Let $X$ be a locally compact space. A subfamily $\mathcal{F}$ of the space$D^\ast( X ; \mathbb{R} )$ of densely continuous forms with nonempty compact values from $X$to \mathbb{R} equipped with the topology $\tau_{UC}$ of uniform convergence on compact setsis compact if and only if ${\rm{sup}(F) : F \in F$ is compact in the space $Q( X; \mathbb{R} )$of quasicontinuous functions from $X$ to $ \mathbb{R} $ equipped with the topology $\tau_{UC}$.
@article{470,
title = {Quasicontinuous functions, densely continuous forms and compactness},
journal = {Tatra Mountains Mathematical Publications},
volume = {68},
year = {2017},
language = {EN},
url = {http://dml.mathdoc.fr/item/470}
}
Holá, Ľubica; Holý, Dušan. Quasicontinuous functions, densely continuous forms and compactness. Tatra Mountains Mathematical Publications, Tome 68 (2017) . http://gdmltest.u-ga.fr/item/470/