The fundamental groups of one-dimensional wild spaces and the Hawaiian earring
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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.References
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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
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1515-1522
- MSC (1991): Primary 55Q20, 55Q70
- DOI: https://doi.org/10.1090/S0002-9939-01-06431-0
- MathSciNet review: 1879978