### Abstract

Let X be a Peano continuum. Then the following hold: (1) The singular cohomology group H^{1}(X) is isomorphic to the Čech cohomology group Ȟ^{1}(X). (2) For each homomorphism h: π_{1}(X) → *_{i∈I} G_{i} there exists a finite subset F of I such that Im(h) ⊆ *_{i∈F} G_{i}. (3) For each injective homomorphism h: π_{1}(X) → G_{0} * G_{1} there exists a finitely generated subgroup F_{0} of G_{0} or a finitely generated subgroup F_{1} of G_{1} such that Im(h) ⊆ F_{0} * G_{1} or Im(h) ⊆ G_{0} * F_{1}.

Original language | English |
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Pages (from-to) | 213-226 |

Number of pages | 14 |

Journal | Topology and its Applications |

Volume | 153 |

Issue number | 2-3 SPEC. ISS. |

DOIs | |

Publication status | Published - 2005 Sep 1 |

### Keywords

- Fundamental group
- Homology group
- Peano continua

### ASJC Scopus subject areas

- Geometry and Topology

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## Cite this

Eda, K. (2005). Algebraic topology of Peano continua.

*Topology and its Applications*,*153*(2-3 SPEC. ISS.), 213-226. https://doi.org/10.1016/j.topol.2003.11.012