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  • Cited by 2
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Bello, Hugo J. Chasco, María Jesús and Domínguez, Xabier 2013. Extending Topological Abelian Groups by the Unit Circle. Abstract and Applied Analysis, Vol. 2013, p. 1.

    Galindo, Jorge and Hernández, Salvador 2004. Interpolation sets and the Bohr topology of locally compact groups. Advances in Mathematics, Vol. 188, Issue. 1, p. 51.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 134, Issue 1
  • January 2003, pp. 33-39

A theorem on cardinal numbers associated with ${\cal L}_{\infty}$ Abelian groups

  • DOI:
  • Published online: 01 March 2003

The topology of a topological group $G$ is called an ${\cal L}_{\infty}$-topology if it can be represented as the intersection of a decreasing sequence of locally compact Hausdorff group topolgies on $G$. If ${\cal L}_1 < {\cal L}_2$ are two distinct ${\cal L}_{\infty}$-topologies on an Abelian group $G$, it is shown that the quotient of the corresponding character groups has cardinality ${\geqslant} 2^{\rm c}$. A conjecture in this sense announced by J. B. Reade in his paper [6] is thereby proved.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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