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Inspired by J.A. Baker [1] and M. Sablik [6] we show that if x is a character of a topological group, then either a power of X is continuous or \ maps nonempty open subsets of the group onto dense subsets of the circle. As a corollary we obtain established in [2] theorem of van der Corput for functionals on topological vector spaces satisfying the congruence (1).
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