| 局部k连通（k道路连通）空间 |
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| 引用本文： | 黄琴,郑春燕. 局部k连通（k道路连通）空间[J]. 宁德师专学报(自然科学版), 2008, 20(3): 229-233 |
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| 作者姓名： | 黄琴 郑春燕 |
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| 作者单位： | 1. 莆田学院数学系,莆田,福建,351100
2. 宁德师范高等专科学校数学研究所,宁德,福建,352100 |
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| 基金项目： | 国家自然科学基金，福建省教育厅科研项目，莆田学院校科研和教改项目，宁德师范高等专科学校资助项目 |
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| 摘 要： | 给出局部连通性与局部道路连通性的定义及等价刻画，研究它们的基本性质，证明它们是拓扑不变性、开遗传性、可商性；最后证明它们是有限可积但不是任意可积，并给出局部连通性可数可积的充要条件．
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| 关 键 词： | 连续映射 局部连通空间 局部道路连通性 可积性 |
Locally sequentially connected space |
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| HUANG Qin,ZHENG Chun-yan. Locally sequentially connected space[J]. Journal of Ningde Teachers College(Natural Science), 2008, 20(3): 229-233 |
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| Authors: | HUANG Qin ZHENG Chun-yan |
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| Affiliation: | HUANG Qin , ZHENG Chun - yan ( 1. Department. of Mathematice, Putian College, Putian Fujian 351100, China; 2. Department of Mathematice, Ningde Teachers College, Ningde Fujian 352100, China) |
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| Abstract: | In this paper,we give the definitions and characterizations of the locally k-connected space and the locally k-path connected space,investigate their basic properties,and show that they are topological invariance,open hereditary and quotient.Finally,we prove that they are finitely multiplicative,but not arbitrary multiplicative,and what's more,we give the necessary and sufficient condition that the locally k-connectedness is countably multiplicative. |
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| Keywords: | k-continuous mapping connected space locally k-connected space locally k-path connected space multiplicative |
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