Strongly countable dimensional compacta form the Hurewicz set

The hyperspaces of strongly countable dimensional compacta of positive dimension and of strongly countable dimensional continua of dimension greater than 1 in the Hilbert cube are homeomorphic to the Hurewicz set of all nonempty countable closed subsets of the unit interval [ 0 , 1 ] . These facts h...

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Bibliographic Details
Published in:Topology and its applications 2007-03, Vol.154 (5), p.996-1001
Main Authors: Krupski, Paweł, Samulewicz, Alicja
Format: Article
Language:English
Subjects:
Absorber
Analytic set
Cohomological dimension
Countable dimensional space
Hilbert cube
Hurewicz set
Hyperspace
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Summary:The hyperspaces of strongly countable dimensional compacta of positive dimension and of strongly countable dimensional continua of dimension greater than 1 in the Hilbert cube are homeomorphic to the Hurewicz set of all nonempty countable closed subsets of the unit interval [ 0 , 1 ] . These facts hold true, in particular, for covering dimension dim and cohomological dimension dim G , where G is any Abelian group.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2005.02.015