### 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 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Co-H-Spaces and Almost Localization'. Together they form a unique fingerprint.

## Cite this

Costoya, C., & Iwase, N. (2014). Co-H-Spaces and Almost Localization.

*Proceedings of the Edinburgh Mathematical Society*,*58*(2), 323-332. https://doi.org/10.1017/S0013091514000078