Strong well-filteredness of upper topology on sup-complete posets
Abstract
Abstract We first introduce and investigate a new class of $T_0$ -spaces – strong $R$ -spaces, which are stronger than both $R$ -spaces and strongly well-filtered spaces. It is proved that any sup-complete poset equipped with the upper topology is a strong $R$ -space, and the Hoare power space of a $T_0$ -space is a strong $R$ -space. Hence, the upper topology on a sup-complete poset is strongly well-filtered, and the Hoare power space of a $T_0$ -space is strongly well-filtered, which answers two problems recently posed by Xu.
Fields of Study & Subjects
Advanced Topology and Set Theory
Fuzzy and Soft Set Theory
Advanced Banach Space Theory
Publication details
- Journal / source
- Mathematical Structures in Computer Science
- Publisher
- Cambridge University Press (CUP)
- Volume
- 36
- Publication date
- 1 January 2026
- Language
- EN