# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## A group topology on the free abelian group of cardinality $\mathfrak{c}$ that makes its square countably compact

### Tom 212 / 2011

Fundamenta Mathematicae 212 (2011), 235-260 MSC: Primary 54H11; Secondary 54A35, 54G20. DOI: 10.4064/fm212-3-3

#### Streszczenie

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.

#### Autorzy

• Ana Carolina BoeroInstituto de Matemática e Estatística
Rua do Matão, 1010, CEP 05508-090
São Paulo, Brazil
e-mail
• Artur Hideyuki TomitaInstituto de Matemática e Estatística