How useful is topology in theoretical physics? By topology, I mean the contents of Munkres book, Hausdorff spaces, homeomorphisms, etc. It seems to me like topology is totally a mathematical construct since the idea of an "open set" in an abstract space seems to have no "physical" meaning outside of Euclidean spaces. So do any of you theoretical physics actually use what is in Munkres? BTW: I am trying to decide whether to take the semester of a topology course and I am really not wanting to for the reasons above.