Finite-to-one maps and dimension

Fundamenta Mathematicae (2004)

• Volume: 182, Issue: 2, page 95-106
• ISSN: 0016-2736

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Abstract

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It is shown that for every at most k-to-one closed continuous map f from a non-empty n-dimensional metric space X, there exists a closed continuous map g from a zero-dimensional metric space onto X such that the composition f∘g is an at most (n+k)-to-one map. This implies that f is a composition of n+k-1 simple ( = at most two-to-one) closed continuous maps. Stronger conclusions are obtained for maps from Anderson-Choquet spaces and ones that satisfy W. Hurewicz's condition (α). The main tool is a certain extension of the Lebesgue-Čech dimension to finite-to-one closed continuous maps.

How to cite

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Jerzy Krzempek. "Finite-to-one maps and dimension." Fundamenta Mathematicae 182.2 (2004): 95-106. <http://eudml.org/doc/286632>.

@article{JerzyKrzempek2004,
abstract = {It is shown that for every at most k-to-one closed continuous map f from a non-empty n-dimensional metric space X, there exists a closed continuous map g from a zero-dimensional metric space onto X such that the composition f∘g is an at most (n+k)-to-one map. This implies that f is a composition of n+k-1 simple ( = at most two-to-one) closed continuous maps. Stronger conclusions are obtained for maps from Anderson-Choquet spaces and ones that satisfy W. Hurewicz's condition (α). The main tool is a certain extension of the Lebesgue-Čech dimension to finite-to-one closed continuous maps.},
author = {Jerzy Krzempek},
journal = {Fundamenta Mathematicae},
keywords = {covering dimension of maps; closed map; at most -to-one map (= map of order ); composition; theorem on dimension-raising maps; Hurewicz’s condition ; Anderson-Choquet space; Cook continuum},
language = {eng},
number = {2},
pages = {95-106},
title = {Finite-to-one maps and dimension},
url = {http://eudml.org/doc/286632},
volume = {182},
year = {2004},
}

TY - JOUR
AU - Jerzy Krzempek
TI - Finite-to-one maps and dimension
JO - Fundamenta Mathematicae
PY - 2004
VL - 182
IS - 2
SP - 95
EP - 106
AB - It is shown that for every at most k-to-one closed continuous map f from a non-empty n-dimensional metric space X, there exists a closed continuous map g from a zero-dimensional metric space onto X such that the composition f∘g is an at most (n+k)-to-one map. This implies that f is a composition of n+k-1 simple ( = at most two-to-one) closed continuous maps. Stronger conclusions are obtained for maps from Anderson-Choquet spaces and ones that satisfy W. Hurewicz's condition (α). The main tool is a certain extension of the Lebesgue-Čech dimension to finite-to-one closed continuous maps.
LA - eng
KW - covering dimension of maps; closed map; at most -to-one map (= map of order ); composition; theorem on dimension-raising maps; Hurewicz’s condition ; Anderson-Choquet space; Cook continuum
UR - http://eudml.org/doc/286632
ER -

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