. J. Math. 58, (1975), 133-142], for the Vietoris topol- ogy on the hyperspace of all nonempty closed subsets and his method was adapted later by others to treat other types of hyperspace topologies. Cao and Tomita in [Proc. Amer. Math. Soc. 135, (2007), 1565-1573], developed a different technique to investigate the relation between the Baire property of Tychonoff poers of X and that of the Vietoris hyperspace.
Modifying these techniques, in the paper under review a generic approach is developed to handle the Baire property of general hit-and-miss topologies and to establish its relation to the Baire property of powers of X. Besides an overview of existing results and methods, important new ones are provided, unifying several results from the literature. The paper moreover contains an interesting list of unsolved questions.