Baire spaces and hyperspace topologies revisited

Steven Bourquin, László Zsilinszky


It is the purpose of this paper to show how to use approach spaces to get a unified method of proving Baireness of various hyperspace topologies. This generalizes results spread in the literature including the general (proximal) hit-and-miss topologies, as well as various topologies generated by gap and excess functionals. It is also shown that the Vietoris hyperspace can be non-Baire even if the base space is a 2nd countable Hausdorff Baire space.


Baire spaces; Approach spaces; (Proximal) hit-and-miss topologies; Weak hypertopologies; Banach-Mazur game.

Subject classification

54B20; 54E52; 54A05.

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