Refinable maps in dimension theory

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Abstract

This paper studies properties of refinable maps and contains applications to dimension theory. It is proved that refinable maps between compact Hausdorff spaces preserve covering dimension exactly and do not raise small cohomological dimension with any coefficient group. The notion of a c-refinable map is introduced and is shown to play a comparable role in the setting of normal spaces. For example, c-refinable maps between normal spaces are shown to preserve covering dimension and S-weak infinite-dimensionality. These facts do not hold for refinable maps.

Original languageEnglish
Pages (from-to)247-255
Number of pages9
JournalTopology and its Applications
Volume17
Issue number3
DOIs
Publication statusPublished - 1984
Externally publishedYes

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ASJC Scopus subject areas

  • Geometry and Topology

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