Can't solve this, does anyone have some hint for me?
Consider the disjoint union $Y:=\mathbb{R} \cup \{ \infty \}$ with the non-Hausdorff topology given by: $$\mathscr{T}:=\{ \emptyset \} \cup \{ \mathscr{U}\cup \{ \infty \} : \mathscr{U} \text{ is open in }\mathbb{R} \text{ with respect to its usual topology} \}.$$ Find a subspace $X\subset \mathbb{R}^2$, a equivalence relation $R$ in $X$, and $\pi:X\rightarrow Y$ a projection so that $Y$ is the topological quotient of $X$ module $R$. (Here, just draw the equivalence classes, without showing that $\pi$ is a topological quotient application).