### Abstract

Let X be a locally n-connectcd compact metric space. Then, the canonical homomorphism from the singular homology group H_{n+1}(X) to the Čech homology group Ȟ_{n+1}(X) is surjective. Consequently, if a compact metric space X is locally connected, then the canonical homomorphism from H_{1} (X) to Ȟ_{1} (X) is surjective.

Original language | English |
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Pages (from-to) | 1487-1495 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 128 |

Issue number | 5 |

Publication status | Published - 2000 |

### Fingerprint

### Keywords

- Čech homology
- Canonical homomorphism
- Singular homology
- Surjectivc

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*128*(5), 1487-1495.

**The subjectivity of the canonical homomorphism from singular homology to čech homology.** / Eda, Katsuya; Kawamura, Kazuhiro.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 128, no. 5, pp. 1487-1495.

}

TY - JOUR

T1 - The subjectivity of the canonical homomorphism from singular homology to čech homology

AU - Eda, Katsuya

AU - Kawamura, Kazuhiro

PY - 2000

Y1 - 2000

N2 - Let X be a locally n-connectcd compact metric space. Then, the canonical homomorphism from the singular homology group Hn+1(X) to the Čech homology group Ȟn+1(X) is surjective. Consequently, if a compact metric space X is locally connected, then the canonical homomorphism from H1 (X) to Ȟ1 (X) is surjective.

AB - Let X be a locally n-connectcd compact metric space. Then, the canonical homomorphism from the singular homology group Hn+1(X) to the Čech homology group Ȟn+1(X) is surjective. Consequently, if a compact metric space X is locally connected, then the canonical homomorphism from H1 (X) to Ȟ1 (X) is surjective.

KW - Čech homology

KW - Canonical homomorphism

KW - Singular homology

KW - Surjectivc

UR - http://www.scopus.com/inward/record.url?scp=27644597069&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27644597069&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:27644597069

VL - 128

SP - 1487

EP - 1495

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 5

ER -