Geodesic
A finite dimensional reduction of the Schauder Conjecture
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 3, pp. 401-404.

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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.
Classification : 46A16, 47H04, 47H10, 54C60, 54H25
Keywords: compact convex set; fixed point property; multivalued map; local convexity; topological vector space; Schauder Conjecture. 
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De Pascale, Espedito. A finite dimensional reduction of the Schauder Conjecture. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 3, pp. 401-404. http://geodesic.mathdoc.fr/item/CMUC_1993__34_3_a0/