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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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/S0002-9939-96-03418-1

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