A group topology on the free abelian group of cardinality 𝔠 that makes its square countably compact

• Autorzy: Ana Carolina Boero , Artur Hideyuki Tomita
• Języki publikacji: EN

Abstrakty

EN

Under 𝔭 = 𝔠, we prove that it is possible to endow the free abelian group of cardinality 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.

Kategorie tematyczne

• 54G20: Counterexamples
• 54A35: Consistency and independence results
• 54H11: Topological groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 212
• Numer: 3
• Strony: 235-260

Daty

wydano

2011

Twórcy

autor

Ana Carolina Boero

• Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, CEP 05508-090, São Paulo, Brazil

autor

Artur Hideyuki Tomita

• Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, CEP 05508-090, São Paulo, Brazil

Identyfikatory

DOI

10.4064/fm212-3-3