COUNTABLE POWERS OF COMPACT ABELIAN GROUPS IN THE UNIFORM TOPOLOGY AND CARDINALITY OF THEIR DUAL GROUPS

摘要

For a topological Abelian group X, we consider in the group X~N the uniform topology and study some properties of the obtained topological group. In particular, we show, that if X = S is the circle group, then the group S~N endowed with the uniform topology has the dual group of cardinality 2~c.