对称及相关空间中的g σ-集

General Topology and its Applications Pub Date : 1978-11-01 DOI:10.1016/0016-660X(78)90029-6

S.W. Davis, G. Gruenhage, P.J. Nyikos

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引用次数: 24

摘要

本文给出了一个正则对称空间的例子，该空间不是次副紧的，并且有一个非gσ集的闭子集，从而回答了Arhangel’skii和Michael的问题。我们还利用顺序的思想得到了一些积极的结果，并给出了几个例子，表明这些结果在某种意义上是最好的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Gσ-sets in symmetrizable and related spaces

In this paper we answer questions of Arhangel'skii and Michael by providing an example of a regular symmetrizable space which is not subparacompact and has a closed subset which is not a G_σ-set. We also use the idea of sequential order to obtain some positive results, and several examples are provided which show that these results are in some sense the best possible.

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