MathDB

Let

V

be the set of non-collinear pairs of vectors in

\mathbb{R}^3

, and

H

be the set of lines passing through the origin. Is is true that for every continuous map

f\colon V\rightarrow H

there exists a continuous map

g\colon V\rightarrow \mathbb{R}^3\,\backslash\,\{ 0\}

such that

g(v)\in f(v)

for all

v\in V

?
(translated by Miklós Maróti)

Problem Statement