We give an affirmative answer to Schauder's fixed point question.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-3-2,
author = {Robert Cauty},
title = {Solution du probl\`eme de point fixe de Schauder},
journal = {Fundamenta Mathematicae},
volume = {167},
year = {2001},
pages = {231-246},
zbl = {0983.54045},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-3-2}
}
Robert Cauty. Solution du problème de point fixe de Schauder. Fundamenta Mathematicae, Tome 167 (2001) pp. 231-246. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-3-2/