Expository

Bohr compactification of separable locally convex spaces

  • Received: 22 December 2024 Revised: 20 February 2025 Accepted: 21 February 2025 Published: 05 March 2025
  • 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 $ \mathbb{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.

    Citation: Sidney A. Morris. Bohr compactification of separable locally convex spaces[J]. Electronic Research Archive, 2025, 33(3): 1333-1336. doi: 10.3934/era.2025060

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  • 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 $ \mathbb{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.



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