Hoim, T., Robbins, D. (2018). Cover topologies, subspaces, and quotients for some spaces of vector-valued functions. Advances in Operator Theory, 3(2), 351-364. doi: 10.15352/aot.1706-1177

Terje Hoim; David Robbins. "Cover topologies, subspaces, and quotients for some spaces of vector-valued functions". Advances in Operator Theory, 3, 2, 2018, 351-364. doi: 10.15352/aot.1706-1177

Hoim, T., Robbins, D. (2018). 'Cover topologies, subspaces, and quotients for some spaces of vector-valued functions', Advances in Operator Theory, 3(2), pp. 351-364. doi: 10.15352/aot.1706-1177

Hoim, T., Robbins, D. Cover topologies, subspaces, and quotients for some spaces of vector-valued functions. Advances in Operator Theory, 2018; 3(2): 351-364. doi: 10.15352/aot.1706-1177

Cover topologies, subspaces, and quotients for some spaces of vector-valued functions

^{1}Wilkes Honors College Florida Atlantic University Jupiter, FL 33458

^{2}Trinity College Hartford, CT 06106

Receive Date: 10 June 2017,
Revise Date: 16 October 2017,
Accept Date: 16 October 2017

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 $\mathcal{D}$.