The Monteiro-Botelho-Teixeira axiom and a "natural" topology in abelian semigroups
Aczel, J. (1965)
Portugaliae mathematica
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Displaying similar documents to “Characterizing topology on an Abelian semigroup by a functional equation”
The Monteiro-Botelho-Teixeira axiom and a "natural" topology in abelian semigroups
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A group topology on the free abelian group of cardinality 𝔠 that makes its square countably compact
Ana Carolina Boero, Artur Hideyuki Tomita (2011)
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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.