The Paranormality of Products and Their Subsets / A. V. Bogomolov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2018. ¹ 4. P. 54-56 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 156-157].

A topological space is called paranormal if any countable discrete system of closed sets \{D_n{:} n=1,2,3,\ldots \} can be expanded to a locally finite system of open sets \{U_n{:} n=1,2,3,\ldots \}, i.e., D_n is contained in U_n for all n, and D_m\cap U_n\neq \emptyset if and only if D_m=D_n. It is proved that if X is a countably compact space whose cube is hereditarily paranormal, then X is metrizable.

Key words: hereditarily paranormality, metrizability, Cartesian product, Cartesian cube, countable paracompactness.