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ArticleOriginal scientific text

Title

Compositions of simple maps

Authors 1

Affiliations

  1. Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

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.

Keywords

ENG
composition, simple map, closed map, map of order ≤ k, finite-dimensional, zero-dimensional, Cantor cube

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Fundamenta Mathematicae
1999/162/2
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Pages:
149-162
Main language of publication
English
Received
1998-01-08
Accepted
1998-10-05
Published
1999
Exact and natural sciences