# Compositions of simple maps

Fundamenta Mathematicae (1999)

- Volume: 162, Issue: 2, page 149-162
- ISSN: 0016-2736

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topKrzempek, Jerzy. "Compositions of simple maps." Fundamenta Mathematicae 162.2 (1999): 149-162. <http://eudml.org/doc/212416>.

@article{Krzempek1999,

abstract = {
A map (= continuous function) is of order ≤ k if each of its point-inverses has at most k elements. Following [4], maps of order ≤ 2 are called simple.
Which maps are compositions of simple closed [open, clopen] maps? How many simple maps are really needed to represent a given map? It is proved herein that every closed map of order ≤ k defined on an n-dimensional metric space is a composition of (n+1)k-1 simple closed maps (with metric domains). This theorem fails to be true for non-metrizable spaces. An appropriate map on a Cantor cube of uncountable weight is described.
},

author = {Krzempek, Jerzy},

journal = {Fundamenta Mathematicae},

keywords = {composition; simple map; closed map; map of order ≤ k; finite-dimensional; zero-dimensional; Cantor cube; metric space; finite dimension},

language = {eng},

number = {2},

pages = {149-162},

title = {Compositions of simple maps},

url = {http://eudml.org/doc/212416},

volume = {162},

year = {1999},

}

TY - JOUR

AU - Krzempek, Jerzy

TI - Compositions of simple maps

JO - Fundamenta Mathematicae

PY - 1999

VL - 162

IS - 2

SP - 149

EP - 162

AB -
A map (= continuous function) is of order ≤ k if each of its point-inverses has at most k elements. Following [4], maps of order ≤ 2 are called simple.
Which maps are compositions of simple closed [open, clopen] maps? How many simple maps are really needed to represent a given map? It is proved herein that every closed map of order ≤ k defined on an n-dimensional metric space is a composition of (n+1)k-1 simple closed maps (with metric domains). This theorem fails to be true for non-metrizable spaces. An appropriate map on a Cantor cube of uncountable weight is described.

LA - eng

KW - composition; simple map; closed map; map of order ≤ k; finite-dimensional; zero-dimensional; Cantor cube; metric space; finite dimension

UR - http://eudml.org/doc/212416

ER -

## References

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