Liping Zhang ; Xiangnan Zhou ; Qingguo Li - A Hofmann-Mislove theorem for $c$-well-filtered spaces

entics:10369 - Electronic Notes in Theoretical Informatics and Computer Science, March 21, 2023, Volume 2 - Proceedings of ISDT 9 - https://doi.org/10.46298/entics.10369
A Hofmann-Mislove theorem for $c$-well-filtered spacesArticle

Authors: Liping Zhang ; Xiangnan Zhou ; Qingguo Li

    The Hofmann-Mislove theorem states that in a sober space, the nonempty Scott open filters of its open set lattice correspond bijectively to its compacts saturated sets. In this paper, the concept of $c$-well-filtered spaces is introduced. We show that a retract of a $c$-well-filtered space is $c$-well-filtered and a locally Lindelöf and $c$-well-filtered $P$-space is countably sober. In particular, we obtain a Hofmann-Mislove theorem for $c$-well-filtered spaces.


    Volume: Volume 2 - Proceedings of ISDT 9
    Published on: March 21, 2023
    Accepted on: November 25, 2022
    Submitted on: November 25, 2022
    Keywords: Mathematics - General Topology,54H99

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