W.Chen. Counterexamples to Knaster's conjecture, Topology Vol. 37, No.2. 401405, 1998  Home/Search   Document Not in Database   Summary   Related Articles

.... lie in an (n k) plane; correspondingly, this question is frequently asked for m = n k 1 only, as originally in [Knas] The answer to the Knaster problem in general is negative: counterexamples were given by Makeev in [Mak2] and [Mak3] by Babenko and Bogatyi in [BaBo] and recently by Chen in [Chen]. However 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 ....

W.Chen. Counterexamples to Knaster's conjecture, Topology Vol. 37, No.2. 401405, 1998

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