局部k连通(k道路连通)空间

Locally sequentially connected space

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.

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.