Geometry of Continued Fractions by Oleg Karpenkov

Author:Oleg Karpenkov
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

The two summands in the last expression are in S and T respectively. Hence the sum is in S⊕T. Hence for any two points of S⊕T the segment connecting these points is also in S⊕T. Therefore, the set S⊕T is convex. □

16.4.2 Integer Approximation Spaces and Affine Irrational Vectors

Let us give some preliminary definitions. We call a subspace L integer if it contains an integer sublattice of full rank in L.

Definition 16.12

Let . We call the intersection of all integer vector subspaces of containing u the integer approximation space of u. It is denoted by R u .

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