Work

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

Year: 2023

Type: article

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.

Source: Electronic Notes in Theoretical Informatics and Computer Science

DOI: 10.46298/entics.10369

Authors: Liping Zhang, Xiangnan Zhou, Qingguo Li

Institution: Hunan University

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: National Natural Science Foundation of China

Award: G5870735432