H. Hopf. Verallgemeinerung bekannter Abbildungs- und Uberdeckungssatze, Portugal. Math. 4 (1944), 129-139, MR 6-165 Home/Search Document Not in Database Summary Related Articles |
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Inscribing Cubes and Covering By Rhombic Dodecahedra Via .. - Hausel, Makai, Jr.. (2000) (1 citation) (Correct)
....there are many positive results: a famous special case is the Borsuk Ulam theorem which states that for every continuous map F : S n 1 R n 1 there is an x 2 S n 1 such that F (x) F ( x) This is Knaster s problem when k = n 1, m = 2 and X = fe 1 ; e 1 g. It was generalized by Hopf in [Hopf] for any two points in S n 1 . Other positive results are proved when k = 1 and X is the set of vertices of any regular (n 1) simplex inscribed to S n 1 in [BoKh] X = fe 1 ; e n g [YaYu] X = f e 1 ; e n 1 g Corollary 7.5, Yang] X any 3 element subset of S 2 [Floyd] X = ....
H. Hopf. Verallgemeinerung bekannter Abbildungs- und Uberdeckungssatze, Portugal. Math. 4 (1944), 129-139, MR 6-165
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