On well-filtered reflections of T-0 spaces
On well-filtered reflections of T-0 spaces
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关于 T-0 空间的良好过滤反射
DOI：
10.1016/j.topol.2019.106869
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发表时间：
2019
影响因子：
0.6
通讯作者：
Zhao Dongsheng
中科院分区：
文献类型：
--
作者：
Shen Chong;Xi Xiaoyong;Xu Xiaoquan;Zhao Dongsheng
遵循Ershov构造T 0 空间的d-完备的方法，我们给出了T 0 空间的良好过滤反射的直接构造。此外，我们使用 KF 集获得了经过良好过滤的空间的优雅表征。然后我们证明，当且仅当每个因子空间都经过良好过滤时，T 0 空间族的乘积是经过良好过滤的。最后，我们得到有限族T 0 空间的乘积的良好过滤反射是所有因子空间的良好过滤反射的乘积。一个共同的主题是，第一作者和第四作者引入的 KF 集在上述所有证明中都发挥着重要作用。
Following Ershov's method of constructing the d-completion of T 0 spaces, we give a direct construction of the well-filtered reflection of T 0 spaces. Also, we obtain an elegant characterization of well-filtered spaces using KF-sets. We then show that a product of a family of T 0 spaces is well-filtered iff each factor space is well-filtered. Finally, we obtain that the well-filtered reflection of a product of a finite family of T 0 spaces is the product of the well-filtered reflections of all factor spaces. A common theme is that KF-sets, introduced by the first and the fourth authors, function prominently in all of the above proofs.