PreprintCC BY 4.0arXiv
Applications of sequential spaces to Smyth power spaces and sober spaces
Abstract
Recently, in the study of topological properties in Domain theory, the first countable spaces and Frechet-Urysohn spaces receive close attention and are frequently employed. In this paper, we focus on sequential spaces weaker than Frechet-Urysohn spaces. The main results are: (1) For a well-filtered space X, the Scott topology and the upper vietoris topology on K(X) coincide if PS(X) is a sequential space; (2) every ω-well-filtered coherent d- space X is sober when the procuct of X is a sequential space.
Related
BibTeX
@misc{he2026applications,
title = {{Applications of sequential spaces to Smyth power spaces and sober spaces}},
author = {Zhengmao He},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27775},
eprint = {2609.27775},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27775},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Applications of sequential spaces to Smyth power spaces and sober spaces
AU - Zhengmao He
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.27775
UR - https://arxiv.org/abs/2609.27775
AB - Recently, in the study of topological properties in Domain theory, the first countable spaces and Frechet-Urysohn spaces receive close attention and are frequently employed. In this paper, we focus on sequential spaces weaker than Frechet-Urysohn spaces. The main results are: (1) For a well-filtered space X, the Scott topology and the upper vietoris topology on K(X) coincide if PS(X) is a sequential space; (2) every ω-well-filtered coherent d- space X is sober when the procuct of X is a sequential space.
ER -