A compact space E is called projective if for each mapping ψ of E into a compact space X, and each continuous mapping τ of a compact space Y onto X, there is a continuous mapping φ of E into Y such that ψ = τ o φ.
© 1965 Duke University Press
Henriksen, M., and M. Jerison. "Minimal projective extensions of compact spaces." Duke Mathematical Journal 32.2 (1965): 291–295. DOI:10.1215/S0012-7094-65-03229-1