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The aim of this article is to present a topological tool for the study ofadditive basis in additive number theory. It will be proposal a metric for theset of all additive basis, in which it will be possible to study properties ofsome additive bases studying basis near the chosen basis. This metric allow,for example, detect some additive basis in which we can add some integers in itwithout change its order.

A metric for the set of all additive basis