Countable powers of compact Abelian groups in the uniform topology and cardinality of their dual groups

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Dikranjan, Dikran and Martín Peinador, Elena and Tarieladze, Vaja (2014) Countable powers of compact Abelian groups in the uniform topology and cardinality of their dual groups. (Submitted)

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Official URL: http://arxiv.org/abs/1305.7369




Abstract

We equip the product of countably many copies of a compact Abelian group X with the uniform topology, and study some properties of the topological group G thus obtained. In particular, we determine the cardinality of the dual group of G, when X is the circle group: it is precisely 2^c.


Item Type:Article
Uncontrolled Keywords:Character, dual group, uniform topology, connected group, precompact group, locally quasiconvex group.
Subjects:Sciences > Mathematics > Topology
ID Code:24220
Deposited On:15 Jan 2014 14:06
Last Modified:12 Dec 2018 15:12

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