Why is a vector bundle called E?

Question

Vector bundles are often denoted as $p:E \to B$, where $p$ is a projection map, $B$ is the base space and $E$ is the total space. Here the choice of the letters $p$ and $B$ is clear, but is there also a reason to denote the total space with $E$? Is it possibly derived from the French 'espace totale'?

Answer 1

Perhaps this should not be an answer, but I give it a try.

I am not sure whether the origin is French, but I believe it is sensible to think it could be for the following reason. In an old work by Daniel Bernard "Sur la géométrie différentielle des $G$-structures" (perhaps one of the oldest works I found on the subject) I see the notation $E(F,G,B)$ for what is called "espace fibré" (so not really "espace totale"). All other letters match the initials of the corresponding objects, "fibre", "group", "base". I hope someone else can comment on this.

EDIT: to be fair, I should also mention that the canonical frame bundle $L_m$ is called "espace de repères". So in this case there is no correspondence at all...