Glasnik Matematicki, Vol. 33, No.1 (1998), 13-17.
A NEW PROOF OF A THEOREM CONCERNING DECOMPOSABLE
GROUPS
Wojciech Chojnacki
Instytut Matematyki Stosowanej i Mechanili, Uniwersytet Warszawski,
ul. Banacha 2, 02-097 Warszawa, Poland
e-mail: wojtekch@appli.mimuw.edu.pl
Department of Computer Science, University of Adalaide, Adelaide,
SA 5005, Australia
e-mail: wojtek@cs.adelaide.edu.au
Abstract. We give an elementary proof of the following
result: If G is a compact non-zero Abelian group with dual
isomorphic to a subgroup of Q, such that
U ∪ (-U)
= G \ G(2) and
U ∩ (-U)
= Ø
for some open subset U
⊂ G,
where G(2) = {a
∈ G : 2a = 0},
then G is topologically isomorphic with
T.
1991 Mathematics Subject Classification.
22C05, 22B05.
Key words and phrases. Compact, connected, decomposable,
Abelian group.
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