We construct various Besicovitch sets using Baire category arguments.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm158-1-6, author = {T. W. K\"orner}, title = {Besicovitch via Baire}, journal = {Studia Mathematica}, volume = {157}, year = {2003}, pages = {65-78}, zbl = {1048.28002}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm158-1-6} }
T. W. Körner. Besicovitch via Baire. Studia Mathematica, Tome 157 (2003) pp. 65-78. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm158-1-6/