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A combinatorial theorem for a symmetric triangulation of the sphere $$S^2$$. (English) Zbl 1003.05033
Summary: We prove a combinatorial lemma from which it follows that the set $$g^{-1}(0)$$ of zeros of a continuous and odd function $$g: S^2\to R$$, $$g(-x)= -g(x)$$, from the 2-dimensional sphere $$S^2$$ contains a symmetric component.

##### MSC:
 05B45 Combinatorial aspects of tessellation and tiling problems 52B70 Polyhedral manifolds 57Q15 Triangulating manifolds
##### Keywords:
combinatorial lemma; sphere
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