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On a generalization of the Borsuk-Ulam theorem / Tucker's lemma for a map from simplex to it...

The Borsuk-Ulam theorem is equivalent to $S^{n-1}$ not being a retract of $B^n$. <totally wrong! or else 2+2=4 is equivalent to the Poincare conjecture/thm> How shall i prove the following stronger v …