Every T0 space admits a well-filterification W(X) with universal property for continuous maps into well-filtered spaces; products of well-filtered spaces are well-filtered.
and Keimel, K.: Quasicontinuous domains and the Smy th powerdo- main, Electronic Notes in Theo
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Existence of well-filterifications of $T_0$ topological spaces
Every T0 space admits a well-filterification W(X) with universal property for continuous maps into well-filtered spaces; products of well-filtered spaces are well-filtered.