\(\sigma\)-products on \(\sigma\)-metacompact spaces and \(\sigma\)-mesocompact spaces (Q2752625)

\textit{K. Chiba} [Math. Jap. 32, 5-10 (1987; Zbl 0614.54021); ibid. 32, 373-378 (1987; Zbl 0632.54017)] studied the \(\sigma\)-products of some covering properties. In this paper, the authors discuss the \(\sigma\)-products on \(\sigma\)-metacompact spaces and \(\sigma\)-mesocompact spaces. The main results areNEWLINENEWLINENEWLINE(1) Let \(X= \sigma\{X_\alpha: \alpha\in\Lambda\}\), if every finite subproduct of \(X\) is a \(\sigma\)-metacompact space, then \(X\) is a \(\sigma\)-metacompact space;NEWLINENEWLINENEWLINE(2) Let \(X= \sigma\{X_\alpha:\alpha\in \Lambda\}\), if \(X\) is a normal space and every finite subproduct of \(X\) is a \(\sigma\)-mesocompact space, then \(X\) is a \(\sigma\)-mesocompact space.