In this paper, we extend the theory of simultaneous Diophantine approximation to infinite dimensions. Moreover, we discuss Dirichlet-type theorems in a very general framework and define what it means for such a theorem to be optimal. We show that optimality is implied by but does not imply the existence of badly approximable points.
|Number of pages||22|
|Journal||Journal de Théorie des Nombres de Bordeaux|
|Publication status||Published - 2014|
Bibliographical noteThis is an author produced version of a paper accepted for publication in Journal de Théorie des Nombres de Bordeaux. Uploaded in accordance with the publisher's self-archiving policy.