Recent content by Zoomingout

So that would result from our space being the natural numbers and using the order topology. But why is that interval open? I suppose that for any element x in [3,5], we can find an open set, U, around x such that U \subset X. For 3 we would choose the open set (2,4)?

My textbook is indicating to me that sometimes {x \in X : a <= x <= b} is an open set. How can this happen? My only guess is that if X has a smallest and largest element, called a and b, then sure. Otherwise?