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Compositions of simple maps

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Krzempek J.

Fundamenta Mathematicae

1999

tom 162

nr 2

149-162

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.

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1 Fundamenta Mathematicae

1 Krzempek J.

1 1999

Wyniki wyszukiwania

Compositions of simple maps