@article {
author = {Hoim, Terje and Robbins, David},
title = {Cover topologies, subspaces, and quotients for some spaces of vector-valued functions},
journal = {Advances in Operator Theory},
volume = {3},
number = {2},
pages = {351-364},
year = {2018},
publisher = {Tusi Mathematical Research Group (TMRG)},
issn = {2538-225X},
eissn = {2538-225X},
doi = {10.15352/aot.1706-1177},
abstract = {Let $X$ be a completely regular Hausdorff space, and let $\mathcal{D}$ be a cover of $X$ by $C_{b}$-embedded sets. Let $\pi :\mathcal{E}$ $\rightarrow X$ be a bundle of Banach spaces (algebras), and let $\Gamma(\pi)$ be the section space of the bundle $\pi .$ Denote by $\Gamma _{b}(\pi,\mathcal{D})$ the subspace of $\Gamma (\pi )$ consisting of sections which are bounded on each $D\in \mathcal{D}$. We construct a bundle $\rho ^{\prime }:\mathcal{F}^{\prime}\rightarrow \beta X$ such that $\Gamma _{b}(\pi ,\mathcal{D}) $ is topologically and algebraically isomorphic to $\Gamma(\rho^\prime)$, and use this to study the subspaces (ideals) and quotients resulting from endowing $\Gamma _{b}(\pi,\mathcal{D})$ with the cover topology determined by $\mathcal{D}$.},
keywords = {cover topology,bundle of Banach spaces,bundle of Banach algebras},
url = {http://www.aot-math.org/article_51020.html},
eprint = {http://www.aot-math.org/article_51020_60279e56eda0cbf7a35f61829763ebe5.pdf}
}