Covering groups of non-connected topological groups revisited
Covering groups of non-connected topological groups revisited
复制标题
重新审视非连通拓扑群的覆盖群
DOI：
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发表时间：
1994
影响因子：
0.8
通讯作者：
Osman Mucuk
中科院分区：
文献类型：
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作者：
Ronald Brown;Osman Mucuk
假设所有空间都是局部路径连通和半局部1-连通的。设X是具有单位e的连通拓扑群，X是X的基础空间的泛覆盖.从提升映射的经典性质到覆盖空间，很容易得出结论：对于pẽ=e中的任一点ẽ，在X上存在唯一的拓扑群结构，使得ẽ是群的恒等式和态射.我们称X上的拓扑群的结构提升到。
All spaces are assumed to be locally path connected and semi-locally 1-connected. Let X be a connected topological group with identity e, and let be the universal cover of the underlying space of X. It follows easily from classical properties of lifting maps to covering spaces that for any point ẽ in with pẽ = e there is a unique structure of topological group on such that ẽ is the identity and is a morphism of groups. We say that the structure of topological group on X lifts to .