## Banach Journal of Mathematical Analysis

### Cover-strict topologies, ideals, and quotients for some spaces of vector-valued functions

#### Abstract

Let $X$ be a completely regular Hausdorff space, let $\mathcal{D}$ be a cover of $X$, and let $\pi:\mathcal{E}\rightarrow X$ be a bundle of Banach spaces (algebras). Let $\Gamma (\pi)$ be the space of sections of $\pi$, and let $\Gamma _{b}(\pi,\mathcal{D})$ be the subspace of $\Gamma(\pi)$ consisting of sections which are bounded on each $D\in \mathcal{D}$. We study the subspace (ideal) and quotient structures of some spaces of vector-valued functions which arise from endowing $\Gamma _{b}(\pi,\mathcal{D})$ with the cover-strict topology.

#### Article information

Source
Banach J. Math. Anal., Volume 10, Number 4 (2016), 783-799.

Dates
Accepted: 18 January 2016
First available in Project Euclid: 20 September 2016

https://projecteuclid.org/euclid.bjma/1474373753

Digital Object Identifier
doi:10.1215/17358787-3649458

Mathematical Reviews number (MathSciNet)
MR3548626

Zentralblatt MATH identifier
1362.46045

#### Citation

Hõim, Terje; Robbins, D. A. Cover-strict topologies, ideals, and quotients for some spaces of vector-valued functions. Banach J. Math. Anal. 10 (2016), no. 4, 783--799. doi:10.1215/17358787-3649458. https://projecteuclid.org/euclid.bjma/1474373753

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