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Spaces of closed subgroups of a connected Lie group

Published online by Cambridge University Press:  18 May 2009

N. Oler
N. Oler
Affiliation:
University Of Pennsylvania, and University Of Birmingham
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 14 , Issue 1 , February 1973 , pp. 77 - 79
Copyright
Copyright © Glasgow Mathematical Journal Trust 1973

References

REFERENCES

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