@article{Xu2026, 
author = {Xiaoquan Xu and Yi Yang and Xintong Yang},
title = {A generalized topological Rudin lemma and sober spaces},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {15513-15523},
keywords = {generalized topological Rudin lemma, F-family, Scott open filter, irreducible set, sober space},
url = {https://www.sciopen.com/article/10.3934/math.2026638},
doi = {10.3934/math.2026638},
abstract = {In this paper, we introduce and study the notion of    F-families in        T    0  -spaces. This concept unifies several important classes of objects in domain theory and non-Hausdorff topology, including irreducible sets, filtered families of upper sets, Scott open filters, and irreducible subsets in Smyth power spaces. Using    F-families, we establish a generalized topological Rudin lemma that extends the classical topological Rudin lemma to a broader setting. As an application, we obtain some characterizations of sober spaces, from which the Hofmann-Mislove theorem and Heckman-Keimel-Schalk theorem can be directly deduced.}
}