PreprintCC BY 4.0arXiv
A study for well-filtered spaces
Abstract
In this paper, we focus on well-filtered spaces. By using the Rudin sets and WD sets, we obtain the following results: (1) The product of arbitrary many Scott well-filtered dcpos is still well-filtered with respect to the Scott topology. Thus we give positive answers for two questions proposed by Xu and Zhao; (2) Let P be a dcpo with ΣK(P) being well-filtered and Q a RB-domain. Then ΣK(P\times Q) is well- filtered if K(P\times Q) is a dcpo; (3) A intrinsic characterization of the WD sets is given by using Scott open filters.
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BibTeX
@misc{he2026study,
title = {{A study for well-filtered spaces}},
author = {Zhengmao He},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01518},
eprint = {2611.01518},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01518},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A study for well-filtered spaces
AU - Zhengmao He
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01518
UR - https://arxiv.org/abs/2611.01518
AB - In this paper, we focus on well-filtered spaces. By using the Rudin sets and WD sets, we obtain the following results: (1) The product of arbitrary many Scott well-filtered dcpos is still well-filtered with respect to the Scott topology. Thus we give positive answers for two questions proposed by Xu and Zhao; (2) Let P be a dcpo with ΣK(P) being well-filtered and Q a RB-domain. Then ΣK(P\times Q) is well- filtered if K(P\times Q) is a dcpo; (3) A intrinsic characterization of the WD sets is given by using Scott open filters.
ER -