Fixed point property on symmetric products (Q649784)

The authors describe a continuum \(X\) such that \(F_2(X)\) has the fixed point property while \(X\) does not have it. A continuum is a compact connected metric space. For a continuum \(X\) and a positive integer \(n\) the symmetric product \(F_n(X)\) is the set of all nonempty, closed subsets of \(X\) having at most \(n\) points. A continuum \(X\) has the fixed point property if for each continuous map \(f : X \rightarrow X\), there exists a point \(p \in X\) such that \(f(p) = p\).