ABSTRACT
A continuum is a compact connected metric space. Given a continuum X, a mean on X is a continuous function m : X x X —> X such that m(x,y) = m(y,x) for every x,y € X, and m(x, x) = x for each x £ X. Means have been studied by a number of authors. Among many other results, it is known that:
—if a continuum X admits a mean, then X is unicoherent ([3]), —the sin(j)-continuum admits no mean ([2]), —the dyadic solenoid admits a mean ([9, Example 76.6]), —if X is an hereditarily unicoherent continuum and X contains a pseudo-arc, then X does not admit a mean ([10, Theorem 2.5]), —there are smooth dendroids which admit no mean ([7, Example 5.53]),
The interested reader can find more information and questions about means in [5], [7] and [9, Section 76].
