The JacobsonBourbaki 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.
