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Reflection (computer programming)

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Discrete mathematics

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Interpolation space

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Biochemistry

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Mathematical proof

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Topology and its Applications

Following Ershov's method of constructing the d-completion of T0 spaces, we give a direct construction of the well-filtered reflection of T0 spaces. Also, we obtain an elegant characterization of well-filtered spaces using KF-sets. We then show that a product of a family of T0 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 T0 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.

On well-filtered reflections of T0 spaces