# Math Help - quotient map, open map

1. ## quotient map, open map

Let $\pi: \mathbb{R} \times \mathbb{R} \rightarrow \mathbb{R}$, $(x, y) \mapsto \pi(x, y)=x$.
Let $A=(\mathbb{R}^{\geq 0} \times \mathbb{R}) \cup (\mathbb{R} \times \{0\})$.
Prove that $f=\pi|_A$ is a quotient map and that $f$ is neither an open map or a closed map.

[ $\mathbb{R}^{\geq 0}=\{ x\in \mathbb{R}: x\geq 0\}$]
[This is Munkres §22.3]