Real Functions, covers and bornologies

Year, pages: 2021, 199 - 214

The paper tries to survey the recent results about relationships between covering properties of a topological space $X$ and the space $\rm{USC}{X}$ of upper semicontinuous functions on $X$ with the topology of pointwise convergence. Dealing with properties of continuous functions $\rm{C}{X}$, we need shrinkable covers. The results are extended for ${\mathcal A}$-measurable and upper ${\mathcal A}$-semimeasurable functions where ${\mathcal A}$ is a family of subsets of $X$. Similar results for covers respecting a bornology and spaces $\rm{USC}$ or $\rm{C}{X}$ endowed by a topology defined by using the bornology are presented. Some of them seem to be new.

Bukovský, L. 2021. Real Functions, covers and bornologies. In Tatra Mountains Mathematical Publications, vol. 78, no.1, pp. 199-214. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2021-0014

Bukovský, L. (2021). Real Functions, covers and bornologies. Tatra Mountains Mathematical Publications, 78(1), 199-214. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2021-0014

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava

https://creativecommons.org/licenses/by-nc-nd/4.0/