Let K be an abelian number field of conductor f and p a prime. Sinnott defined circular units CKs of K using the norm maps from the cyclotomic units of the nth cyclotomic fields for all n and Washington defined circular units CKw of K to be the Galois invariant of the cyclotomic units of the f th cyclotomic field. In this note, we investigate a question raised by Kolster in  of whether the projective limits of circular units of Sinnott and Washington over the cyclotomic Z p-extension of K are equal. Belliard  and Kučera  found independently some counter examples to this question. The purpose of this note is to find some conditions on the ground field K under which Kolster's question has an affirmative answer.
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