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A note on badly approximabe sets in projective space

Harrap, S.; Hussain, M.


M. Hussain


Recently, Ghosh and Haynes (J Reine Angew Math 712:39–50, 2016) proved a Khintchine-type result for the problem of Diophantine approximation in certain projective spaces. In this note we complement their result by observing that a Jarník-type result also holds for ‘badly approximable’ points in real projective space. In particular, we prove that the natural analogue in projective space of the classical set of badly approximable numbers has full Hausdorff dimension when intersected with certain compact subsets of real projective space. Furthermore, we also establish an analogue of Khintchine’s theorem for convergence relating to ‘intrinsic’ approximation of points in these compact sets.


Harrap, S., & Hussain, M. (2017). A note on badly approximabe sets in projective space. Mathematische Zeitschrift, 285(1), 239-250.

Journal Article Type Article
Acceptance Date Mar 17, 2016
Online Publication Date May 30, 2016
Publication Date 2017-02
Deposit Date May 15, 2017
Journal Mathematische Zeitschrift
Print ISSN 0025-5874
Electronic ISSN 1432-1823
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 285
Issue 1
Pages 239-250