Real Functions, covers and bornologies

Rok, strany: 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.

ISO 690:

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

APA:

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

Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava

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