Coherence of Smyth powerspaces

2026/07/07 by Rongqi Xiao, Xiaodong Jia · 1 voice
Mathematics · #math.GN

paper · pdf

Abstract

In this paper, we study when the Smyth powerspace Q^*_v(X) of a topological space X is coherent, and prove that X is coherent and weakly Hausdorff if and only if Q^*_v(X) is coherent and weakly Hausdorff. We give examples to show that neither coherence nor weak Hausdorffness of X solely implies that Q^*_v(X) is coherent or weakly Hausdorff. As a byproduct, our work gives an affirmative answer to a question raised by Xu.

Citations

• A Few Projective Classes of (Non-Hausdorff) Topological Spaces
• On Weakly Hausdorff Spaces and Locally Strongly Sober Spaces
• A complete Heyting algebra whose Scott space is non-sober

Discussions

• Rongqi Xiao, Xiaodong Jia: Coherence of Smyth powerspaces https://arxiv.org/abs/2607.05828 https://arxiv.org/pdf/2607.05828 https://arxiv.org/html/2607.05828 [bsky, 0 points, 0 comments]

Related

• Core-compactness of Smyth powerspaces
• Coherence of local and global hulls
• Forbidden substructures for coherence of domains
• On Scott power spaces
• Introduction to coherent spaces