### 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 σ-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.

Original language | English |
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Pages (from-to) | 1515-1522 |

Number of pages | 8 |

Journal | Proceedings of the American Mathematical Society |

Volume | 130 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2002 |

### Fingerprint

### Keywords

- Fundamental group
- Hawaiian earring
- Menger curve
- One-dimensional
- Sierpinski gasket

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**The fundamental groups of one-dimensional wild spaces and the Hawaiian earring.** / Eda, Katsuya.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 130, no. 5, pp. 1515-1522. https://doi.org/10.1090/S0002-9939-01-06431-0

}

TY - JOUR

T1 - The fundamental groups of one-dimensional wild spaces and the Hawaiian earring

AU - Eda, Katsuya

PY - 2002

Y1 - 2002

N2 - 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 σ-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.

AB - 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 σ-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.

KW - Fundamental group

KW - Hawaiian earring

KW - Menger curve

KW - One-dimensional

KW - Sierpinski gasket

UR - http://www.scopus.com/inward/record.url?scp=0035994116&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035994116&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-01-06431-0

DO - 10.1090/S0002-9939-01-06431-0

M3 - Article

VL - 130

SP - 1515

EP - 1522

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 5

ER -