A characterization of pseudocompactness - Prabduh Ram Misra; Vinodkumar (International Journal of Mathematics and Mathematical Sciences)
It is proved here that a completely regular Hausdorff space X is pseudocompact if and only if for any continuous function f from X to a pseudocompact space (or a compact space) Y, f*ϕ is z-ultrafilter whenever ϕ is a z-ultrafilter on X.