Baire spaces and hyperspace topologies revisited

• Bourquin, Steven ^[1] ; Zsilinszky, Laszlo ^[1]
  1. [1] University of North Carolina at Pembroke

     University of North Carolina at Pembroke

     Township of Pembroke, Estados Unidos

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 15, Nº. 1, 2014, págs. 85-92
• Idioma: inglés
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• Resumen

  • 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.