Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Countably compact groups from a selective ultrafilter

Authors: S. Garcia-Ferreira, A. H. Tomita and S. Watson
Journal: Proc. Amer. Math. Soc. 133 (2005), 937-943
MSC (2000): Primary 54G20, 54D80, 22A99; Secondary 54H11
Published electronically: September 29, 2004
MathSciNet review: 2113947
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Abstract: We prove that the existence of a selective ultrafilter on $\omega$ implies the existence of a countably compact group without non-trivial convergent sequences all of whose powers are countably compact. Hence, by using a selective ultrafilter on $\omega$, it is possible to construct two countably compact groups without non-trivial convergent sequences whose product is not countably compact.

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Additional Information

S. Garcia-Ferreira
Affiliation: Instituto de Matemáticas (UNAM), Apartado Postal 61-3, Xangari, 58089, Morelia, Michoacán, México

A. H. Tomita
Affiliation: Departamento de Matemática, Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, CEP 05315-970, São Paulo, Brasil

S. Watson
Affiliation: Department of Mathematics, York University, 474700 Keele Street, M3P 1P3, Toronto, Ontario, Canada

Keywords: $p$-limit, $p$-compact, selective ultrafilter, countably compact group, topological group
Received by editor(s): March 3, 2003
Received by editor(s) in revised form: November 20, 2003
Published electronically: September 29, 2004
Additional Notes: This research was supported by CONACYT grant no. 40057-F and DGAPA grant no. IN104601
Communicated by: Alan Dow
Article copyright: © Copyright 2004 American Mathematical Society