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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The fundamental groups of one-dimensional wild spaces and the Hawaiian earring


Author: Katsuya Eda
Journal: Proc. Amer. Math. Soc. 130 (2002), 1515-1522
MSC (1991): Primary 55Q20, 55Q70
Published electronically: November 9, 2001
MathSciNet review: 1879978
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Abstract: Let $X$ be a one-dimensional space which contains a copy $C$of a circle and let it not be semi-locally simply connected at any point on $C.$ Then the fundamental group of $X$ cannot be embeddable into a free $\sigma$-product of n-slender groups, for instance, the fundamental group of the Hawaiian earring. Consequently, any one of the fundamental groups of the Sierpinski gasket, the Sierpinski curve, and the Menger curve is not embeddable into the fundamental group of the Hawaiian earring.


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Additional Information

Katsuya Eda
Affiliation: School of Science and Engineering, Waseda University, Tokyo 169-8555, Japan
Email: eda@logic.info.waseda.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06431-0
PII: S 0002-9939(01)06431-0
Keywords: Fundamental group, one-dimensional, Menger curve, Sierpinski gasket, Hawaiian earring
Received by editor(s): February 10, 1999
Received by editor(s) in revised form: October 31, 2000
Published electronically: November 9, 2001
Communicated by: Ralph Cohen
Article copyright: © Copyright 2001 American Mathematical Society