The Bohr compactification, modulo a metrizable subgroup
Fundamenta Mathematicae, Tome 143 (1993) no. 2, pp. 119-136
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
The authors prove the following result, which generalizes a well-known theorem of I. Glicksberg [G]: If G is a locally compact Abelian group with Bohr compactification bG, and if N is a closed metrizable subgroup of bG, then every A ⊆ G satisfies: A·(N ∩ G) is compact in G if and only if {aN:a ∈ A} is compact in bG/N. Examples are given to show: (a) the asserted equivalence can fail in the absence of the metrizability hypothesis, even when N ∩ G = {1}; (b) the asserted equivalence can hold for suitable G and N with N closed in bG but not metrizable; (c) an Abelian group may admit two topological group topologies U and T, with U totally bounded, T locally compact,U ⊆ T, with U and T sharing the same compact sets, and such that nevertheless U is not the topology inherited from the Bohr compactification of 〈 G, T〉. There are applications to topological groups of the form kG for G a totally bounded Abelian group.
Affiliations des auteurs :
W. W. Comfort 1 ; F. Javier Trigos-Arrieta 2 ; Ta-Sun Wu 3
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author = {W. W. Comfort and F. Javier Trigos-Arrieta and Ta-Sun Wu},
title = {The {Bohr} compactification, modulo a metrizable subgroup},
journal = {Fundamenta Mathematicae},
pages = {119--136},
publisher = {mathdoc},
volume = {143},
number = {2},
year = {1993},
doi = {10.4064/fm-143-2-119-136},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-143-2-119-136/}
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W. W. Comfort; F. Javier Trigos-Arrieta; Ta-Sun Wu. The Bohr compactification, modulo a metrizable subgroup. Fundamenta Mathematicae, Tome 143 (1993) no. 2, pp. 119-136. doi: 10.4064/fm-143-2-119-136
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