>>11287378open set means that with each point lying in the set, there's also a space around the point which also lies in the set
for example if a function is defined on an open set, that means that if f(x_0) is defined, then so is f(x) whenever x is close to x_0
in calculus you see functions assumed to be defined on open sets all the time. that's because you want to use differentation which is always some kind of limit. and to do this, there needs to be some room around the point to do the limit (clearly limits nor derivatives don't make sense in isolated points).
