The space of composants of an indecomposable continuum
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.
scientific article; zbMATH DE number 1751413
scientific article