@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} }