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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


An answer to A.D.Wallace's question about countably compact cancellative semigroups

Authors: Desmond Robbie and Sergey Svetlichny
Journal: Proc. Amer. Math. Soc. 124 (1996), 325-330
MSC (1991): Primary 22A05, 54D20; Secondary 22A15
MathSciNet review: 1328373
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Abstract: It is shown under CH that there exists a countably compact topological semigroup with two-sided cancellation which is not a topological group. Wallace's question" of 40 years standing is thus settled in the negative unless CH is explicitly denied. The example is a topological subsemigroup of an uncountable product of circle groups.

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Desmond Robbie

Sergey Svetlichny

PII: S 0002-9939(96)03418-1
Keywords: Countably compact space, toplogical group, cancellative topological semigroup, Abelian group
Received by editor(s): July 19, 1994
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1996 American Mathematical Society