KAKEYA‐TYPE SETS IN LOCAL FIELDS WITH FINITE RESIDUE FIELD. Issue 2 (17th February 2016) - Fraser, Robert
Abstract : We present a construction of a measure‐zero Kakeya‐type set in a finite‐dimensional space K n over a local field with finite residue field. The construction is an adaptation of the ideas appearing in works by Sawyer [ Mathematika 34 (1) (1987), 69–76] and Wisewell [ Mathematika 51 (1–2) (2004), 155–162]. The existence of measure‐zero Kakeya‐type sets over discrete valuation rings is also discussed, giving an alternative construction to the one over F l 〚 t 〛 presented by Dummit and Hablicsek [ Mathematika 59 (2) (2013), 257–266].