H-连通空间的乘积

Multipliable Property of H-Connected Space

主要研究有关H -连通空间乘积的理论 .首先给出了Jungck[1] 关于“紧T2 的H -连通第一可数空间具有有限乘积”的一个不依赖Whyburn[2 ] 工作的一个初等证明 .其次对局部连通的H -连通空间得到了同样的定理 :有限个具有第一可数性质的局部连通的H -连通空间的乘积空间是H -连通空间 .最后还把这个乘积扩充到了一般情况 ,即具有第一可数性质的T2的紧的 (或局部连通的 )H -连通空间的笛卡尔乘积空间亦是H -连通空间 .

Devoted to the study on the theory of H-connected space,which has been investigated by Jungck [1] in detail,we first give Jungck’s theorem another proof free from Whyburn [2] ,and then give another theorem in which“compact”hypothesis in Jungck’s theorem is replaced by the locally connected one.That is,let M 1 and M 2 be first countable H-connected space,if M 2 is locally connected,M 1 ×M 2 is H-connected.Moveover,we further extend the products from two factors to arbitrarily infinite factors,and prove that if every Y i (i∈I)is T 2 and compact(or locally connected)first countable space,then the product space Y=∏｛Y i ∶i∈I｝is also an H-connected space.