A group topology on the free abelian group of cardinality $\mathfrak{c}$ that makes its square countably compact
Volume 212 / 2011
Fundamenta Mathematicae 212 (2011), 235-260
MSC: Primary 54H11; Secondary 54A35, 54G20.
DOI: 10.4064/fm212-3-3
Abstract
Under $\mathfrak{p} = \mathfrak{c}$, we prove that it is possible to endow the free abelian group of cardinality $\mathfrak{c}$ with a group topology that makes its square countably compact. This answers a question posed by Madariaga-Garcia and Tomita and by Tkachenko. We also prove that there exists a Wallace semigroup (i.e., a countably compact both-sided cancellative topological semigroup which is not a topological group) whose square is countably compact. This answers a question posed by Grant.
