What's the difference between open and closed sets? What's the difference between open and closed sets?
Especially with relation to topology - rigorous definitions are appreciated, but just as important is the intuition!

An open set is a set S for which, given any of its element A, you can find a ball centered in A and whose points are all in S.
A closed set is a set S for which, if you have a sequence of points in S who tend to a limit point B, B is also in S.
Intuitively, a closed set is a set which contains its own boundary, while an open set is a set where you are able not to leave it if you move just a little bit.
