Spaces of closed subgroups of a connected Lie group
Spaces of closed subgroups of a connected Lie group
复制标题
连通李群的闭子群空间
作者：
N. Oler
在一系列的两篇论文出现在1968年和1969年的赫伯特Abels [1，2]已经制定了，从一个方法起源于Gerstenhaber [6]，一种手段，扩大研究适当的不连续群的变换，以适当的变换群一般。我们记得，如果G是局部紧空间X的变换的Hausdorff局部紧群，则当对任意两个紧子集K和L，G的子集G（K，L）= {g <$G：gL <$K # 0}是紧的时，G的作用是真的（见[3]，第55页）。在下文中，所有群和空间都将是豪斯多夫的且局部紧的。如果H是G的闭子群，那么很明显，H作为G的左平移群的作用具有刚才定义的性质。
In a sequence of two papers which appeared in 1968 and 1969 Herbert Abels [1, 2] has developed, from a method originated by Gerstenhaber [6], a means for extending the study of properly discontinuous groups of transformations to that of proper transformation groups in general. We recall that, if G is a Hausdorff locally compact group of transformations of a locally compact space X, then the action of Gis proper when, for any two compact subsets K and L, the subset G(K, L) = {g ɛ G: gL∩K # 0} of G is compact (see [3], p. 55). In what follows all groups and spaces will be Hausdorff and locally compact. If H is a closed subgroup of G, then it is clear that the property just defined is possessed by the action of H as a group of left translations of G.