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arXiv · 2610.30967

On U_c-admitting spaces and U_c-completions of T_0 spaces

Kangming Lu·Qingguo Li·Shengwen Wang·Rongqi Xiao
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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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Kangming Lu, Qingguo Li, Shengwen Wang, Rongqi Xiao. 2026-10-22. On U_c-admitting spaces and U_c-completions of T_0 spaces. https://arxiv.org/abs/2610.30967

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