### 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 |
---|---|

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 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*130*(10), 3091-3096. https://doi.org/10.1090/S0002-9939-02-06402-X

**On classes of maps which preserve finitisticness.** / Koyama, Akira; Moron, Manuel A.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 130, no. 10, pp. 3091-3096. https://doi.org/10.1090/S0002-9939-02-06402-X

}

TY - JOUR

T1 - On classes of maps which preserve finitisticness

AU - Koyama, Akira

AU - Moron, Manuel A.

PY - 2002/10

Y1 - 2002/10

N2 - 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.

AB - 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.

KW - C-refinable maps

KW - Cohomological dimension

KW - Extension dimension

KW - Finitistic spaces

KW - Hereditary shape equivalences

KW - Refinable maps

UR - http://www.scopus.com/inward/record.url?scp=0036788791&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036788791&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-02-06402-X

DO - 10.1090/S0002-9939-02-06402-X

M3 - Article

AN - SCOPUS:0036788791

VL - 130

SP - 3091

EP - 3096

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 10

ER -