We show that a completely regular space Y is a p-space (a Čech-complete space, a locally compact space) if and only if given a dense subspace A of any topological space X and a continuous f: A → Y there are a p-embedded subset (resp. a G δ-subset, an open subset) M of X containing A and a quasicontinuous subcontinuous extension f*: M → Y of f continuous at every point of A. A result concerning a continuous extension to a residual set is also given.
@article{bwmeta1.element.doi-10_2478_s11533-013-0311-z,
author = {\v Lubica Hol\'a},
title = {Functional characterizations of p-spaces},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {2197-2202},
zbl = {1291.54024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0311-z}
}
Ľubica Holá. Functional characterizations of p-spaces. Open Mathematics, Tome 11 (2013) pp. 2197-2202. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0311-z/
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