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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On classes of maps which preserve finitisticness


Authors: Akira Koyama and Manuel A. Moron
Journal: Proc. Amer. Math. Soc. 130 (2002), 3091-3096
MSC (2000): Primary 55M10, 54F45
Published electronically: March 13, 2002
MathSciNet review: 1908934
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Abstract: We shall prove the following: $(1)$ Let $r:X \to Y$ be a refinable map between paracompact spaces. Then $X$ is finitistic if and only if $Y$ is finitistic. $(2)$ Let $f:X \to Y$ be a hereditary shape equivalence between metric spaces. Then if $X$ is finitistic, $Y$ is finitistic.


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Additional Information

Akira Koyama
Affiliation: Division of Mathematical Sciences, Osaka Kyoiku University, Kashiwara, Osaka 582-8582, Japan
Email: koyama@cc.osaka-kyoiku.ac.jp

Manuel A. Moron
Affiliation: Unidad Dovente de Matematicas, E. T. S. I. Montes, Universidad Polittecnica, 28040, Madrid, Spain
Email: mam@montes.upm.es

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06402-X
PII: S 0002-9939(02)06402-X
Keywords: Finitistic spaces, refinable maps, c-refinable maps, hereditary shape equivalences, extension dimension, cohomological dimension
Received by editor(s): December 12, 2000
Received by editor(s) in revised form: April 24, 2001
Published electronically: March 13, 2002
Additional Notes: This work was started when the first author visited Departmento de Geometria y Topologia, Facultad de Ciencias Matematicas, Universidad Complutense de Madrid.
Communicated by: Alan Dow
Article copyright: © Copyright 2002 American Mathematical Society