Remark

Let B be a topological space. Let E be a B-space and let $p$ be its projection. If E is a covering of B, it follows from corollary 1 above that the mapping $p$ is étale (I, p. 28, Def. 2) and separated (I, p. 25, Prop. 1, (iii)). These conditions do not suffice, however, to ensure that E is a covering. Consider, for example, an open set U of B. The canonical injection $i: U\rightarrow B$ is étale and separated. In order that the B-space $(U, i)$ be a covering, it is necessary and sufficient that the open set U be also closed.