Abstract
Let K be a number field, let S be the set of all normalized, non-conjugate Archimedean valuations of K, and let K-s = K be the Minkowski space associated with K. We v is an element of S strengthen recent results of [ESK10] and [EGL15] by showing that the set of badly approximable elements of K-s is H-absolute winning for a certain family of subspaces of K-s. (C) 2016 Elsevier Inc. All rights reserved.