Journal of Mathematical Sciences

, Volume 211, Issue 1, pp 127–135 | Cite as

Countable Powers of Compact Abelian Groups in the Uniform Topology and Cardinality of Their Dual Groups



For a topological Abelian group X, we consider in the group X the uniform topology and study some properties of the obtained topological group. In particular, we show, that if \( X\kern0.5em =\kern0.5em \mathbb{S} \) is the circle group, then the group \( {\mathbb{S}}^{\mathbb{N}} \) endowed with the uniform topology has the dual group of cardinality 2c.


Abelian Group Topological Vector Space Dual Group Compact Abelian Group Topological Abelian Group 
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© Springer Science+Business Media New York 2015

Authors and Affiliations

  • D. Dikranjan
    • 1
  • E. Martin-Peinador
    • 2
  • V. Tarieladze
    • 3
  1. 1.Università di UdineUdineItaly
  2. 2.Universidad Complutense de MadridMadridSpain
  3. 3.N. Muskhelishvili Institute of Computational Mathematics of the Georgian Technical UniversityTbilisiGeorgia

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