On finite-dimensional maps and other maps with "small" fibers
Sternfeld, Yaki
Fundamenta Mathematicae, Tome 146 (1995), p. 127-133 / Harvested from The Polish Digital Mathematics Library
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We prove that if f is a k-dimensional map on a compact metrizable space X then there exists a σ-compact (k-1)-dimensional subset A of X such that f|X∖A is 1-dimensional. Equivalently, there exists a map g of X in Ik such that dim(f × g)=1. These are extensions of theorems by Toruńczyk and Pasynkov obtained under the additional assumption that f(X) is finite-dimensional.  These results are then extended to maps with fibers restricted to some classes of spaces other than the class of k-dimensional spaces. For example: if f has weakly infinite-dimensional fibers then dim(f|X∖A) ≤ 1 for some σ-compact weakly infinite-dimensional subset A of X. The proof applies essentially the properties of hereditarily indecomposable continua.

Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:212078 
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     title = {On finite-dimensional maps and other maps with "small" fibers},
     journal = {Fundamenta Mathematicae},
     volume = {146},
     year = {1995},
     pages = {127-133},
     zbl = {0833.54020},
     language = {en},
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Sternfeld, Yaki. On finite-dimensional maps and other maps with "small" fibers. Fundamenta Mathematicae, Tome 146 (1995) pp. 127-133. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv147i2p127bwm/

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