On well-filtered reflections of T0 spaces

By Chong Shen, Xiaoyong Xi, Xiaoquan Xu, Dongsheng Zhao. Topology and its Applications, 2019

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Abstract 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.

Subfields: Algebra and Number Theory, Computational Mechanics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/92cef53c07254c7ec87fa297217ad9447b8781f0