  In our previous paper [9], we have introduced topological nearly entropy,
Ent_N (f) by restricting X into a class of nearly compact spaces. In the
present paper, some additional properties of this notion are studied.
Furthermore, we introduce another new notion of topological nearly entropy of f
denoted by Ent_n (f) when the whole space X itself is nearly compact. We show
the relationship between these two notions for the class of nearly compact
subspaces. We also propose new space, namely, R-space in studying the
topological nearly entropy on nearly compact and Hausdorff space. As a
consequence, the topological nearly entropy of f and it restriction f|K
coincides. Finally, some fundamental properties of topological nearly entropy
for product space are obtained.
