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Jean Calbrix 《Transactions of the American Mathematical Society》1996,348(5):2085-2090
We say that a countable, Hausdorff, topological space with one and only one accumulation point is a point-space. For such a space, we give several properties which are equivalent to the property of being a k-space. We study some free filters on the set of integers and we determine if the associated point-spaces are k-spaces or not. We show that the filters of Lutzer-van Mill-Pol are k-filters. We deduce that, for each countable ordinal , there exists a free filter of true additive class (Baire's classification) and a free filter of true multiplicative class for which the associated point-spaces are k-spaces but not , the existence being true in the additive case for . In particular, we answer negatively a question raised in J. Calbrix, C. R. Acad. Sci. Paris 305 (1987), 109--111.
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k网与Michael的两个问题 总被引:3,自引:1,他引:2
本文通过1973年Michael提出的关于乘积空间的k空间性质问题及1973年Michael和Nagami提出的关于度量空间的紧覆盖商s象问题的进展来说明k网是研究广义度量空间的有效工具。 相似文献
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Chuan LIU Shou LIN 《数学学报(英文版)》2005,21(4):929-936
In this paper, we discuss the countable tightness of products of spaces which are quotient simages of locally separable metric spaces, or k-spaces with a star-countable k-network. The main result is that the following conditions are equivalent: (1) b = ω1; (2) t(Sω×Sω1) 〉 ω; (3) For any pair (X, Y), which are k-spaces with a point-countable k-network consisting of cosmic subspaces, t(X×Y)≤ω if and only if one of X, Y is first countable or both X, Y are locally cosmic spaces. Many results on the k-space property of products of spaces with certain k-networks could be deduced from the above theorem. 相似文献
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本文讨论了特殊的度量空间Tω和Tω1在探讨具有点可数k网的k空间类中乘积性质与映射性质方面的作用.一方面,通过Tω分析了为解决1973年Michael提出的“k空间的乘积问题”而引入的三个空间类的相互关系;另一方面,利用Tω1研究了局部可分度量空间的闭映象的内在刻画. 相似文献
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