On well-filtered reflections of T0 spaces

Some open problems on well-filtered spaces and sober spaces

“…Based on the topological Rudin's Lemma, we introduce a new type of spaces -Rudin spaces (see [42,51]).…”

“…Therefore, it is a Rudin space and a WD space. In [42], it is shown that the closed subspaces and retracts of Rudin spaces are again Rudin spaces. Lemma 5.16.…”

“…Lemma 5.16. ( [42]) Let X = i∈I X i be the product of a family {X i : i ∈ I} of T 0 spaces and A ∈ Irr(X). Then the following conditions are equivalent:…”

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

“…The Rudin property is called the compactly filtered property in [14]. In order to emphasize its origin, here we call such property the Rudin property.…”

“…Remark 3.2. The equivalence of (1) and (3) in Proposition 3.1 has been proved in [14] in a different way.…”