### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Fundamenta Mathematicae*,

*165*(1), 17-28.

**Homotopy and homology groups of the n-dimensional Hawaiian earring.** / Katsuya, Eda; Kawamura, Kazuhiro.

Research output: Contribution to journal › Article

*Fundamenta Mathematicae*, vol. 165, no. 1, pp. 17-28.

}

TY - JOUR

T1 - Homotopy and homology groups of the n-dimensional Hawaiian earring

AU - Katsuya, Eda

AU - Kawamura, Kazuhiro

PY - 2000

Y1 - 2000

N2 - For the n-dimensional Hawaiian earring ℍn, n ≥ 2, πn(ℍn, o) ≃ ℤω and πi(ℍn,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 Hn(X V Y) ≃ Hn(X) ⊕ Hn(Y) ⊕ Hn(CX V CY) for n ≥ 1.

AB - For the n-dimensional Hawaiian earring ℍn, n ≥ 2, πn(ℍn, o) ≃ ℤω and πi(ℍn,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 Hn(X V Y) ≃ Hn(X) ⊕ Hn(Y) ⊕ Hn(CX V CY) for n ≥ 1.

KW - Cech homotopy group

KW - Homology group

KW - n-dimensional Hawaiian earring

UR - http://www.scopus.com/inward/record.url?scp=0034360837&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034360837&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0034360837

VL - 165

SP - 17

EP - 28

JO - Fundamenta Mathematicae

JF - Fundamenta Mathematicae

SN - 0016-2736

IS - 1

ER -