Abstract A Tychonoff space X is called strongly Cech-complete if there exist paracompact open subsets V 1 , V 2 , … of βX such that ⋂ n = 1 ∞ V n = X . Strong Cech-completeness of a Tychonoff space is characterized in terms of the existence of certain kinds of complete sequence of open covers, for example, of a complete sequence consisting of star-finite open covers. A metrizable space is shown to be strongly Cech-complete if, and only if, the space is Cech-complete and strongly metrizable. Universal spaces for strongly Cech-complete metrizable spaces are indicated. A compatible complete metric is constructed for R such that, for each r > 0 , every open r-ball meets at most 25 distinct r-balls. This metric is used to derive characterizations for strongly Cech-complete metrizable spaces and strongly metrizable spaces in terms of special compatible metrics.

中文翻译：

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在强Čech-完全空间上

摘要 如果存在 βX 的超紧开子集 V 1 , V 2 , … 使得 ⋂ n = 1 ∞ V n = X ，则称 Tychonoff 空间 X 为强 Cech-complete。Tychonoff 空间的强切赫完备性表现为某些类型的开覆盖的完全序列的存在性，例如由星-有限开覆盖​​组成的完全序列。当且仅当空间是 Cech 完备且强可度量化的，一个可度量化空间被证明是强 Cech 完备的。指出了强切赫完全可度量空间的通用空间。为 R 构建了一个兼容的完整度量，使得对于每个 r > 0 ，每个开放的 r-ball 最多遇到 25 个不同的 r-ball。