We prove that an infinite compact abelian group G is connected if and only if its arc component G_a contains a super-sequence converging to 0 that is qc-dense in G. This gives as a corollary a recent theorem of Außenhofer: For a connected locally compact abelian group G, the restriction homomorphism r : G → G_a is a topological isomorphism. We show that an infinite compact group G is connected if and only if its arc component Ga contains a super-sequence converging to the identity that is qc-dense in G and generates a dense subgroup of G. We also offer a short alternative proof of the result of Hofmann and Morris on the existence of suitable sets of minimal size in the arc component of a compact connected group.

Quasi-convexly dense and suitable sets in the arc component of a compact group

DIKRANJAN, Dikran;
2012-01-01

Abstract

We prove that an infinite compact abelian group G is connected if and only if its arc component G_a contains a super-sequence converging to 0 that is qc-dense in G. This gives as a corollary a recent theorem of Außenhofer: For a connected locally compact abelian group G, the restriction homomorphism r : G → G_a is a topological isomorphism. We show that an infinite compact group G is connected if and only if its arc component Ga contains a super-sequence converging to the identity that is qc-dense in G and generates a dense subgroup of G. We also offer a short alternative proof of the result of Hofmann and Morris on the existence of suitable sets of minimal size in the arc component of a compact connected group.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/868274
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