We show that every compact connected group is the limit of a continuous inverse sequence, in the category of compact groups, where each successor bonding map is either an epimorphism with finite kernel or the projection from a product by a simple compact Lie group. As an application, we present a proof of an unpublished result of Charles Mills from 1978: every compact group is supercompact.
@article{bwmeta1.element.doi-10_2478_s11533-011-0019-x,
author = {Wies\l aw Kubi\'s and S\l awomir Turek},
title = {A decomposition theorem for compact groups with an application to supercompactness},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {593-602},
zbl = {1235.22007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0019-x}
}
Wiesław Kubiś; Sławomir Turek. A decomposition theorem for compact groups with an application to supercompactness. Open Mathematics, Tome 9 (2011) pp. 593-602. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0019-x/
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