On classes of maps which preserve finitisticness

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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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2002-10, Vol.130 (10), p.3091-3096
Main Authors: Koyama, Akira, Moron, Manuel A.
Format: Article
Language:English
Subjects:
Algebraic topology
Compactification
Equivalence relation
Exact sciences and technology
General topology
Geometric shapes
Mathematical theorems
Mathematics
Polyhedrons
Sciences and techniques of general use
Separable spaces
Topological spaces
Topological theorems
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Vertices
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Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-02-06402-X