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arXiv · 1911.11617

On topological Rudin's lemma, well-filtered spaces and sober spaces

Xiaoquan Xu·Dongsheng Zhao
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Abstract

Based on topological Rudin's Lemma, we investigate two new kinds of sets - Rudin sets and well-filtered determined sets in $T_0$ topological spaces. Using such sets, we formulate and prove some new characterizations for well-filtered spaces and sober spaces. Part of the work was inspired by Xi and Lawson's work on well-filtered spaces. Our study also lead to a new class of spaces - strong $d$-spaces and some problems whose solutions will strengthen our understanding of the related structures.

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Xiaoquan Xu, Dongsheng Zhao. 2019-11-25. On topological Rudin's lemma, well-filtered spaces and sober spaces. https://arxiv.org/abs/1911.11617

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