Universal Cover of a space I do not know what tools one uses to find the universal cover of a space.  In particular I want to find the universal cover of two copies of $RP^3$ glued together at a single point at the endpoints by the unit interval.  I know the universal cover of $RP^3$ is the 3-sphere are that is as far as I can get.  Any help would be greatly appreciated.  Thank you!
 A: According to mathoverflow, Topological Methods in Group Theory (Scott, Wall) is, in general, the key to computing covering spaces of wedge sums. Your problem is actually set up in an example in the section on covering spaces.
A: Let $Y$ denote your space and let $X$ denote, as User 24601 calls it, a string of pearls - that is, it's the real line $\mathbb{R}$ where each integer point has been expanded into an $S^3$.  In other words, $X$ is formed by taking your space $Y$ with two modifications.  First, each $\mathbb{R}P^3$ is replaced by $S^3$ and second, the
I claim that $X$ is the univeral cover of $Y3$.
To see this, first note that $X$ is simply connected.  This follows because $X$ is homotopy equivalent to an infinite bouquet of $S^3$s.
Second, I claim that $X$ covers $Y$.  More specifically, I'll define the covering $\pi:X\rightarrow Y$.  To do this, first consider the space $X'$ which is made by two $S^3$s together with two line segments.  I'll label the $S^3$s $A$ and $B$ and line segments $l_1$, and $l_2$.  Line segment $l_1$ will emanate out of the north pole of $A$ and $l_2$ will connect the south pole of $A$ to the north pole of $B$.  This will be a fundamental domain of the cover.
Thinking of $Y$ as the segment $[-1,1]$ with two $\mathbb{R}P^3$s, called $a$ and $b$, attached to the left and right end, define $\pi(l_1)$ to be a homeomorphism so that the top of $l_1$ is mapped to $0$, the bottom of $l_1$ (which is the north pole of $A$) is mapped to the point $-1$ on $a$.  Define $\pi$ on $A$ to have image $a$ and other wise be the usual double cover.  Define $\pi(l_2) = [-1,1]$ to be a homeomorphism with the top of $l_2$ (the south pole of $A$) mapping to $-1$ and the bottom of $l_2$ mapping to $1$.  We also define $\pi$ on $B$ to be the usual double cover of $B$ onto $b$.
Finally, we can express $X$ as a union of these $X's$ and define $\pi$ accordingly.  I'll leave it to you to check that this really is a covering map.
