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Topology

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Do You Even Lift?

TOPO-E4DRW9

Consider the covering space $p:(\mathbb R,0)\rightarrow(\mathbb R/\mathbb Z,\bar{0})$ given by $x\mapsto x\pmod 1$. Which of the following maps $(\mathbb R/\mathbb Z,\bar{0})\rightarrow(\mathbb R/\mathbb Z,\bar{0})$ has a lift $(\mathbb R/\mathbb Z,\bar{0})\rightarrow(\mathbb R,0)$?

A

$\bar{x}\mapsto\overline{-x}$

B

$\bar{x}\mapsto\bar{0}$

C

$\bar{x}\mapsto\bar{x}$

D

$\bar{x}\mapsto\overline{2x}$

E

$\bar{x}\mapsto\overline{3x}$