Notes on relative topological conditional entropy

In order to provide a non-trivial sufficient condition for the existence of invariant measures with maximal relative measure-theoretic entropy, in [16] the concept of relative topological conditional entropy was introduced for any factor map between topological dynamical systems, and a Ledrappier's type variational principle concerning it was obtained and some basic properties were discussed. In this paper, following the ideas of Bowen in [2] and Misiurewicz in [13], we present a purely topological proof of some results from [16], where they were first proved in [16] via measure-theoretic methods. Furthermore, we will also explore some properties of relative topological conditional entropy.