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...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.展开更多
In this paper, we show, among other results, that if X is a [separable] locally compact space X [satisfying the first countability axiom] then the space Cc （X） has countable tightness [if and only if it has bounding...In this paper, we show, among other results, that if X is a [separable] locally compact space X [satisfying the first countability axiom] then the space Cc （X） has countable tightness [if and only if it has bounding tightness] if and only if it is Frechet-Urysohn, if and only if Cc （X） contains a dense （LM） subspace and if and only if X is a-compact.展开更多
基金Supported by the National Science Foundation of China(No.10271026)
文摘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.
文摘In this paper, we show, among other results, that if X is a [separable] locally compact space X [satisfying the first countability axiom] then the space Cc （X） has countable tightness [if and only if it has bounding tightness] if and only if it is Frechet-Urysohn, if and only if Cc （X） contains a dense （LM） subspace and if and only if X is a-compact.
