A decomposition theorem for compact groups with an application to supercompactness
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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As an application, we present a proof of an unpublished result of Charles Mills from 1978: every compact group is supercompact.
KeywordsSimple compact Lie group Supercompact space
MSC22C05 54D30 54H11
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- Mills C.F., Compact groups are supercompact, Free University of Amsterdam, Faculty of Mathematics, September 1978, seminar reportGoogle Scholar