Assume that $f,g:S^{2n}\to \mathbb{R}^{n}$ are $2$ maps. Assume that the set valued map $p(x)=\{f(x),g(x)\}$ is a continuous set valued map. Does there exist a point $p\in S^{2n}$ such that $p(x)=p(-x)$?

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    $\begingroup$ For $n=1$ this us reduced to usual Borsuk - - Ulam for the map $x\to (f+g,fg)$. $\endgroup$ – Fedor Petrov Jun 25 at 17:11
  • $\begingroup$ @FedorPetrov yes. Very intetesting comment. Thanks! $\endgroup$ – Ali Taghavi Jun 25 at 18:28

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