Functor \(\lambda\) and metrizability of compacta (Q1596155)

\textit{V.~V.~Fedorchuk} [Mosc. Univ. Math. Bull. 44, No. 4, 102-106 (1989); translation from Vestn. Mosk. Univ., Ser. I 1989, No. 4, 93-96 (1989; Zbl 0698.54006)] proved that if for any normal functor \({\mathcal F}\) of power \( \geq 3 \) acting on a category of compacta the bicompactum \({\mathcal F}(X)\) is hereditarily normal, then the bicompactum \(X\) is metrizable. In the present note the author shows that in some concrete cases the theorem of Fedorchuk remains valid when the conditions for normality of the functor \({\mathcal F}\) are absent.