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作 者:葛英[1]
出 处:《数学杂志》2004年第3期275-279,共5页Journal of Mathematics
基 金:江苏省教委自然科学基金资助项目 (0 2KJB110 0 0 1)
摘 要:本文给出了度量空间序列商 ,k 映象的一些内部刻画 ,证明了空间X是度量空间的序列商 ,k 映象当且仅当X具有紧有限k 闭cs 覆盖列的点星sn 网 ,当且仅当X具有紧有限k 闭覆盖列的点星网 .作为上述结果的一个推论 ,不仅得到了空间X是度量空间序列商 ,k 映象当且仅当X是度量空间的k 映象 ,而且还证明了空间X是度量空间当且仅当X具有局部有限 (紧有限 )闭 (k 闭 )覆盖列的点星弱邻域网 .这里“闭”(“k闭”)In this paper, we give some internal characterizations of sequentially quotient, k-images of metric spaces, and prove that a space X is a sequentially quotient, k-image of a metric space if and only if X has a point-star sn-network consisting of sequence of compact finite k-closed cs *-covers of X, if and only if X has a point-star network consisting of sequence of compact finite k-closed covers of X. As a corollary of the above results, we obtain that X is a sequentiall quotient, k-image of a metric space if and only if X is an k-image of a metric space. We also prove that a space X is a metric space if and only if X has a point-star weak neighborhood network consisting of sequence of locally finite (compact finite) closed (k-closed) cover of X, where “closed” (“k-closed”) can not be omitted.
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