### Abstract

For the n-dimensional Hawaiian earring ℍ_{n}, n ≥ 2, π_{n}(ℍ_{n}, o) ≃ ℤ^{ω} and π_{i}(ℍ_{n},o) is trivial for each 1 ≤ i ≤ n - 1. Let CX be the cone over a space X and CXVCY be the one-point union with two points of the base spaces X and Y being identified to a point. Then H_{n}(X V Y) ≃ H_{n}(X) ⊕ H_{n}(Y) ⊕ H_{n}(CX V CY) for n ≥ 1.

Original language | English |
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Pages (from-to) | 17-28 |

Number of pages | 12 |

Journal | Fundamenta Mathematicae |

Volume | 165 |

Issue number | 1 |

Publication status | Published - 2000 |

### Keywords

- Cech homotopy group
- Homology group
- n-dimensional Hawaiian earring

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Katsuya, E., & Kawamura, K. (2000). Homotopy and homology groups of the n-dimensional Hawaiian earring.

*Fundamenta Mathematicae*,*165*(1), 17-28.