The Jacobson-Bourbaki correspondence induces the traditional, finite Galois correspondence by suitable restriction; I've been pondering two things: 1. Are there any (other) interesting applications of this correspondence known ? (It only seems to lead an existence as an exercise in algebra textbooks, and never appears in lectures.) 2. Does there exist an infinite(-dimensional) version, exploiting something akin to the Krull topology ? Thanks in advance for any helpful remarks or insights ! Kind regards, Stephan.