### Abstract

The concept of C _{k}-spaces is introduced, situated at an intermediate stage between H-spaces and T-spaces. The C _{k}-space corresponds to the k-th Milnor-Stasheff filtration on spaces. It is proved that a space X is a C _{k}-space if and only if the Gottlieb set G(Z, X) = [Z, X] for any space Z with cat Z ≤ k, which generalizes the fact that X is a T-space if and only if G(σB, X) = [σB, X] for any space B. Some results on the C _{k}-space are generalized to the C _{k}-space for a map f : A → X. Projective spaces, lens spaces and spaces with a few cells are studied as examples ofC _{k}-spaces, and non-C _{k}-spaces.

Original language | English |
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Pages (from-to) | 523-536 |

Number of pages | 14 |

Journal | Canadian Mathematical Bulletin |

Volume | 55 |

Issue number | 3 |

DOIs | |

Publication status | Published - Aug 29 2012 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Iwase, N., Mimura, M., Oda, N., & Yoon, Y. S. (2012). The Milnor-stasheff filtration on spaces and generalized cyclic maps.

*Canadian Mathematical Bulletin*,*55*(3), 523-536. https://doi.org/10.4153/CMB-2011-130-8