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The Wallace Problem: A Counterexample from MaCountable and p-Compactness

Published online by Cambridge University Press:  20 November 2018

Artur H. Tomita
Artur H. Tomita*
Affiliation:
Department of Mathematics, Universidade de São Paulo, Caixa Postal 66281, CEP 05389-970, São Paulo SP Brasil, e-mail: tomita@ime.usp.br
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Abstract

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We construct, under MAcountable, a countably compact topological subsemigroup of which is not a group, hence a counterexample for the Wallace problem. We also show that there is no p-compact counterexample for the Wallace problem, answering a question of D. Grant. Finally, we show that—in some sense—our counterexample for the Wallace problem constructed under MAcountable cannot be done in ZFC.

Keywords

22A9954A3503E50Wallace problemMAcountablep-compactnesscountable compactnesstopological semigroups
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 4 , 01 December 1996 , pp. 486 - 498
Copyright
Copyright © Canadian Mathematical Society 1996

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