= Solution
{c}
A <covering map> is a <continuous> <surjection> $p:\widetilde X\to X$ such that every $x\in X$ has an <open> <neighbourhood> $U$ for which
$$
\boxed{p^{-1}(U)=\bigsqcup_{\alpha\in A}U_\alpha,\qquad
p|_{U_\alpha}:U_\alpha\longrightarrow U\text{ a homeomorphism},}
$$
where the $U_\alpha$ are pairwise disjoint <open subsets> of $\widetilde X$. Such a $U$ is an <evenly covered neighbourhood>, and the sets $U_\alpha$ are its <covering sheets>. The index <set> may be infinite. The requirement that every sheet map onto all of $U$ is part of the definition.
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