Cook continuum, function spaces and free topological groups, Part II

A Cook continuum is a one-dimensional compact connected metric space M which is rigid in a very strong sense: for every subcontinuum C of M, every continuous map f : C→M is either the identity or is constant. In my talk, I will show that a Cook continuum can serve as a counterexample to some natural questions in the theory of function spaces as well as in the theory of free topological groups.