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arXiv · 2211.07972

A Hofmann-Mislove theorem for $c$-well-filtered spaces

Liping Zhang·Xiangnan Zhou·Qingguo Li
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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 $c$-well-filtered spaces is introduced. We show that a retract of a $c$-well-filtered space is $c$-well-filtered and a locally Lindel\"{o}f and $c$-well-filtered $P$-space is countably sober. In particular, we obtain a Hofmann-Mislove theorem for $c$-well-filtered spaces.

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BibTeXRIS

Liping Zhang, Xiangnan Zhou, Qingguo Li. 2022-11-15. A Hofmann-Mislove theorem for $c$-well-filtered spaces. https://doi.org/10.46298/entics.10369

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