Evenly covered neighbourhood

An open neighbourhood $U$ of a point in the base of a covering map $p$ is an evenly covered neighbourhood if $p^{-1}(U)$ is a disjoint union of open subsets, each mapped onto all of $U$ by a homeomorphism obtained by restricting $p$.

A covering sheet over an evenly covered neighbourhood $U$ is one of the disjoint open subsets of $p^{-1}(U)$ mapped onto $U$ by a homeomorphism obtained by restricting the covering map.