Subshifts on open proximal extensions

In this paper, we construct a minimal subshift which is an open proximal extension of its maximal equicontinuous factor. We will show this subshift has positive topological entropy, which gives a negative answer to the question whether open proximal extensions preserve topological entropy. We also show that, in this subshift, its relation corresponding to its maximal equicontinuous factor is the union of the diagonals and the set of entropy pairs.