Hawaiian earring

The Hawaiian earring is the subset of the plane consists of infinitely many circles with just one point in common:

$n$-th circle is centered at $\frac{1}{n}$ radius $(\frac{1}{n},0), n=1,2,3,... $

The circles have only $(0,0)$ in common. The space is

• X is Hausdorff,
• X is path-connected,
• X is not simply connected.