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An answer to A.D.Wallace's question about countably compact cancellative semigroups
Author(s):
Desmond
Robbie;
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.
References:
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- C2
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- D
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- D. L. Grant, Sequentially compact cancellative topological semigroups: some progress on the Wallace problem, in Papers on General Topology and Applications, Seventh Summer Conference at the University of Wisconsin" (Madison, 1991), Annals of the New York Acad. Sci. 704 (1993), Susan Andima et al (eds.), NY, 150-154, MR 95b:22006.
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- Artur H. Tomita, Extending the Robbie-Svetlichny solution of Wallace's problem to MA, preprint (November 1994).
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- A.D. Wallace, The structure of topological semigroups, Amer. Math. Soc. Bull. 61 (1955), 95-112, MR 16:796d.
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Additional Information:
Desmond
Robbie
Affiliation:
Department of Mathematics, The University of Melbourne, Parkville, Victoria, Australia 3052
Email:
robbie@mundoe.maths.mu.oz.au
Sergey
Svetlichny
Affiliation:
Department of Mathematics, The University of Melbourne, Parkville, Victoria, Australia 3052
Email:
svet@mundoe.maths.mu.oz.au
DOI:
10.1090/S0002-9939-96-03418-1
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
Copyright of article:
Copyright
1996,
American Mathematical Society
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