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Topology

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Moderate

Universal Covers

TOPO-4GGYG1

Which of the following has a universal cover?

A

$[0,1]\cup[2,3]$, the union of two disjoint closed intervals in $\mathbb R$

B

The comb space $(\{0\}\times[0,1])\cup(\{1/n:n\in\mathbb N\}\otimes[0,1])\cup([0,1]\times\{0\})$

C

The topologist's sine curve $\{(x,\sin(1/x))\in\mathbb R^2:x\in(0,1]\}\cup\{(0,0)\}$

D

The Hawaiian earing $\displaystyle\bigcup_{n\in\mathbb N}\{(x,y)\in\mathbb R^2:(x-1/n)^2+y^2=1/n^2\}$

E

The Cayley graph of $\mathbb Z*\mathbb Z$