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

Ana Carolina Boero, and Artur Hideyuki Tomita. "A group topology on the free abelian group of cardinality 𝔠 that makes its square countably compact." Fundamenta Mathematicae 212.3 (2011): 235-260. <http://eudml.org/doc/282787>.

@article{AnaCarolinaBoero2011,
abstract = {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.},
author = {Ana Carolina Boero, Artur Hideyuki Tomita},
journal = {Fundamenta Mathematicae},
keywords = {topological group; countable compactness; free Abelian group; Wallace's problem},
language = {eng},
number = {3},
pages = {235-260},
title = {A group topology on the free abelian group of cardinality 𝔠 that makes its square countably compact},
url = {http://eudml.org/doc/282787},
volume = {212},
year = {2011},
}

TY - JOUR
AU - Ana Carolina Boero
AU - Artur Hideyuki Tomita
TI - A group topology on the free abelian group of cardinality 𝔠 that makes its square countably compact
JO - Fundamenta Mathematicae
PY - 2011
VL - 212
IS - 3
SP - 235
EP - 260
AB - 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.
LA - eng
KW - topological group; countable compactness; free Abelian group; Wallace's problem
UR - http://eudml.org/doc/282787
ER -