Functional characterizations of certain p-spaces
The authors prove the following theorem. A completely regular space Y is a p-space (respectively, a Čech-complete space) with a \(G_{\delta}\)-diagonal iff given a dense subspace A of any space X and a continuous \(f: A\to Y\) there is a p-embedded subset (resp. a \(G_{\delta}\)-subset) M of X which contains A and a continuous \(\hat f:\) \(M\to Y\) which extends f. This generalizes the well-known analogous result for completely metrizable spaces.
scientific article; zbMATH DE number 3899729