Structure of the family of composants of an indecomposable continuum
by
Slawomir Solecki
Indiana University

One of the questions on the structure of composants of an indecomposable continuum was that about the existence of a Borel set which has precisely one point in common with each composant (Borel transversal). Partial answers were obtained by Kuratowski, Rogers, Mauldin, and others. The material presented in the talk was motivated by this question and answers it in the negative for all indecomposable continua. In fact, we show that there are only two fundamental types, to be defined precisely in the talk, of the ``space'' of all composants (both of which exclude the existence of a Borel transversal). Additionally, we prove that a connection exists between the type of the space of composants and hereditary indecomposability. It is also shown that there is no straightforward characterization of indecomposable continua with a given type of the composant space. Among other techniques, we use methods and notions developed in descriptive set theory to study Borel equivalence relations.

Date received: February 8, 2001