On countable-to-one maps
On countable-to-one maps
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DOI：
10.1016/j.topol.2006.06.002
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发表时间：
2007-01
影响因子：
0.6
通讯作者：
Chuan Liu;Shou Lin
中科院分区：
文献类型：
--
作者：
Chuan Liu;Shou Lin
本文证明了具有点可数基的空间是度量空间的开的、可数到一的映象，度量空间的商、可数到一的映象是由点可数的ℵ0-弱基刻画的。提供的例子是为了回答Gruenage等人提出的否定问题。书名/作者Defined by Points-Counable Covers，Pacific J.113(1984)303-332]和田中[Y.Tanaka，闭映射和对称空间，问题回答拓扑学11(1993)215-233]。
In this paper, it is proved that a space with a point-countable base is an open, countable-to-one image of a metric space, and a quotient, countable-to-one image of a metric space is characterized by a point-countable ℵ0-weak base. Examples are provided in order to answer negatively questions posed by Gruenhage et al. [G. Gruenhage, E. Michael, Y. Tanaka, Spaces determined by point-countable covers, Pacific J. Math. 113 (1984) 303–332] and Tanaka [Y. Tanaka, Closed maps and symmetric spaces, Questions Answers Gen. Topology 11 (1993) 215–233].