# Finite-to-one maps and dimension

Fundamenta Mathematicae (2004)

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

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topJerzy 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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