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| 序列覆盖的闭映射保持可度量性 | |
| 引用本文： | 燕鹏飞,林寿,江守礼.序列覆盖的闭映射保持可度量性[J].数学学报,2004,47(1):87-90. |
| 作者姓名： | 燕鹏飞 林寿 江守礼 |
| 作者单位： | 1. 安徽大学数学系,合肥,230039;南京师范大学数学系,南京,210097 2. 福建师范大学数学系,福州,350007 3. 山东大学数学系,济南,250100 |
| 基金项目： | 国家自然科学基金资助项目(10171043,10271026) |
| 摘 要： | 设f:X→Y是连续的满映射. f称为序列覆盖映射,若{y})是Y中的收敛序列,则存在X中的收敛序列{xn},使得每一xn∈f-1(yn);f称为1序列覆盖映射,若对于每-y∈Y,存在x∈f-1(y),使得如果{yn}是Y中收敛于点y的序列,则有X中收敛于点x的序列{xn},使得每一xn∈f-1(yn).本文研究度量空间序列覆盖的闭映射之构造,否定地回答了Topology and its Applications上提出的一个问题. |
| 关 键 词： | 度量空间 闭映射 序列覆盖映射 |
| 文章编号： | 0583-1431(2004)01-0087-04 |
Metrizability is Preserved by Sequence-Covering and Closed Maps |
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| Peng Fei YAN.Metrizability is Preserved by Sequence-Covering and Closed Maps[J].Acta Mathematica Sinica,2004,47(1):87-90. | |
| Authors: | Peng Fei YAN |
| Institution: | Peng Fei YAN (Department of Mathematics, Nanjing Normal University, Nanjing 210097, P. R. China) (Department of Mathematics, Anhui University, Hefei 230039, P. R. China) Shou LIN (Department of Mathematics, Fujian Normal University, Fuzhou 350007, P. R. China) Shou Li JIANG (Department of Mathematics, Shandong University, Jinan 250100, P. R. China) |
| Abstract: | Let f : X →Y be a continuous and surjective map. f is a sequence-covering map if whenever {yn} is a convergent sequence in Y there is a convergent sequence {xn} in X with each xn ∈ f-1(yn). f is a 1-sequence-covering map if for each y ∈ Y, there is x ∈ f-1(y) such that whenever {yn} is a sequence converging to y in y there is a sequence {xn} converging to x in X with each xn ∈ f-1(yn}. In this paper the structure of sequence-covering and closed maps of metric spaces is investigated, a problem posed by "Topology and its Applications" is negatively answered. |
| Keywords: | Metric spaces Closed maps Sequence-covering maps |
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