Refinable maps in dimension theory
type: Item
instance of: scholarly article
title: Refinable maps in dimension theory
zbMATH Open document ID: 0541.54045
DOI: 10.1016/0166-8641(84)90045-2
author: Akira Koyama
published in: Topology and its Applications
publication date: 1984-01-01T00:00:00Z
review text: A map f from a compact metric space X onto a compact metric space Y is said to be refinable if for each \(\epsilon>0\) there is an \(\epsilon\)-map from X onto Y whose distance from f is less than \(\epsilon\). The notion of refinability can be extended to maps between arbitrary spaces. It is proved that refinable maps between compact Hausdorff spaces preserve covering dimension exactly and also preserve weak infinite-dimension. A more specialized notion of a closed-refinable (c-refinable) map is introduced. It is shown that if a surjective map between normal spaces is c-refinable, then its Stone-Čech extension is refinable, from which it is deduced that c-refinable maps between normal spaces preserve covering dimension exactly. The paper concludes with a discussion of the relationship between the classes of c-refinable and proper refinable mappings.
Mathematics Subject Classification ID: 54F45
Mathematics Subject Classification ID: 54C10
zbMATH DE Number: 3859992
zbMATH Keywords: preservation by c-refinable maps
zbMATH Keywords: covering dimension
zbMATH Keywords: weak infinite- dimension
zbMATH Keywords: normal spaces
MaRDI profile type: Publication
full work available at URL: 0166-8641(84)90045-2
OpenAlex ID: W1967770718
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description: scientific article; zbMATH DE number 3859992