Abstract: Let T:X→X be a continuous mapping on a compact metric space (X,d). In this paper, the authors give a direct proof of the equality of the pressure of T and that of T restricted to its non-wandering set, P(T,f)=(T|_\Omega,f|_\Omega),f\in C(X,R,without applying the variational principle. The authors also discuss the relation of the pressures of two systems which are semiconjugate, and show that the pressure is invariant under the uniformly finite-to-one semi-conjugacy.

Key words: Topological entropy, Topological pressure, Topological semi-conjugacy.