Baire spaces and hyperspace topologies revisited


  • Steven Bourquin University of North Carolina at Pembroke
  • László Zsilinszky University of North Carolina at Pembroke



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


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.


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How to Cite

S. Bourquin and L. Zsilinszky, “Baire spaces and hyperspace topologies revisited”, Appl. Gen. Topol., vol. 15, no. 1, pp. 85–92, Apr. 2014.