## Banach Journal of Mathematical Analysis

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

### 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 $\pi :\mathcal{E}\to X$ be a bundle of Banach spaces (algebras). Let $\Gamma \left(\pi \right)$ be the space of sections of $\pi $, and let ${\Gamma}_{b}(\pi ,\mathcal{D})$ be the subspace of $\Gamma \left(\pi \right)$ 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**

Received: 10 August 2015

Accepted: 18 January 2016

First available in Project Euclid: 20 September 2016

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.1215/17358787-3649458

**Mathematical Reviews number (MathSciNet)**

MR3548626

**Zentralblatt MATH identifier**

1362.46045

**Subjects**

Primary: 46H25: Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)

Secondary: 46H10: Ideals and subalgebras

**Keywords**

cover-strict topology bundle of Banach spaces bundle of Banach algebras

#### 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