θ-连通空间是比连通空间更广泛的一类空间，在前人的研究基础之上得到了局部θ-连通空间的充分必要条件，证明了局部θ-连通空间在商映射下是不变的，同时也得到了和空间⊕α∈A Xα与乘积空间∏s∈S Xs 是局部θ-连通空间的充分必要条件。%Every local connected space is local u0012-connected space. And some sufficient and essential conditions of local u0012-connected space are obtained based on previous research. It is also shown that local u0012-connectedness is an invariant of quotient mappings. It also obtained that the sufficient and essential conditions of the sum space ⊕ 2A X and the Cartesian product Π s2S Xs are local u0012-connected spaces.
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