| 林寿,郑春燕.一类仿紧连通空间的几乎开映像[J].数学年刊A辑,2009,30(1):107~114 |
| 一类仿紧连通空间的几乎开映像 |
| The Almost-Open Images of a Class of Connected Paracompact Spaces |
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| DOI： |
| 中文关键词: 连通空间 仿紧空间 Lasnev空间 M1空间 几乎开映射 闭映射 |
| 英文关键词:Connected spaces, Paracompact spaces, Laˇsnev spaces, M1-spaces,
Almost-open mappings, Closed mappings |
| 基金项目:国家自然科学基金，宁德师范高等专科学校建设项目 |
| Author Name | Affiliation | E-mail | | LIN Shou | Department of Mathematics, Zhangzhou Normal University, Zhangzhou
363000, Fujian, China. Institute of Mathematics, Ningde Teachers’ College,
Ningde 352100, Fujian, China. | linshou@public.ndptt.fj.cn | | ZHENG Chunyan | Institute of Mathematics, Ningde Teachers’ College, Ningde 352100, Fujian,
China. | zhengchunyan211@163.com |
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| 中文摘要: |
| 讨论了包含仿紧连通空间的一些广义度量空间类的映射性质,证明了T1的连通第一可数空间是连通Lasnev空间的几乎开映像,部分回答了1998年Tkachuk关于连通空间逆像的一个问题;证明了T1的连通的具有点Gδ性质的空间是连通M1空间的几乎开映像,其中建立了M1空间的一个映射定理,回答了1976年Nyikos提出的一个问题. |
| 英文摘要: |
| In this paper the mapping properties about generalized metric spaces which
are connected paracompact are discussed. It is shown that a T1 connected space with
first countability is an almost-open image of a Laˇsnev connected space, which gives partial
answers to a Tkachuk’s question on the preimages of connected spaces in 1998. It is also
shown that a T1 connected space with point-G property is an almost-open image of a
connectedM1-space, where a mapping theorem onM1-spaces is established and then answers
the question posed by Nyikos P. J. in 1976. |
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