Geodesic
A group topology on the free abelian group of cardinality $\mathfrak{c}$ that makes its square countably compact
Ana Carolina Boero 1   ; Artur Hideyuki Tomita 1
1 Instituto de Matemática e Estatística Universidade de São Paulo Rua do Matão, 1010, CEP 05508-090 São Paulo, Brazil
Fundamenta Mathematicae, Tome 212 (2011) no. 3, pp. 235-260 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm212-3-3
Keywords: under mathfrak mathfrak prove possible endow abelian group cardinality mathfrak group topology makes its square countably compact answers question posed madariaga garcia tomita tkachenko prove there exists wallace semigroup countably compact both sided cancellative topological semigroup which topological group whose square countably compact answers question posed grant

Ana Carolina Boero  1   ; Artur Hideyuki Tomita  1

1 Instituto de Matemática e Estatística Universidade de São Paulo Rua do Matão, 1010, CEP 05508-090 São Paulo, Brazil 
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Ana Carolina Boero; Artur Hideyuki Tomita. A group topology on the free abelian group of cardinality $\mathfrak{c}$ that makes its square countably compact. Fundamenta Mathematicae, Tome 212 (2011) no. 3, pp. 235-260. doi: 10.4064/fm212-3-3

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