### Abstract

We shall prove the following: (1) Let r: X → Y be a refinable map between paracompact spaces. Then X is finitistic if and only if Y is finitistic. (2) Let f: X → Y be a hereditary shape equivalence between metric spaces. Then if X is finitistic, Y is finitistic.

Original language | English |
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Pages (from-to) | 3091-3096 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 130 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2002 Oct 1 |

Externally published | Yes |

### Keywords

- C-refinable maps
- Cohomological dimension
- Extension dimension
- Finitistic spaces
- Hereditary shape equivalences
- Refinable maps

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Koyama, A., & Moron, M. A. (2002). On classes of maps which preserve finitisticness.

*Proceedings of the American Mathematical Society*,*130*(10), 3091-3096. https://doi.org/10.1090/S0002-9939-02-06402-X