The space of composants of an indecomposable continuum
type: Item
instance of: scholarly article
title: The space of composants of an indecomposable continuum
zbMATH Open document ID: 1014.54021
published in: Advances in Mathematics
publication date: 2003-07-01T00:00:00Z
review text: This is a very substantial and well written paper concerning the possible complexity of the family of composants of a metric continuum. A composant of an indecomposable continuum (no two proper subcontinua cover) is a maximal set any two points of which lie in a proper subcontinuum. These form a partition and the theme of study in this paper, measuring the size and complexity of the space, is a very important line of investigation. A natural question to ask is whether there is a Borel function from the continuum into the reals which sends distinct composants to distinct points. Rogers noticed the relationship between such questions and the Effros theorem. The approach in this paper is to analyze thoroughly the Borel complexity of the space of composants. It is shown that up to Borel bireducibility there are only two types, one ``simple'' and the second quite complex.
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 54D05
zbMATH DE Number: 1751413
zbMATH Keywords: composant
zbMATH Keywords: indecomposable
zbMATH Keywords: Borel equivalence
author: Sławomir Solecki
reviewed by: Alan Dow
MaRDI profile type: Publication
full work available at URL: aima.2001.2002
OpenAlex ID: W1965565947
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DOI: 10.1006/AIMA.2001.2002
description: scientific article; zbMATH DE number 1751413