Pseudocompactness and invariance of continuity

Authors

Joe A. Guthrie, University of Texas at El PasoFollow
H. E. Stone, University of Pittsburgh

Publication Date

1977

Document Type

Article

Comments

Guthrie JA, Stone HE. Pseudocompactness and invariance of continuity. General Topology and its Applications 1977 March 1977;7(1):1-13.

Abstract

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.