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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Compactifications of locally compact groups and closed subgroups


Authors: A. T. Lau, P. Milnes and J. S. Pym
Journal: Trans. Amer. Math. Soc. 329 (1992), 97-115
MSC: Primary 43A60; Secondary 22D05
DOI: https://doi.org/10.1090/S0002-9947-1992-1062191-1
MathSciNet review: 1062191
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Abstract: Let $ G$ be a locally compact group with closed normal subgroup $ N$ such that $ G/N$ is compact. In this paper, we construct various semigroup compactifications of $ G$ from compactifications of $ N$ of the same type. This enables us to obtain specific information about the structure of the compactifi cation of $ G$ from the structure of the compactification of $ N$. Our results seem to be interesting and new even when $ G$ is the additive group of real numbers and $ N$ is the integers. Applications and other examples are given.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1062191-1
Keywords: locally compact group, subgroup, flow, compactification, weakly almost periodic function, distal function, uniformly continuous function, euclidean motion group
Article copyright: © Copyright 1992 American Mathematical Society