I have to find the Alexandroff One Point Compactification of $[0,1]\times[0,1)$, which should be a triangle.
I need a map $\phi:[0,1]\times[0,1)\to \mathrm{T}\setminus\{\mathrm{V}\}$, where $\mathrm{T}=\{(x,y)\in\Bbb R^2:x,y\ge 0\text{ and }x+y\le 1\}\;.$
Could $\phi(x,y)=(x|y|,y)$ work?