PreprintCC BY 4.0arXiv
The sobriety for locally compact dcpos
Abstract
In this paper, we focus on an open problem whether every locally compact dcpo is sober for the Scott topology. Specifically, we obtain two sufficient conditions for answering this problem. The main results are (1) every meet continuous locally compact coherent dcpo is sober with respect to the Scott topology; (2) the Scott space of every locally compact second countable dcpo is a sober space.
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BibTeX
@misc{he2026sobriety,
title = {{The sobriety for locally compact dcpos}},
author = {Zhengmao He and Yujing Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17759},
eprint = {2610.17759},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17759},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The sobriety for locally compact dcpos
AU - Zhengmao He
AU - Yujing Zhang
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17759
UR - https://arxiv.org/abs/2610.17759
AB - In this paper, we focus on an open problem whether every locally compact dcpo is sober for the Scott topology. Specifically, we obtain two sufficient conditions for answering this problem. The main results are (1) every meet continuous locally compact coherent dcpo is sober with respect to the Scott topology; (2) the Scott space of every locally compact second countable dcpo is a sober space.
ER -