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), 325330
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 twosided 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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Additional Information
Desmond Robbie
Email:
robbie@mundoe.maths.mu.oz.au
Sergey Svetlichny
Email:
svet@mundoe.maths.mu.oz.au
DOI:
http://dx.doi.org/10.1090/S0002993996034181
PII:
S 00029939(96)034181
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
