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On U_c-admitting spaces and U_c-completions of T_0 spaces
Abstract
In this paper, we introduce a new class of spaces, termed U_c-admitting spaces, and investigate their relationships with U_s-admitting spaces and well-filtered spaces. Adopting the perspective of H-sobriety, we show that every U_c-admitting space is H-sober, so that U_c-admitting spaces arise as a special case of H-sober spaces. Consequently, the category U_c-Sob of U_c-admitting spaces and continuous maps is complete and forms a reflective subcategory of Top_0. In addition, we prove that a T_0 space X is U_c-admitting if and only if its Smyth power space is U_c-admitting. Finally, we present the standard U_c-completion of an arbitrary T_0 space.
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BibTeX
@misc{lu2026ucadmitting,
title = {{On U_c-admitting spaces and U_c-completions of T_0 spaces}},
author = {Kangming Lu and Qingguo Li and Shengwen Wang and Rongqi Xiao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30967},
eprint = {2610.30967},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30967},
}
RIS
TY - UNPB
TI - On U_c-admitting spaces and U_c-completions of T_0 spaces
AU - Kangming Lu
AU - Qingguo Li
AU - Shengwen Wang
AU - Rongqi Xiao
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30967
UR - https://arxiv.org/abs/2610.30967
AB - In this paper, we introduce a new class of spaces, termed U_c-admitting spaces, and investigate their relationships with U_s-admitting spaces and well-filtered spaces. Adopting the perspective of H-sobriety, we show that every U_c-admitting space is H-sober, so that U_c-admitting spaces arise as a special case of H-sober spaces. Consequently, the category U_c-Sob of U_c-admitting spaces and continuous maps is complete and forms a reflective subcategory of Top_0. In addition, we prove that a T_0 space X is U_c-admitting if and only if its Smyth power space is U_c-admitting. Finally, we present the standard U_c-completion of an arbitrary T_0 space.
ER -