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 | References | Similar Articles | Additional Information

Abstract: We prove that the existence of a selective ultrafilter on 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 , 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

Email:
sgarcia@matmor.unam.mx

**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

Email:
tomita@ime.usp.br

**S. Watson**

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

Email:
watson@mathstat.yorku.ca

DOI:
http://dx.doi.org/10.1090/S0002-9939-04-07684-1

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