Baire spaces and hyperspace topologies revisited | Zendy

Steven Bourquin | Zendy; László Zsilinszky | Zendy

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Baire spaces and hyperspace topologies revisited

Author(s) -

Steven Bourquin,

László Zsilinszky

Publication year - 2014

Publication title -

applied general topology

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.638

H-Index - 13

eISSN - 1989-4147

pISSN - 1576-9402

DOI - 10.4995/agt.2014.1897

Subject(s) - hyperspace , baire space , mathematics , baire category theorem , network topology , hausdorff space , countable set , space (punctuation) , base (topology) , baire measure , hausdorff distance , topological space , urysohn and completely hausdorff spaces , topology (electrical circuits) , discrete mathematics , pure mathematics , combinatorics , hausdorff dimension , mathematical analysis , hausdorff measure , computer science , operating system

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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