Geodesic
Compositions of simple maps
Fundamenta Mathematicae, Tome 162 (1999) no. 2, pp. 149-162 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm-162-2-149-162
Mots-clés : composition, simple map, closed map, map of order ≤ k, finite-dimensional, zero-dimensional, Cantor cube

Jerzy Krzempek 1

1 
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Jerzy Krzempek. Compositions of simple maps. Fundamenta Mathematicae, Tome 162 (1999) no. 2, pp. 149-162. doi: 10.4064/fm-162-2-149-162

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