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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...

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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.

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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.

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    This is an intuition developing question! To just blurt an answer out... In addition, it's good to note that we are explicitly considering the string of Hawaiian earrings as a subspace of R2, so the topology is different than the weak CW topology. So it's not as bad as it might at first seem.2012-03-20