Smyth power space of a co-sober space is not always co-sober

Xiaoquan Xu; Fengshuo Xu; Haitao Ji; Dong Qiu

Smyth power space of a co-sober space is not always co-sober

General Topology 2026-08-03 v1

Authors: Xiaoquan Xu , Fengshuo Xu , Haitao Ji , Dong Qiu

Abstract

In this paper, we give a co-sober space $X$ whose Smyth power space $P_S(X)$ is not co-sober, which gives a negative answer to an open problem.

Keywords

co-sober space Smyth power space open problem topology negative answer

Cite

@article{arxiv.2608.02047,
  title  = {Smyth power space of a co-sober space is not always co-sober},
  author = {Xiaoquan Xu and Fengshuo Xu and Haitao Ji and Dong Qiu},
  journal= {arXiv preprint arXiv:2608.02047},
  year   = {2026}
}

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