It is well known that infinite minimal sets for continuous functions on
the interval are Cantor sets; that is, compact zero dimensional metrizable sets without
isolated points. On the other hand, it was proved in Alcaraz and Sanchis (Bifurcat
Chaos 13:1665–1671, 2003) that infinite minimal sets for continuous functions on
connected linearly ordered spaces enjoy the same properties as Cantor sets except
that they can fail to be metrizable. However, no examples of such subsets have been
known. In this note we construct, in ZFC, 2c non-metrizable infinite pairwise nonhomeomorphic
minimal sets on compact connected linearly ordered space
