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| 摘要: |
| 本文研究了s-空间的性质.利用加法定理及剩余性质，得到以下结论：（1）如果s-空间X是可数多个度量子空间的并，则X是序列空间；（2）如果非局部紧拓扑群G在某个紧化bG中的剩余是遗传s-空间，则G是可分度量空间或σ-紧空间.以上性质推广了Arhangel'skii关于s-空间的一些已有结论. |
| 关键词: s-空间 Lindelöf ∑-空间 剩余 可度量的 拓扑群 |
| DOI： |
| 分类号:O189.1 |
| 基金项目:Supported by the Natural Science Foundation of Shandong Province (ZR2014AL002) and the National Natural Science Foundation of China (11571175). |
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| A NOTE ON S-SPACES |
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WANG Han-feng,HE Wei
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| Abstract: |
| In this paper, we study some properties of s-spaces. By means of the addition theorem and the theory of remainders, the following properties are established: (1) if an s-space X is the union of a countable family of metrizable subspaces, then X is sequential; (2) if G is a nonlocally compact topological group with a compactification bG such that Y=bG\G is hereditarily an s-space, then either G is separable and metrizable, or G is σ-compact, which generalize and improve some results about s-spaces by Arhangel'skii. |
| Key words: s-space Lindelöf ∑-space remainder metrizable topological group |
