Remark 2

An etale mapping is continuous and open (TG, I, p. 33, prop. 5) ; in particular, the image of an etale mapping is open. Conversely, if $p: E\rightarrow B$ is a continuous and open mapping, and if every point $x$ of E possesses a neighbourhood V such that the mapping $p|V$ is injective, the mapping $p$ is etale. The fibres of an etale mapping are discrete.