We show that every subspace of finite codimension of the space C[0,1] is extremal with respect to the minimal displacement problem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-3-1, author = {Krzysztof Bolibok}, title = {The minimal displacement problem in subspaces of the space of continuous functions of finite codimension}, journal = {Studia Mathematica}, volume = {223}, year = {2014}, pages = {193-201}, zbl = {1322.47050}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-3-1} }
Krzysztof Bolibok. The minimal displacement problem in subspaces of the space of continuous functions of finite codimension. Studia Mathematica, Tome 223 (2014) pp. 193-201. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-3-1/