Under š¯” = š¯” , we prove that it is possible to endow the free abelian group of cardinality š¯” 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm212-3-3,
author = {Ana Carolina Boero and Artur Hideyuki Tomita},
title = {A group topology on the free abelian group of cardinality c that makes its square countably compact},
journal = {Fundamenta Mathematicae},
volume = {215},
year = {2011},
pages = {235-260},
zbl = {1234.54045},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm212-3-3}
}
Ana Carolina Boero; Artur Hideyuki Tomita. A group topology on the free abelian group of cardinality š¯” that makes its square countably compact. Fundamenta Mathematicae, Tome 215 (2011) pp. 235-260. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm212-3-3/