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中文摘要：
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．
英文摘要：
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 muhiplicative, but not arbi- trary multiphcative, and what＇ s more, we give the necessary and sufficient condition that the locally k - connectedness is countably multiplicative.
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