Z-pseudocompact

Definition

Let C(X,Z) denote the ring of all integer-valued continuous functions on a topological spaces and C^*(X,Z) the ring of all bounded integer-valued continuous functions.
X is called Z-pseudocompact if C(X,Z)=C^*(X,Z).

Reference

R. S. Pierce, Rings of Integer-Valued Continuous Functions, Transactions of the American Mathematical Society, Vol.100, No.3(1961), pp.371-394.