Compositions of simple maps
Tom 162 / 1999
Fundamenta Mathematicae 162 (1999), 149-162
DOI: 10.4064/fm-162-2-149-162
Streszczenie
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.
