TITLE: Covering spaces Hatcher question 6.
QUESTION [12 upvotes]: Let X be the shrinking wedge of circles. Which is the radius of circles $X \in R^2$ such that it's the union of $C_n$ circles centered at $(\frac{1}{n},0)$ with radius $\frac{1}{n}$ for n=1,2,3... 

I'm having a bit of trouble with sheeted aspect. I'm thinking that the answer is two straight lines intersecting in a point. Does sheeted refer to covering it twice? 
So like a straight line can cover that space I think.

REPLY [12 votes]: See this : 

the composition is not a covering space because there is no open neighboorhood of the "connecting point" that pullbacks homeomorphically onto copies of itself.
For any neighboorhood you try, you will have to take a small circle in it, and this circle will be pulled apart in one of the pullbacks.