Uncountable families of fans that admit transitive homeomorphisms

Recently, we constructed transitive homeomorphisms on the Cantor fan and the Lelek fan. In this paper, we construct a family of uncountably many pairwise non-homeo­morphic smooth fans that admit transitive homeomorphisms. In order to do this, we use our recently developed techniques of combining Mahavier products of closed relations on intervals with quotients of dynamical systems. In addition, we show that the star of Cantor fans admits a transitive homeomorphism. At the end of the paper, we also construct a family of uncountably many pairwise non-homeomorphic non-smooth fans that admit transitive homeomorphisms.