@johncarlosbaez@boarders@joshuagrochow@MartinEscardo
There is no such phonetic proximity in french, revêtement et recouvrement are quite different words. However, both Serre and Grothendieck had thought a lot about topology, having thought about fiber spaces in particular.
In his PhD thesis, Serre generalized the concept of Hurewicz fibration to what we now call Serre fibration— requiring the lifting property for maps from cubes only.
The first work of Grothendieck in algebraic geometry was in 1955, about fiber spaces.