A Hofmann-Mislove theorem for $c$-well-filtered spaces
General Topology
2023-06-22 v2
Abstract
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 -well-filtered spaces is introduced. We show that a retract of a -well-filtered space is -well-filtered and a locally Lindel\"{o}f and -well-filtered -space is countably sober. In particular, we obtain a Hofmann-Mislove theorem for -well-filtered spaces.
Keywords
Cite
@article{arxiv.2211.07972,
title = {A Hofmann-Mislove theorem for $c$-well-filtered spaces},
author = {Liping Zhang and Xiangnan Zhou and Qingguo Li},
journal= {arXiv preprint arXiv:2211.07972},
year = {2023}
}