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Infinite Tychonoloff products of hereditarily weak \(\overline{\delta\theta}\)-refinable spaces. (Chinese. English summary) Zbl 1150.54345

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
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