### Abstract

Apart from simply connected spaces, a non-simply connected co-H-space is a typical example of a space X with a coaction of Bπ _{1} (X) along r^{X} : X → Bπ _{1} (X), the classifying map of the universal covering. If such a space X is actually a co-H-space, then the fibrewise p-localization of r^{X} (or the 'almost' p-localization of X) is a fibrewise co-H-space (or an 'almost' co-H-space, respectively) for every prime p. In this paper, we show that the converse statement is true, i.e. for a non-simply connected space X with a coaction of Bπ _{1} (X) along r^{X} , X is a co-H-space if, for every prime p, the almost p-localization of X is an almost co-H-space.

Original language | English |
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Pages (from-to) | 323-332 |

Number of pages | 10 |

Journal | Proceedings of the Edinburgh Mathematical Society |

Volume | 58 |

Issue number | 2 |

DOIs | |

Publication status | Published - Oct 27 2014 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Proceedings of the Edinburgh Mathematical Society*,

*58*(2), 323-332. https://doi.org/10.1017/S0013091514000078

**Co-H-Spaces and Almost Localization.** / Costoya, Cristina; Iwase, Norio.

Research output: Contribution to journal › Article

*Proceedings of the Edinburgh Mathematical Society*, vol. 58, no. 2, pp. 323-332. https://doi.org/10.1017/S0013091514000078

}

TY - JOUR

T1 - Co-H-Spaces and Almost Localization

AU - Costoya, Cristina

AU - Iwase, Norio

PY - 2014/10/27

Y1 - 2014/10/27

N2 - Apart from simply connected spaces, a non-simply connected co-H-space is a typical example of a space X with a coaction of Bπ 1 (X) along rX : X → Bπ 1 (X), the classifying map of the universal covering. If such a space X is actually a co-H-space, then the fibrewise p-localization of rX (or the 'almost' p-localization of X) is a fibrewise co-H-space (or an 'almost' co-H-space, respectively) for every prime p. In this paper, we show that the converse statement is true, i.e. for a non-simply connected space X with a coaction of Bπ 1 (X) along rX , X is a co-H-space if, for every prime p, the almost p-localization of X is an almost co-H-space.

AB - Apart from simply connected spaces, a non-simply connected co-H-space is a typical example of a space X with a coaction of Bπ 1 (X) along rX : X → Bπ 1 (X), the classifying map of the universal covering. If such a space X is actually a co-H-space, then the fibrewise p-localization of rX (or the 'almost' p-localization of X) is a fibrewise co-H-space (or an 'almost' co-H-space, respectively) for every prime p. In this paper, we show that the converse statement is true, i.e. for a non-simply connected space X with a coaction of Bπ 1 (X) along rX , X is a co-H-space if, for every prime p, the almost p-localization of X is an almost co-H-space.

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UR - http://www.scopus.com/inward/citedby.url?scp=84945448618&partnerID=8YFLogxK

U2 - 10.1017/S0013091514000078

DO - 10.1017/S0013091514000078

M3 - Article

AN - SCOPUS:84945448618

VL - 58

SP - 323

EP - 332

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

IS - 2

ER -