Compactifications of locally compact groups and closed subgroups

Lau, A. T.; Milnes, P.; Pym, J. S.

doi:10.1090/S0002-9947-1992-1062191-1

Compactifications of locally compact groups and closed subgroups
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by A. T. Lau, P. Milnes and J. S. Pym

Trans. Amer. Math. Soc. 329 (1992), 97-115

DOI: https://doi.org/10.1090/S0002-9947-1992-1062191-1

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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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