MathDB

Let

\mathcal{L}

be the set of all lines in the plane and let

\mathcal{P}

be the set of all points in the plane. Determine whether there exists a function

g : \mathcal{L} \to \mathcal{P}

such that for any two distinct non-parallel lines

\ell_1, \ell_2 \in \mathcal{L}

, we have

(a)

g(\ell_1) \neq g(\ell_2)

, and

(b)

\ell_3

is the line passing through

g(\ell_1)

and

g(\ell_2)

, then

g(\ell_3)

is the intersection of

\ell_1

and

\ell_2

Problem Statement