Definition 2

A covering is a locally trivial fibre space all of whose fibres are discrete.

Instead of saying that a B-space E is a covering, we also say that E is a covering of B.

Let E be a B-space, and let us denote by $p$ its projection; let A be a subset of B. If E is a covering of B, the fibres of $p$ are discrete, hence so are those of $p_A:\overset{-1}{p}(A)\rightarrow A$, and the locally trivial fibred A-space $(\overset{-1}{p}(A), p_A)$ is a covering.