Quasicontinuous functions, densely continuous forms and compactness

Year, pages: 2017, 93 - 102

Let $X$ be a locally compact space. A subfamily $\mathcal F$ of the space $D^\star (X,\Bbb R)$ of densely continuous forms with nonempty compact values from $X$ to $\Bbb R$ equipped with the topology $\tau_{UC}$ of uniform convergence on compact sets is compact if and only if $\{\sup (F): F\in\mathcal F\}$ is compact in the space $Q(X,\Bbb R)$ of quasicontinuous functions from $X$ to $\Bbb R$ equipped with the topology $\tau_{UC}$.

Holá, Ľ., Holý, D. 2017. Quasicontinuous functions, densely continuous forms and compactness. In Tatra Mountains Mathematical Publications, vol. 68, no.1, pp. 93-102. 1210-3195.

Holá, Ľ., Holý, D. (2017). Quasicontinuous functions, densely continuous forms and compactness. Tatra Mountains Mathematical Publications, 68(1), 93-102. 1210-3195.