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

Tomita, Artur H.

Canadian mathematical bulletin, Tome 39 (1996) no. 4, pp. 486-498

Résumé

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.

Détail

DOI : 10.4153/CMB-1996-057-6

Mots-clés : 22A99, 54A35, 03E50, Wallace problem, MAcountable, p-compactness, countable compactness, topological semigroups

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