  In his 1964 paper on f-expansions, Parry studied piecewise-continuous,
piecewise-monotonic maps F of the interval [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^ny for some n\ge 0} of some x\in[0,1) is dense. We
take topological transitivity (TT) to mean that some $x$ has a dense forward
orbit. Parry's application to f-expansions is that PTT implies the partition of
[0,1) into the "fibers" of F is a generating partition (i.e., f-expansions are
"valid"). We prove the same result for TT, and use this to show that for
interval maps F, TT implies PTT. A separate proof is provided for continuous
maps F of compact metric spaces. The converse is false.
