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Ends of locally compact groups and their coset spaces

Published online by Cambridge University Press:  09 April 2009

C. H. Houghton
C. H. Houghton
Affiliation:
Department of Pure Mathematics, University College, Cardiff, Wales
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Freudenthal [5, 7] defined a compactification of a rim-compact space, that is, a space having a base of open sets with compact boundary. The additional points are called ends and Freudenthal showed that a connected locally compact non-compact group having a countable base has one or two ends. Later, Freudenthal [8], Zippin [16], and Iwasawa [11] showed that a connected locally compact group has two ends if and only if it is the direct product of a compact group and the reals.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 17 , Issue 3 , May 1974 , pp. 274 - 284
Copyright
Copyright © Australian Mathematical Society 1974

References

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