PreprintCC BY-NC-SA 4.0arXiv
A non-sober core-compact meet-continuous dcpo
Abstract
We construct a meet-continuous dcpo whose Scott space is core-compact but neither sober nor locally compact. The example is a proper sub-dcpo of a locally compact sober complete lattice, and restriction induces an isomorphism between their lattices of Scott-closed sets. It follows that a locally compact sober dcpo need not be determined, among all dcpos, by its Scott-closed-set lattice.
Related
BibTeX
@misc{chen2026nonsober,
title = {{A non-sober core-compact meet-continuous dcpo}},
author = {Yuxu Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22033},
eprint = {2610.22033},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22033},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - A non-sober core-compact meet-continuous dcpo
AU - Yuxu Chen
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22033
UR - https://arxiv.org/abs/2610.22033
AB - We construct a meet-continuous dcpo whose Scott space is core-compact but neither sober nor locally compact. The example is a proper sub-dcpo of a locally compact sober complete lattice, and restriction induces an isomorphism between their lattices of Scott-closed sets. It follows that a locally compact sober dcpo need not be determined, among all dcpos, by its Scott-closed-set lattice.
ER -