Ren, Ping; Yin, Jichao Infinite Tychonoloff products of hereditarily weak \(\overline{\delta\theta}\)-refinable spaces. (Chinese. English summary) Zbl 1150.54345 J. Sichuan Norm. Univ., Nat. Sci. 30, No. 6, 678-680 (2007). Summary: This paper mainly proves the following conclusions:(1) Let \(X=\prod\limits_{\alpha\in\Lambda}X_\alpha\) be hereditarily \(|\Lambda|\)-paracompact; \(X\) is hereditarily normal weak \(\overline{\delta\theta}\)-refinable if and only if \(\prod\limits_{\alpha\in F}X_\alpha\) is hereditarily normal weak \(\overline{\delta\theta}\)-refinable for every \(F\in [\Lambda]^{<\omega}\).(2) Let \(X=\prod\limits_{i\in\omega} X_i\) be hereditarily countable paracompact; then the following are equivalent:(i) \(X\) is hereditarily normal weak \(\overline{\delta\theta}\)-refinable;(ii) every \(F\in [\Lambda]^{<\omega}\) is hereditarily normal weak \(\overline{\delta\theta}\)-refinable;(iii) \(\prod\limits_{i\leqslant n} X_i\) is hereditarily normal weak \(\overline{\delta\theta}\)-refinable for each \(F\in [\Lambda]^{<\omega}\). MSC: 54E99 Topological spaces with richer structures 55N45 Products and intersections in homology and cohomology Keywords:hereditarily \(|\Lambda|\)-paracompact; hereditarily countable paracompact; hereditarily normal weak \(\overline{\delta\theta}\)-refinable PDFBibTeX XMLCite \textit{P. Ren} and \textit{J. Yin}, J. Sichuan Norm. Univ., Nat. Sci. 30, No. 6, 678--680 (2007; Zbl 1150.54345)