The composant equivalence relation of an indecomposable continuum
by
David Ryden
Baylor University

The composant equivalence relation of an indecomposable continuum X comes in two varieties. For the simpler of the two, which includes Knaster continua and all indecomposable inverse limits of Markov maps on intervals, there is a Borel function f from X into {0, 1}^N such that two points, x and y, of X belong to the same composant of X if and only if f(x) agrees with f(y) in cofinitely many coordinates. For inverse limits of Markov maps on intervals, there is a natural way to define such a function f. In this talk we will consider the following question: What, if anything, does the function f, or rather its range as a subset of {0, 1}^N, tell us about the topology of the continuum X?

Date received: February 28, 2006