Schauder's Conjecture (i.e\. every compact convex set in a Hausdorff topological vector space has the f.p.p.) is reduced to the search for fixed points of suitable multivalued maps in finite dimensional spaces.
@article{118595, author = {Espedito De Pascale}, title = {A finite dimensional reduction of the Schauder Conjecture}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {34}, year = {1993}, pages = {401-404}, zbl = {0805.47056}, mrnumber = {1243070}, language = {en}, url = {http://dml.mathdoc.fr/item/118595} }
De Pascale, Espedito. A finite dimensional reduction of the Schauder Conjecture. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 401-404. http://gdmltest.u-ga.fr/item/118595/
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