在开放的过滤良好的空间

Log. Methods Comput. Sci. Pub Date : 2020-01-21 DOI:10.23638/LMCS-16(4:18)2020

Chong Shen, Xiaoyong Xi, Xiaoquan Xu, Dongsheng Zhao

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引用次数: 3

摘要

我们引入并研究了一类新的$T_0$空间，称为开良好过滤空间。我们证明的主要结果包括:(1)每一个良滤空间都是一个开的良滤空间;(2)每一个芯压开滤良好的空间都是清醒的。作为一个直接推论，我们推导出每一个核紧的良好过滤空间都是清醒的。这提供了另一种不同的、相对更直接的方法来回答Jia和Jung提出的开放性问题:每个核心紧凑的过滤良好的空间都是清醒的吗?

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On open well-filtered spaces

We introduce and study a new class of $T_0$ spaces, called open well-filtered spaces. The main results we proved include (1) every well-filtered space is an open well-filtered space; (2) every core-compact open well-filtered space is sober. As an immediate corollary, we deduce that every core-compact well-filtered space is sober. This provides another different and relatively more straight forward method to answer the open problem posed by Jia and Jung: Is every core-compact well-filtered space sober?

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Log. Methods Comput. Sci.

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