Return to Revisions

Start with the interval $[0,1)$ embedded in the $x$-axis. Fill in the closed unit disc minus the point $(1,0)$ using half-open intervals that point inward. Add the interval $[1,2)$ in the $x$-axis. Fill in the closed disc of radius 2 minus the point $(2,0)$ using half-open intervals that point inward. Repeat: For each $n \geq 0$, you get a closed disc of radius $n$ minus a point. The union of these is the plane.