In his 1964 paper on f f -expansions, Parry studied piecewise- continuous, piecewise-monotonic maps F F of the interval [ 0 , 1 ] [0,1] , and introduced a notion of topological transitivity different from any of the modern definitions. This notion, which we call Parry topological transitivity (PTT), is that the backward orbit O − ( x ) = { y : x = F n y \ for\ some\  n ≥ 0 } O^-(x)=\{y:x=F^ny\text {\ for\ some\ }n\ge 0\} of some x ∈ [ 0 , 1 ] x\in [0,1] is dense. We take topological transitivity (TT) to mean that some x x has a dense forward orbit. Parry’s application of PTT to f f -expansions is that PTT implies the partition of [ 0 , 1 ] [0,1] into the “fibers” of F F is a generating partition (i.e., f f -expansions are “valid”). We prove the same result for TT, and use this to show that for interval maps F F , TT implies PTT. A separate proof is provided for continuous maps F F of perfect Polish spaces. The converse is false.