There Is a Katĕtov Space That Is Not Countably Paracompact - Kurosaki, Makoto (Topology Proceedings, 2022)
We construct, in ZFC, a Katětov space that is not countably paracompact. This answers a question of M. Katětov [Extension of locally finite coverings (Russian), Colloq. Math. 6 (1958), 145-151] and Teodor C. Przymusiński and Michael L. Wage [Collectionwise normality and extensions of locally finite coverings, Fund. Math. 109 (1980), no. 3, 175-187].