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中文摘要：
给出了序列连续映射的等价刻画及局部序列连通性的定义．讨论了拓扑空间的局部序列连通性，给出局部序列连通空间的刻画及基本性质，证明了序列连续开映射保持局部序列连通性，局部序列连通性具有开遗传性，可商性，有限可积性；最后给出局部序列连通性可数可积的充要条件．
英文摘要：
In this paper, we give characterizations of sequentially continuous mappings and the definition of locally sequentially connected space, and investigate basic properties of locally sequentially connected space, so we obtain the following main results： sequence-continuous-open mappings can preserve locally sequential connectedness; locally sequentially connectedness is open hereditary, quotient and finitely multiplicative. Finally, we give the necessary and sufficient condition that locally sequentially connectedness is countably multiplicative.
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