= Degree of a covering map
{title2=$\deg p=|p^{-1}(x)|$}
For a <covering map> with nonempty <connected> base, the <degree of a covering map> is the common <cardinality> of its <fibres>. Each <evenly covered neighbourhood> makes this number <locally constant>, so <connectedness> makes it constant. The total <covering space> need not be connected. On a <path-connected> base the <path lifting theorem> gives a <fibre bijection by path lifting>. A disconnected base may have different degrees on different <connected components>.
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