Paper
Strong well-filteredness of upper topology on sup-complete posets
Authors
Xiaoquan Xu, Yi Yang, Lizi Chen
Abstract
We first introduce and investigate a new class of 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 -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 -space is strongly well-filtered, which answers two problems recently posed by Xu.