TITLE: Difference between Wedge of countable infinite circle and Hawaiian ear ring?
QUESTION [5 upvotes]: Hawaiian ear ring is the union of countable  circles at  points (0,1/n) with radius 1/n.It seems to me that wedge sum of countable infinite circle is same as Hawaiian ring.But I found that this not true.
I am thinking wedge of countable infinite circle as take a big circle and the put all the rest of the circle subsequently inside one another attaching to a common point,then diagram looks like Hawaiian ring.
I can't figure out what is the difference  between them.Can anyone help me in this direction.
My second question is that why Hawaiian ring is not a CW complex but wedge of countable infinite circle is a CW complex?
Thank you.

REPLY [2 votes]: The Hawaiian Earring's topology is the subspace topology thinking of it as embedded in the plane. As such, any neighborhood of the point of intersection will contain infinitely many concentric circles. On the other hand, looking at the infinite wedge of circles, there are neighborhoods of the wedge point that do not contain any of the circles.