Pseudocompactness and invariance of continuity
Given a space (X, ˕) and a class Σ of spaces, we study the topologies comparable to ˕ which determine the same continuous functions into all spaces of Σ, which we call the Σ-invariant expansions and compressions of ˕. We extend results of E. Kocela relating pseudo-compactness and real-invariant expansions to obtain characterizations of minimal perfectly Hausdorff and perfectly Hausdorff-closed spaces. We solve by a counterexample the problem posed by Kocela of whether his necessary conditions for a real-invariant expansion of the unit interval are sufficient. Nontrivial examples of maximal real-invariant expansions are given.