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Expository | Open Access

Bohr compactification of separable locally convex spaces

Department of Mathematical and Physical Sciences, La Trobe University, Melbourne, Victoria 3086, Australia
School of Engineering, IT and Physical Sciences, Federation University Australia, PO Box 663, Ballarat, Victoria 3353, Australia
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Abstract

It is not well-known that for each separable real locally convex space, its Bohr compactification is isomorphic as a topological group to the Bohr compactification of the topological group R of all real numbers. This is the case for each separable real Banach space. In this expository research note, we state the results explicitly and provide accessible proofs.

Keywords

Bohr compactificationabelian topological groupBanach spacePontryagin dualitydual groupseparable locally convex space

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Electronic Research Archive
Volume 33 Issue 3,
March 2025
Pages 1333-1336
DOI: 10.3934/era.2025060

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Cite this article:
Morris SA. Bohr compactification of separable locally convex spaces. Electronic Research Archive, 2025, 33(3): 1333-1336. https://doi.org/10.3934/era.2025060

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Received: 22 December 2024
Revised: 20 February 2025
Accepted: 21 February 2025
Published: 15 March 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)