What is the relationship between topology, functional analysis, and group theory? All three seem to overlap, and I can't quite see how to distinguish them / what they're each for.
I'm trying to understand what a one-parameter group of transformations really is. At one lecture I was told that they are trivial lie groups. In Arnold's "Ordinary Differential Equations" they are defined as an action by the group of real numbers; a collection of transformations parametrised by...